text:
\section{Introduction}

\IEEEPARstart{T}{he} perspective-$n$-point (P$n$P) problem aims to determine the position and orientation of a calibrated camera from $n$ known correspondences between three-dimensional (3D) object points and their two-dimensional (2D) image projections. P$n$P is a core problem in the computer vision field and has found many applications, such as robot vision navigation \cite{mur2015orb}, augmented reality \cite{muller2013mobile}, and computer animation. In the past decades, many effective P$n$P approaches have been proposed with very fast computational speed \cite{ferraz2014very}\cite{lepetit2009epnp} and high accuracy \cite{zheng2013revisiting}\cite{lu2000fast}.

To date, most P$n$P algorithms are designed under the assumption that no outlier exists among the given 3D-2D correspondences. However, in practical applications, this outlier-free assumption is often difficult to satisfy. This is because image feature detection and matching approaches, such as SURF \cite{bay2006surf}, BRISK \cite{leutenegger2011brisk} and ORB \cite{rublee2011orb}, do not always give perfect results due to scaling, illumination, shadow and occlusion. Outliers are often unavoidable and they have a significant impact on the P$n$P methods. Even a small percentage of outliers will lead to a significant decrease in accuracy. Hence, the ability to handle outliers is essential for performing P$n$P algorithms in practical applications. The most common outliers handling mechanism is to combine a P$n$P ($n=$ 3 or 4) algorithm \cite{nister2004minimal}\cite{gao2003complete}\cite{josephson2009pose} with the RANSAC-based scheme \cite{fischler1981random} to eliminate outliers, and then perform a more accurate P$n$P algorithm with the remaining inliers to refine the result. A number of very fast closed-form P3P \cite{kneip2011novel} or P4P \cite{bujnak2008general} algorithms have been proposed. However, their RANSAC combination scheme still needs many trials until the selected three or four 3D-2D correspondences are all inliers, which results in a high time complexity. Hence, the computational speed decreases significantly as the percentage of outliers increases. To reduce the time complexity, one natural idea is to utilize the P$n$P algorithm with a smaller $n$. However, when $n=$ 1 or 2, the P$n$P problem has infinitely many solutions, which makes the conventional RANSAC-based scheme infeasible.

To the best of our knowledge, except for RANSAC-based methods, the only P$n$P method that addresses outliers is REPP$n$P \cite{ferraz2014very} proposed by Ferraz \textit{et al}., which is the state-of-the-art P$n$P method that is robust to outliers. REPP$n$P integrates an outlier rejection mechanism with camera pose estimation. It formulates the pose estimation problem as a low-rank homogeneous system in which the solution lies on its one-dimensional (1D) null space. Outlier correspondences are those rows of the linear system that perturb the null space and are progressively detected by projecting them on an iteratively estimated solution of the null space. Although REPP$n$P is very fast and accurate, it suffers from a severe limitation that it cannot handle more than approximately $50\%$ of outliers.

In this paper, we propose a robust 1-point RANSAC-based P$n$P method named R1PP$n$P. We first present an optimal iterative process as the core P$n$P algorithm of R1PP$n$P. The core algorithm takes a random 3D-2D correspondence as the control point. To address outliers, we propose a soft weight assignment method according to reprojection errors to distinguish inliers and outliers, and integrate it into the core algorithm. The weight factors associated with outliers decrease significantly during the iteration to reduce the impact of outliers. Finally, we employ the 1-point RANSAC scheme to try different control points for the core P$n$P algorithm. By using this combination of the RANSAC scheme and the soft weight assignment, the algorithm is capable of eliminating outliers when the selected control point is an inlier.

The main advantage of R1PP$n$P is that it has much lower time complexity and is much faster than conventional RANSAC+P3P or P4P methods, especially when the percentage of outliers is large. Compared with REPP$n$P, the proposed R1PP$n$P does not suffer from the percentage of outliers limitation.

This paper is organized as follows. In Section II, we describe the fundamental model used in R1PP$n$P. The details of the core algorithm are given in Section III, in which we also provide its proof of convergence, local minima analysis and the strategy to select control points. The outliers handling mechanism, including soft weight assignment and the 1-point RANSAC scheme, is introduced in Section IV. We also provide details of termination conditions in Section IV.  Evaluation results are presented in Section V. A discussion and description of planned future work is described in Section VI.

\subsection{Related Works}

The P$n$P problem, coined by Fischler and Bolles \cite{fischler1981random}, is articulated as follows: \emph{Given the relative spatial locations of $n$ control points, and given the angle to every pair of control points $P_i$ from an additional point called the center of perspective $C$, find the lengths of the line segments joining $C$ to each of the control points.} The P$n$P problem has been studied for many years. In early studies, direct linear transformation (DLT) \cite{hartley2003multiple} was used as a solution in a straightforward way by solving a linear system. However, DLT ignores the intrinsic camera parameters, which are assumed to be known, and therefore generally leads to a less stable pose estimate.

In the past decade, researchers have proposed many P$n$P methods to improve speed, accuracy, and robustness to outliers. The P$n$P methods can be roughly classified into non-iterative and iterative methods. Generally speaking, non-iterative methods are more efficient but are unstable under image noise and outliers. Many non-iterative P$n$P methods are based on a set of small number of points ($n=3,4$). They are referred to as P3P \cite{dementhon1992exact} \cite{gao2003complete} \cite{kneip2011novel} or P4P \cite{abidi1995new} \cite{bujnak2008general}\cite{horaud1989analytic}\cite{quan1999linear} methods. P3P is the smallest subset of control
points that yields a finite number of solutions \cite{kneip2011novel}\cite{wolfe1991perspective}. When the intrinsic camera parameters are known and we have $n\geq 4$ points, the solution is generally unique. Triggs proposed a P$n$P method with four- or five- correspondences \cite{triggs1999camera}. These P$n$P methods based on less than four correspondences do not make use of redundant points and are very sensitive to noise and outliers. However, due to their efficiency and capability to calculate from a small point set, P3P or P4P methods are very useful for combing a RANSAC-like scheme to reject outliers. There are also many non-iterative P$n$P methods that are able to make use of redundant points but are quite time consuming. For example, Ansar's method is $O(n^8)$ \cite{ansar2003linear} and Fiore's is $O(n^2)$ \cite{fiore2001efficient}. Schweighofer proposed an $O(n)$ P$n$P method named SDP, but is slow \cite{schweighofer2008globally}. In recent years, three excellent $O(n)$ effective non-iterative P$n$P methods, EP$n$P \cite{lepetit2009epnp}, RP$n$P \cite{li2012robust} and UP$n$P\cite{kneip2014upnp}, have been proposed, and these methods are very efficient and accurate even compared to iterative methods.

Iterative P$n$P methods \cite{lu2000fast}\cite{lowe1991fitting}\cite{dementhon1995model}\cite{horaud1997object} are mostly optimization methods that decrease their energy function in the iterative process. They are generally more accurate and robust, but slower. For example, Dementhon proposed POSIT that is easy to implement \cite{dementhon1995model} and further proposed SoftPOSIT to handle situations when the correspondence relationships are unknown \cite{david2004softposit}. Although SoftPOSIT has a certain ability to handle outliers, the strong assumption that all correspondences are unknown make it slow. Lu's method \cite{lu2000fast} is the most accurate iterative P$n$P method but may get stuck in local minima. Schweighofer discussed the local minima situation of Lu's method and proposed a method to avoid this limitation \cite{schweighofer2006robust}.

P$n$P algorithms are widely used in applications such as structure from motion \cite{havlena2010efficient} and monocular SLAM \cite{mur2014fast}, which require dealing with hundreds or even thousands of noisy feature points and outliers in real-time. The fact that outliers have a much greater impact on P$n$P accuracy than image Gaussian white noise makes it is necessary for the P$n$P algorithm to handle outliers efficiently. Conventional method to handle outliers is to combine a RANSAC-like scheme with the P3P or P4P algorithms. Besides, L1-norm is also widely used to handle a certain amount of outliers \cite{kahl2008practical}\cite{ke2007quasiconvex} because the L1-norm penalty is less sensitive to outliers than the L2-norm penalty. Although a L1-norm-based energy function is more robust to outliers, it cannot absolutely get rid of outliers and its computation is more complex.

Ferraz \textit{et al}. proposed a very fast P$n$P method that can handle up to 50\% of outliers \cite{ferraz2014very}. The outlier rejection mechanism is integrated within the pose estimation pipeline with negligible computational overhead. Compared to Ferraz's method, the R1PP$n$P algorithm proposed in this paper demonstrates much stronger robustness, but is slower.

\section{Fundamental Model}

In this paper we denote the camera frame as $c$ and the world frame as $w$. For point $i$, without taking into account the distortion, the perspective projection equations are employed to describe the pinhole camera model,

\begin{equation}
{u_i} = f\frac{{x_i^c}}{{z_i^c}},{v_i} = f\frac{{y_i^c}}{{z_i^c}},
\label{eq_1}
\end{equation}

\noindent where $f$ is the camera focal length, ${\bf{x}}_i = {[{u_i},{v_i},f]^T}$ is the image homogeneous coordinate in pixels, and ${\bf{X}}_i^c = [x_i^c,y_i^c,z_i^c]^T$ is the real-world coordinate with respect to the camera frame.

According to \eqref{eq_1},

\begin{equation}
{\bf{X}}_i^c = \lambda_i^* {\bf{x}}_i,
\label{eq_2}
\end{equation}

\noindent where $\lambda_i^* = z_i^c / f$ is the normalized depth of point $i$. \eqref{eq_2} indicates that an object point lies on the straight line of sight of the related image point.

The relationship between the camera and world frame coordinate of point $i$ is
\begin{equation}
{\bf{X}}_i^c = {\bf{R}}{\bf{X}}_i^w + {\bf{t}},
\label{eq_3}
\end{equation}

\noindent where ${\bf{R}}\in SO(3)$ is the rotation matrix and ${\bf{t}}\in R^3$ is the translation vector. ${\bf{R}}$ and ${\bf{t}}$ are the variables that need to be estimated in the P$n$P problem.

Similarly to the translation elimination method used in works \cite{kneip2013using}\cite{lee2015minimal}, with two points $i$ and $o$,

\begin{equation}
{\bf{X}}_i^c - {\bf{X}}_{o}^c = {\bf{R}}({\bf{X}}_i^w - {\bf{X}}_o^w),{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} i \ne o.
\label{eq_4}
\end{equation}

In the proposed R1PP$n$P algorithm, $o \in [1,N]$ suggests the index of the control point, $N$ is the number of 3D-2D correspondences. R1PP$n$P represents the shape of the point cloud by the relative positions between the control point $o$ and other $N-1$ points. Denoting ${\bf{S}}_i = {\bf{X}}_i^w - {\bf{X}}_o^w$, where $S$ means "shape", then, according to \eqref{eq_2} and \eqref{eq_4},

\begin{equation}
\lambda_i^* {\bf{x}}_i - \lambda_o^* {\bf{x}}_o = {\bf{R}}{\bf{S}}_i.
\label{eq_5}
\end{equation}

We divide both sides of \eqref{eq_5} by the depth of the control point $\lambda_o^*$, and rewrite \eqref{eq_5} as

\begin{equation}
\lambda_i {\bf{x}}_i - {\bf{x}}_o = \mu{\bf{R}}{\bf{S}}_i,
\label{eq_6}
\end{equation}

\noindent where $\lambda_i = \mu \lambda_i^*$ and $\mu=1/\lambda_o^*$ is the scale factor. We have

\begin{equation}
{\bf{t}} =  1/\mu {\bf{x}}_o - {\bf{RX}}_o^w.
\label{eq_7}
\end{equation}

According to \eqref{eq_6} and \eqref{eq_7}, the P$n$P problem can be solved by minimizing the objective function

\begin{equation}
f({\bf{R}},\mu,{\lambda _i}) = \sum\limits_{i = 1,i\neq o}^N {{{\left\| {{\lambda _i}{{\bf{x}}_i} - {{\bf{x}}_o} - \mu {\bf{R}}{{\bf{S}}_i}} \right\|^2}}},
\label{eq_objfun1}
\end{equation}

\noindent where $\left\|  \cdot  \right\|$ is the L2-norm.

The objective function \eqref{eq_objfun1} is based on Euclidean distances in the 3D space. Compared with the reprojection error cost, Eq.\eqref{eq_objfun1} gives more weights to points with larger depths. For example, the same level of reprojection error has relatively larger effects when related to an object point with greater depth. To solve this problem, we normalize the cost function \eqref{eq_objfun1} with depths of points and propose the objective function of our R1PP$n$P algorithm, that is

\begin{equation}
f({\bf{R}},\mu ,{\lambda _i}) = {\sum\limits_{i = 1,i \ne o}^N {\left( {\frac{1}{{{\lambda _i}}}\left\| {{\lambda _i}{{\bf{x}}_i} - {{\bf{x}}_o} - \mu {\bf{R}}{{\bf{S}}_i}} \right\|} \right)} ^2},
\label{eq_objfun1_lambda}
\end{equation}

\noindent where $1/\lambda_i$ is introduced to adjust the weight of point $i$ to eliminate the inequity among points in Eq.\eqref{eq_objfun1}.

We estimate $\bf{R}$, $\mu$ and $\lambda_i$ $(i=1,...,N,i\neq o)$ by minimizing the objective function \eqref{eq_objfun1_lambda}, the variables of which consist of two parts: the camera pose \{$\bf{R}$, $\mu$\} and the relative depths with respect to the control point $\{ \lambda_i \}$. To describe the following algorithm intuitively, we introduce two sets of points: ${\bf{p}}_i$ and ${\bf{q}}_i$. With a randomly selected control $o$, points ${\bf{p}}_i$ are determined by the camera pose \{$\bf{R}$, $\mu$\}, and points ${\bf{q}}_i$ are determined by depths $\lambda_i$. We have

\begin{equation}
{\bf{p}}_i = {\bf{x}}_o + \mu {\bf{RS}}_i,
\label{eq_p}
\end{equation}

\begin{equation}
{\bf{q}}_i = \lambda_i {\bf{x}}_i.
\label{eq_q}
\end{equation}

\begin{figure} [ht]
\vspace{0.0cm}
\centering
  \includegraphics[height =8.5cm]{figures/bunnyimg.pdf}
 \caption{Demonstration of geometrical relationships with a bunny model. The mouth point is the control point $o$. In algorithm, all virtual points rotate and scale around the control point ${\bf{p}}_o={\bf{q}}_o={\bf{x}}_o$. We use the tail point to exemplify ${\bf{p}}_i$ and its projection ${\bf{q}}_i$. Plane A is parallel to the imaging plane and passes the camera optical center. Without loss of generality and for clearer demonstration, in this figure we use focal length $f=1$ and all depths are distances between points and plane A.}
\label{fig_bunnyimg}
\end{figure}

As shown in Fig. \ref{fig_bunnyimg}, points ${\bf{p}}_i$ are attached with the virtual object obtained by rotating and scaling the real object around the control point ${\bf{p}}_o = {\bf{q}}_o = {\bf{x}}_o$. ${\bf{q}}_i$ is the projection of ${\bf{p}}_i$ on the corresponding line of sight. The objective function \eqref{eq_objfun1_lambda} is equivalent to

\begin{equation}
f({{\bf{p}}_i},{{\bf{q}}_i}) = {\sum\limits_{i = 1,i \ne o}^N {\left( {\frac{1}{{{\lambda _i}}}\left\| {{{\bf{p}}_i} - {{\bf{q}}_i}} \right\|} \right)} ^2}.
\label{eq_objfun2}
\end{equation}

As this objective function approaches the global optimal solution and as shown in Fig. \ref{fig_bunnyimg}, point ${\bf{p}}_i$ gets close to ${\bf{q}}_i$ and the $z$-component of ${\bf{p}}_i$ gets close to $f\lambda_i$. Hence, it is expected that the objective function \eqref{eq_objfun2} has similar optimal solutions as the conventional reprojection error cost, because

\begin{equation}
\begin{array}{*{20}{l}}
{f({{\bf{p}}_i},{{\bf{q}}_i})}\\
{ = \sum\limits_{i = 1,i \ne o}^N {{{\left\| {{{\left[ {\frac{{{{\bf{p}}_{i,x}}}}{{{\lambda _i}}},\frac{{{{\bf{p}}_{i,y}}}}{{{\lambda _i}}},\frac{{{{\bf{p}}_{i,z}}}}{{{\lambda _i}}}} \right]}^T} - {{\bf{x}}_i}} \right\|}^2}} }\\
{ \approx \sum\limits_{i = 1,i \ne o}^N {{{\left\| {{{\left[ {f\frac{{{{\bf{p}}_{i,x}}}}{{{{\bf{p}}_{i,z}}}},f\frac{{{{\bf{p}}_{i,y}}}}{{{{\bf{p}}_{i,z}}}},f} \right]}^T} - {{\left[ {{u_i},{v_i},f} \right]}^T}} \right\|}^2}} }.
\end{array}
\label{eq_objfun2_explaination}
\end{equation}

\section{Core Algorithm Design}

We first introduce the core algorithm of R1PP$n$P, which solves the P$n$P problem in outlier-free situations. This section introduces the core algorithm process, proof of convergence, the local minima avoidance mechanism and the strategy to select the control point.

The core algorithm of R1PP$n$P is an optimal iterative process with the objective function \eqref{eq_objfun1_lambda} or \eqref{eq_objfun2}. In each iteration, it estimates the points set ${\bf{q}}_i$ and ${\bf{p}}_i$ $(i=1,...,N,i\neq o)$ alternately by fixing one points set and updating the other one according to the objective function minimization.

\noindent \textbf{(1) ${\bf{q}}_i$ estimation stage.}

Because each ${\bf{q}}_i$ are independent with each other, our algorithm seeks the closest ${\bf{q}}_i$ for each ${\bf{p}}_i$. According to \eqref{eq_q}, points ${\bf{q}}_i$ are constrained to the related lines of sight. Hence, we vertically project ${\bf{p}}_i$ onto the related lines of sight to obtain the points' relative depths with respect to the control point $o$ by

\begin{equation}
\lambda_i =  {\bf{x}}_i^T {\bf{p}}_i / ({\bf{x}}_i^T {\bf{x}}_i),  {\kern 5pt} i = 1,...,N {\kern 5pt} {\rm{and}} {\kern 5pt} i\ne o.
\label{eq_lambda}
\end{equation}

Then, points ${\bf{q}}_i$ are updated according to Eq.\eqref{eq_q}.

\noindent \textbf{(2) ${\bf{p}}_i$ estimation stage.}

Points ${\bf{p}}_i$ are determined by $\bf{R}$ and $\mu$. According to \eqref{eq_p}, the updated $\bf{R}$ and $\mu$ should make points \{$\mu {\bf{RS}}_i$\} have the smallest weighted sum of squared distances to points \{${\bf{q}}_i - {\bf{x}}_o$\}, and subject to ${\bf{R}}^T{\bf{R}} = {\bf{I}}_{3\times 3}$.  According to the objective function \eqref{eq_objfun2}, the weights used in this stage are $1/\lambda_i$ in the previous iteration.

Denoting matrices ${\bf{A}} = \left[ {\frac{{{{\bf{q}}_1} - {{\bf{x}}_o}}}{{{\lambda _1}}},...,\frac{{{{\bf{q}}_N} - {{\bf{x}}_o}}}{{{\lambda _N}}}} \right]_{3\times N}$ and ${\bf{S}} = \left[ {\frac{{{{\bf{S}}_1}}}{{{\lambda _1}}},...,\frac{{{{\bf{S}}_N}}}{{{\lambda _N}}}} \right]_{3\times N}$, then according to Ref. \cite{arun1987least}
\begin{equation}
[{\bf{U}},{\bf{\Sigma }},{{\bf{V}}^T}] = {\rm{svd}}({\bf{A}}{{\bf{S}}^T}), {\bf{R}} = {\bf{U}}{{\bf{V}}^T},
\label{eq_R}
\end{equation}

\begin{figure} [!htb]
\vspace{0.0cm}
\centering
  \includegraphics[height = 5.2cm]{figures/fig_newmu.pdf}
\caption{Demonstration of the updating method of the scale factor $\mu$. One possible method is to update $\mu$ according to the Euclidean distances between ${\bf{p}}_i$, ${\bf{q}}_i$ and $\bf{o}$, which works for ${\bf{p}}_1$ and ${\bf{q}}_1$ because they have close depths as $\bf{o}$. However, this method may result in slow $\mu$ updating rate for ${\bf{p}}_2$ and ${\bf{q}}_2$ because $\left\| {\bf{q}}_2 - {\bf{o}} \right\| \approx \left\| {\bf{p}}_2 - {\bf{o}} \right\|$. Hence, it is more efficient to compare ${\bf{v}}_i$ and ${\bf{x}}_i$ to move points ${\bf{p}}_i$ to the related lines of sight.}
\label{fig_newmu}
\end{figure}

Because points ${\bf{p}}_i$ are directly generated from ${\bf{S}}_i$ according to Eq.\eqref{eq_p}, Eq.\eqref{eq_R} suggests that $\bf{R}$ is updated according to the differences between points ${\bf{p}}_i$ and ${\bf{q}}_i$ in the 3D space. However, Fig.\ref{fig_newmu} demonstrates that by using this method, the updating rate of $\mu$ may be slow in situations when the range of depths is large. To achieve faster convergence rate, we update the scale factor $\mu$ by comparing the projected image coordinates of ${\bf{p}}_i$, which are denoted as ${{\bf{v}}_i}$, and the real image points ${\bf{x}}_i$. Denoting matrices ${\bf{B}} = \left[ {{{\bf{v}}_1} - {{\bf{x}}_{o}},...,{{\bf{v}}_N} - {{\bf{x}}_o}} \right]_{3\times N}$ and ${\bf{C}} = \left[ {{{\bf{x}}_1} - {{\bf{x}}_o},...,{{\bf{x}}_N} - {{\bf{x}}_o}} \right]_{3\times N}$. $\mu$ is updated by

\begin{equation}
\Delta \mu  = \left\| {{\rm{vector}}({\bf{C}})} \right\|/\left\| {{\rm{vector}}({\bf{B}})} \right\|
\label{eq_mu1}
\end{equation}

\begin{equation}
{\mu _{{\rm{new}}}} = {\mu _{{\rm{old}}}}\Delta \mu
\label{eq_mu2}
\end{equation}

Finally, points ${\bf{p}}_i$ are updated according to Eq.\eqref{eq_p}.

\subsection{Proof of Convergence}

We first provide the mathematical proof of the convergence of R1PP$n$P when not using $1/\lambda_i$ as weights in the objective function \eqref{eq_objfun2}. $k$ denotes the number of iterations, ${\bf{q}}_i^{(k+1)}$ is obtained by vertically projecting ${\bf{p}}_i^{(k)}$ to the line of sight $i$, and ${\bf{q}}_i^{(k+1)}$ and ${\bf{q}}_i^{(k)}$ are on the line of sight $i$. Hence, the three points, ${\bf{p}}_i^{(k)}$,${\bf{q}}_i^{(k)}$, and ${\bf{q}}_i^{(k+1)}$ comprise a right-angled triangle. Therefore, for each index $i,i \neq o$,

\begin{equation}
\left\| {{\bf{p}}_i^{(k)}-{\bf{q}}_i^{(k+1)}} \right\|^2 = \left\| {{\bf{p}}_i^{(k)}-{\bf{q}}_i^{(k)}} \right\|^2 - \left\| {{\bf{q}}_i^{(k + 1)}-{\bf{q}}_i^{(k)}} \right\|^2.
\label{eq_8}
\end{equation}

In the ${\bf{p}}^{(k+1)}$ updating stage, the updated $\bf{R}$ and $\mu$ make the objective function \eqref{eq_objfun2} smaller. Hence,

\begin{equation}
\sum\limits_{i = 1}^N {{{\left\| {{\bf{p}}_i^{(k + 1)} - {\bf{q}}_i^{(k + 1)}} \right\|}^2}}  \le \sum\limits_{i = 1}^N {{{\left\| {{\bf{p}}_i^{(k)} - {\bf{q}}_i^{(k + 1)}} \right\|}^2}} .
\label{eq_9}
\end{equation}

According to \eqref{eq_8}, \eqref{eq_9}, and the objective function \eqref{eq_objfun2},

\begin{equation}
\begin{array}{l}
\begin{array}{l}
f{({\bf{p}}_i^{(k + 1)},{\bf{q}}_i^{(k + 1)})} \le f{({\bf{p}}_i^{(k)},{\bf{q}}_i^{(k)})} - \sum\limits_{i = 1}^N {{{\left\| {{\bf{q}}_i^{(k + 1)} - {\bf{q}}_i^{(k)}} \right\|}^2}}
\end{array}.
\end{array}
\label{eq_10}
\end{equation}

Hence, the objective function will strictly decrease until ${\bf{q}}_i^{(k + 1)} = {\bf{q}}_i^{(k)}$ when not using $1/\lambda_i$ as weights. However, when $1/\lambda_i$ is applied in the objective funtion, the above convergence proof is not rigorous in mathematics because $\lambda_i^{(k+1)} \neq \lambda_i^{(k)}$. As the iteration process, the changes of $\lambda_i$ become small, which makes the formula \eqref{eq_10} hold. In addition, our experimental results in this paper also support the assumption that our algorithm is convergent.

\subsection{Local Minima Avoidance}

We have concluded that the iterative process of R1PP$n$P is convergent. However, we still need to address situations that R1PP$n$P may get stuck in local minima. To demonstrate the iterative process more intuitively, we introduce a 1D camera working in the 2D space, as shown in Fig. \ref{fig_iterprocess}. In this demonstration, an object with four points ${\bf{P}}_i$, $i=1,...,4$ are projected to the camera image plane and their image points ${\bf{x}}_i$ are obtained. ${\bf{P}}_1$ is selected as the control point, which means $o=1$. Different initial values may result in different convergence results.

\begin{figure} [ht]
\vspace{0.0cm}
\centering
  \includegraphics[height =7.1cm]{figures/iterprocess1.pdf}
  \includegraphics[height =7.0cm]{figures/iterprocess2.pdf}
\caption{Iterative process with 2D space and 1D camera imaging plane. ${\bf{P}}_1$, ${\bf{P}}_2$, ${\bf{P}}_3$ and ${\bf{P}}_4$ are the object points; ${\bf{P}}_1$ is selected as the control point ($o=1$). (a) The process ${\bf{p}}^{(k)} \rightarrow {\bf{q}}^{(k+1)}\rightarrow {\bf{p}}^{(k+1)}\rightarrow ... $ makes the estimation pose approach the correct solution; (b) the rotation related to ${\bf{p}}^{(k+1)}$ is worse than that related to ${\bf{p}}^{(k)}$, which means the process is approaching a local minima, which is a mirror-image form of the true object shape.}
\label{fig_iterprocess}
\end{figure}

Fig. \ref{fig_iterprocess}(a) demonstrates a process that is approaching the correct global optimal results. Beginning with points ${\bf{p}}^{(k)}$, the algorithm projects ${\bf{p}}^{(k)}$ to their related lines of sight and obtains points ${\bf{q}}^{(k+1)}$. Then, according to ${\bf{q}}^{(k+1)}$, the algorithm updates the rotation $\bf{R}$ and scale factor $\mu$ to generate points ${\bf{p}}^{(k+1)}$. In this process, the rotation and scale factor related to ${\bf{p}}^{(k+1)}$ are closer to the truth compared to that related to ${\bf{p}}^{(k)}$, and finally the algorithm will reach the correct solution.

However, as the progress shown in Fig. \ref{fig_iterprocess}(b) indicates, ${\bf{p}}^{(k+1)}$ has a larger pose error than ${\bf{p}}^{(k)}$, and the algorithm will finally get stuck in local minima. The reconstructed points ${\bf{p}}^{(k)}$ or ${\bf{p}}^{(k+1)}$ come in mirror-image forms of the real object points ${\bf{P}}$. Without loss of generality, in either 2D or 3D space, a mirror-image form suggests that the left-right-handed shape of the point cloud has been changed, which should not happen in reality. The reason the core algorithm of R1PP$n$P may generate points with different left-right-handed shape is that its rotation estimation equation \eqref{eq_R} does not constrict $\det ({\bf{R}}) = 1$.

In practice we found it not appropriate to constrain $\det ({\bf{R}}) = 1$ from the beginning of the algorithm. Instead, we allow the iteration process to approach the mirror-image form. This is because we found that, with the constrain $\det ({\bf{R}}) = 1$ from the beginning, the algorithm has many types of local minima and they are unpredictable. However, without this constrain, the convergence direction of the core algorithm becomes predictable, with only two types of convergence. The algorithm may reach the global optimal result directly or the approximate mirror-image form. For the latter case, the estimated $\det ({\bf{R}}) = -1$.

Hence, according to the above analysis, we propose the local minima avoidance mechanism. The algorithm begins with a random initial value and control point. When the algorithm converges to a result with $\det ({\bf{R}}) = -1$, we perform a mirror flip by

\begin{equation}
{\lambda _{i,\rm{new}}} = 1/{\lambda _{i,\rm{old}}},{\kern 5pt} i = 1,...,N {\kern 5pt} {\rm{and}} {\kern 5pt} i\ne o.
\label{eq_lambdaflip}
\end{equation}

\subsection{Control Point $o$ Selection}

\begin{figure} [htp]
\vspace{0.0cm}

\centering
 \subfigure[]{
  \includegraphics[height = 3.8cm]{figures/chooseO_1.pdf}
    }
 \subfigure[]{
  \includegraphics[height = 3.2cm]{figures/IternumChangeWithO.png}

  \caption{In R1PP$n$P, the selection of control point $o$ is related to the convergence rate. (a) An example to illustrate this behavior with 2D space and 1D camera imaging plane . According to the $\bf{R}$ and $\mu$ updating methods in Eqs.\eqref{eq_R} and \eqref{eq_mu1}. $\angle \left( {{p} - {{{o}}_1},{q} - {{{o}}_1}} \right) > \angle \left( {{p} - {{o}_2},{q} - {{o}_2}} \right)$ and $\left\| {{{\bf{x}}_i} - {{\bf{x}}_{o1}}} \right\|/\left\| {{{\bf{v}}_i} - {{\bf{x}}_{o1}}} \right\| > \left\| {{{\bf{x}}_i} - {{\bf{x}}_{o2}}} \right\|/\left\| {{{\bf{v}}_i} - {{\bf{x}}_{o2}}} \right\|$ suggest that the iteration process is more likely to have larger $\bf{R}$ and $\mu$ updating rate when $o$ is closer to ${p}$. (b) A real-world example to illustrate this behavior, the radius of a circle represents the required number of iterations when using this feature point as the control point $o$.}
\label{fig_convergencerate}
\end{figure}

To select different points as the control point $o$ may result in different convergence rates. Without taking into account noise, the correct value of rotation $\bf{R}$ should be the same for any control point $o$ in a P$n$P task. Hence, larger rotation updating steps in the iteration process suggest that less number of iterations are required to converge to the correct value when starting from the same initial value. In R1PP$n$P, $\bf{R}$ is updated according to the differences between points ${\bf{p}}_i$ and ${\bf{q}}_i$, $i=1,...,N, i \neq o$. When point $o$ is close to ${\bf{p}}_i$, the rotation updating steps are more likely to be large, as shown in Fig.\ref{fig_convergencerate}(a). The updating rates of $\mu$ also follow this analysis. Therefore, we are prone to select the control point $o$ from the center of the point cloud, which has better odds of having smaller distances to the rest of the point cloud to achieve faster convergence rate, as shown in Fig.\ref{fig_convergencerate}(b).

\section{Outliers Handling Mechanism}

The robust and fast capability of handling outliers is the main contribution of the proposed R1PP$n$P algorithm. Our outliers handling mechanism combines a soft weight assignment method and the 1-point RANSAC scheme.

\subsection{Soft Re-weighting}

R1PP$n$P mainly consists of ${\bf{q}}_i$ and ${\bf{p}}_i$ estimation stages. As described in Section 3, in the ${\bf{q}}_i$ stage, calculations related to each point are independent from the others. Hence, outliers do not affect inliers in the ${\bf{q}}_i$ stage. However, in the ${\bf{p}}_i$ stage, outliers perturbs the camera pose estimation results. To reduce the impact of outliers, the basic idea of our soft re-weighting method is to assign each 3D-2D correspondence a weight factor, and to make weight factors related to outliers small when estimating the camera pose in the ${\bf{p}}_i$ stage.

One possible method to assign weights is based on least median of squares \cite{simpson1997introduction}, however this method cannot handle more than $50\%$ of outliers. We designed a soft weight assignment method embedded in the iteration process. To distinguish inliers and outliers, the weights of 3D-2D correspondences are determined by

\begin{equation}
\label{eq_reweighting}
{w_i} = \left\{ {\begin{array}{*{20}{c}}
{1.0}\\
{H/{e_i}}
\end{array}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \begin{array}{*{20}{c}}
{if{\kern 1pt} {\kern 1pt} {e_i} \le H}\\
{if{\kern 1pt} {\kern 1pt} {e_i} > H}
\end{array}} \right.,
\end{equation}

\noindent where $e_i$ suggests the reprojection error of point $i$ with the current $\bf{R}$ and $\mu$ during iteration, $H$ is the inliers threshold that points with final reprojection errors smaller than $H$ are considered as inliers. The reweighting rule \eqref{eq_reweighting} suggests that a point with a large reprojection error will have a small weight during the estimation of camera pose, which is designed under a reasonable assumption that outliers have much larger reprojection errors than inliers. Although inliers may also have larger reprojection errors than $H$ during the iteration process, it is acceptable to assign weights that are smaller than 1 to inliers as long as outliers have much smaller weights. Hence, we simply use $H$ as the benchmark to assign weights.

According to $\bf{R}$ estimation given by equations \eqref{eq_R}, we multiply the weight factors with each item of matrices $\bf{A}$ and $\bf{S}$,

\begin{equation}
{\bf{A}}_i = w_i {\bf{A}}_i, {\bf{S}}_i = w_i {\bf{S}}_i.
\end{equation}

Similarity, to update $\mu$ using \eqref{eq_mu1},

\begin{equation}
{\bf{B}}_{i} = w_i {{\bf{B}}}_{i}, {\bf{C}}_{i} = w_i {{\bf{C}}}_{i}.
\end{equation}

Since inliers have much larger weights, $\bf{R}$ and $\mu$ are mainly estimated with inliers.

\subsection{1-Point RANSAC Scheme}

The core algorithm of R1PP$n$P is based on a randomly selected control point $o$. In outlier-free situations, our algorithm works with any control point. However, in situations with outliers, the control point $o$ should be an inlier to make the algorithm work. Hence, we employ the 1-point RANSAC scheme to try different 3D-2D correspondences as the control point until the algorithm finds the correct solution. The 1-point RANSAC scheme combines the core algorithm naturally because the core algorithm can perform the computation with any control point $o \in [1,N]$. We assume that 2D-3D correspondences have the same the possibility to be an inlier, without loss of generality, we select the control point $o$ from the center of all image points to the outside. This is because we found that R1PP$n$P needs less iterations to converge when $o$ is closer to the center, the details of which has been discussed in Section 3.3.

\subsection{Algorithm Flow Chart}
In general, the overall flow chart of R1PP$n$P is shown in Fig. \ref{fig_algorithmstep}, we first detect as many inliers as possible inside the RANSAC framework, then based on the detected inliers, we perform the R1PP$n$P algorithm without re-weighting mechanism to get more accurate results.

\begin{figure} [ht]
\vspace{0.0cm}
\centering
  \includegraphics[width=.48\textwidth]{figures/MethodSteps.pdf}
\caption{The overall flow chart of R1PP$n$P.}
\label{fig_algorithmstep}
\end{figure}

Appropriate termination conditions seek balance between speed and precision for RANSAC-based or iterative algorithms. As shown in Fig. \ref{fig_algorithmstep}, two types of termination conditions need to be specified for R1PP$n$P.

\noindent (1) \emph{RANSAC Termination Condition}

The standard RANSAC termination condition \cite{fischler1981random} was employed for R1PP$n$P, that is

\begin{equation}
\label{eq_ransactermination}
trials \ge \log (1 - p)/\log (1 - {p_{\rm{inliers}} ^s}),
\end{equation}

\noindent where $p$ is the certainty and we use $p = 0.99$ for all RANSAC-based methods in this paper, $trials$ is the number of RANSAC trials, $p_{\rm{inliers}} = $ (maximum number of detected inliers) / (number of all points), $s$ is the number of control points needed in each RANSAC trial. $s = 1$ for R1PP$n$P, and $s = 3,4$ for RANSAC+P3P and P4P respectively.

During the RANSAC process, the camera pose estimated by conventional RANSAC+P3P or P4P methods is based on very small number of points. Because of image noise, the estimated pose varies with different inliers as the control points. This is especially serious when the image noise is large. To improve accuracy, the termination condition \eqref{eq_ransactermination} suggests that the standard RANSAC scheme may continue looking for better results after finding a large percentage of inliers. In contrast, R1PP$n$P takes into account all points when estimating the pose, which makes it insensitive to the selected control point $o$. Therefore it is a reasonable assumption that when $p_{\rm{inliers}}$ is large enough (we used the threshold of $60\%$), no improvement can be found and the RANSAC process of R1PP$n$P could be terminated. Accuracy evaluation results in this paper have testified the rationality of this assumption.

\noindent (2) \emph{Termination Conditions for R1PPnP Iterations}

As shown in Fig. \ref{fig_algorithmstep}, we first detect as many inliers as possible and the related \emph{termination condition A} is satisfied when the detected number of inliers becomes stable, that is,

\begin{equation}
\label{eq_terminationA}
N_{\rm{inlier}}^{(k)} - N_{\rm{inlier}}^{(k-20)} \le 0 \text{  and  } k>20,
\end{equation}

\noindent where $k$ is the index of iterations, $N_{\rm{inlier}}$ is the number of detected inliers. According to our experience, in most cases no more inliers would be detected if $N_{\rm{inlier}}$ has not increased in 20 iterations.

\begin{figure} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.24\textwidth]{figures/testTerminationA1.pdf}
  \includegraphics[width=.24\textwidth]{figures/testTerminationA2.pdf}
\caption{Experiments with synthetic data (ordinary 3D case, $50\%$ of outliers) to demonstrate the iteration process of R1PP$n$P when the control point $o$ is an outlier. Randomly colored lines are results with different control points. (a) The changes of estimated camera pose between frames $k$ and $k-1$ are complex during the iteration process, based on which it is difficult to decide when to stop the process. (b) It is more robust and efficient to stop the process when no more inliers can be detected.}
\label{fig_testTerminationA}
\end{figure}

A good \emph{termination condition A} should be able to stop the iteration process as early as possible when point $o$ is an outlier, and do not interrupt when point $o$ is an inlier. We proposed the \emph{termination condition A} with a window size = 20 iterations to seek balance between speed and robustness. This termination condition is not based on the comparison of parameters of adjacent iterations because in R1PP$n$P, the dynamically updated weights $w_i$ may make the convergence process complex, especially when point $o$ is an outlier. As shown in Fig. \ref{fig_testTerminationA}(a), with an outlier as the control point, $\left\| {{{\bf{R}}^{(k)}} - {{\bf{R}}^{(k - 1)}}} \right\|$ may take many iterations to converge to zero, which is slow. With the change of detected number of inliers in a larger window size, the termination decision can be more robust and efficient, as shown in Fig. \ref{fig_testTerminationA}(b).

The refinement stage makes pose estimation results more accurate based on the detected inliers. Without the reweighting mechanism, the convergence process is much simple. Hence the \emph{termination condition B} is satisfied when the estimated rotation becomes stable, that is,

\begin{equation}
\label{eq_terminationB}
\left\| {{{\bf{R}}^{(k)}} - {{\bf{R}}^{(k - 1)}}} \right\| < 1e-5.
\end{equation}

\section{Experiments}

\begin{figure} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.24\textwidth]{figures/cannothandleoutlierR.pdf}
  \includegraphics[width=.24\textwidth]{figures/cannothandleoutlierT.pdf}
\caption{Except for REPP$n$P and R1PP$n$P, most P$n$P methods cannot handle outliers.}
\label{fig_pnpcannothandleoutliers}
\end{figure}

\begin{figure*} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.42\textwidth]{figures/ordinary_no_outliers_sigma/Rmean.pdf}
  \includegraphics[width=.42\textwidth]{figures/ordinary_no_outliers_sigma/Tmean.pdf}
\caption{Accuracy with outlier-free synthetic data (ordinary 3D cases). Number of points was 100. Different levels of image noises were added.}
\label{fig_nooutlers_accuracy_ordinary}
\end{figure*}

\begin{figure*} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.42\textwidth]{figures/quasi_no_outliers_sigma/Rmean.pdf}
  \includegraphics[width=.42\textwidth]{figures/quasi_no_outliers_sigma/Tmean.pdf}
\caption{Accuracy with outlier-free synthetic data (quasi-singular cases). Number of points was 100. Different levels of image noises were added. PPnP is out of range. The accuracy of all P$n$P methods decreased significantly compared with those in ordinary 3D cases, as shown in Fig.\ref{fig_nooutlers_accuracy_ordinary}. }
\label{fig_nooutlers_accuracy_quasi}
\end{figure*}

\begin{figure*} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.42\textwidth]{figures/ordinary_no_outliers_npts/Timemean.pdf}
  \includegraphics[width=.42\textwidth]{figures/quasi_no_outliers_npts/Timemean.pdf}
\caption{Runtime results with outlier-free synthetic data. Standard deviation of image noise $\sigma=5$ pixels. The number of points increased from 100 to 1000. (Left) Ordinary 3D cases. (Right) Quasi-singular cases.}
\label{fig_nooutlers_runtime}
\end{figure*}

The performance of the proposed R1PP$n$P algorithm was evaluated by comparing against the state-of-the-art P$n$P methods. The source code was implemented in MATLAB scripts and executed on a computer with an Intel Core i7 2.60 GHz CPU. We used both synthetic and real-world data to conduct evaluation experiments. The initial values for R1PP$n$P are ${\bf{R}} = diag\left \{ 1,1,1\right \} $ and $\mu = 1e-4$. RANSAC+P3P or P4P methods also used the standard termination condition \eqref{eq_ransactermination}.

\subsection{Synthetic Experiments}

 Synthetic experiments in this paper shared the following parameters. The camera focal length is 1,000 pixels with a resolution of $640\times480$. Two types of synthetic data were generated. (1) \textbf{Ordinary three-dimensional (3D) case}: object points were randomly and uniformly distributed in a cube region $[-2,2]\times[-2,2]\times[4,8]$. (2) \textbf{Quasi-singular case}: The distribution cube is $[1,2]\times[1,2]\times[4,8]$. For each experiment result, we report the mean values of 100 trials.

For accuracy evaluation, the rotation error is measured in degrees between the truth rotation $\bf{R}_{\rm{true}}$ and the estimated $\bf{R}$ as ${e_{{\rm{rot}}}}(\deg ) = \left\| {{{\left[ {{\rm{acos}}{{({\bf{r}}_{k,{\rm{true}}}^T \cdot {{\bf{r}}_k})}_{k = 1,2,3}}} \right]}^T}} \right\| \times {\rm{180/}}\pi  $, where ${{\bf{r}}_{k,{\rm{true}}}}$ and ${\bf{r}}_k$ are the $k$th column of $\bf{R}_{\rm{true}}$ and $\bf{R}$ respectively. The translation error is ${e_{{\rm{trans}}}}(\% ) = \left\| {{{\bf{t}}_{{\rm{true}}}} - {\bf{t}}} \right\|/\left\| {\bf{t}} \right\| \times 100\%$.

\subsubsection{Outlier-Free Synthetic Situations}

Most P$n$P algorithms do not have the ability to handle outliers, and even a small percentage of outliers will significantly reduce the accuracy, as shown in Fig.\ref{fig_pnpcannothandleoutliers}. Thus, although outlier-free situations are not the main concern of R1PP$n$P, we first conducted comparison experiments between the proposed R1PP$n$P and other P$n$P algorithms in outlier-free situations. The reason for this comparison is that RANSAC+P3P or P4P methods usually need other P$n$P methods as the final refinement step. Hence the accuracy and speed in outlier-free situations are also related to the performance in situations with outliers.

Here we only performed the core algorithm of R1PP$n$P without outliers handling mechanism. The termination condition for R1PP$n$P iterations was as Eq.\eqref{eq_terminationB}. In this experiment, we compared our proposed R1PP$n$P with the following P$n$P methods: LHM \cite{lu2000fast}, EP$n$P \cite{lepetit2009epnp}, RP$n$P \cite{li2012robust}, DLS \cite{hesch2011direct}, OP$n$P \cite{zheng2013revisiting}, ASP$n$P \cite{zheng2013aspnp}, SDP \cite{schweighofer2008globally}, PP$n$P \cite{garro2012solving}, EPP$n$P \cite{ferraz2014very} and REPP$n$P \cite{ferraz2014very}.

\begin{figure*} [htp]
\vspace{0.0cm}
\centering
 \subfigure[]{
  \includegraphics[width=.42\textwidth]{figures/ordinary_ransac/Rmean.pdf}
    }
 \subfigure[]{
  \includegraphics[width=.42\textwidth]{figures/ordinary_ransac/Tmean.pdf}
    }
 \subfigure[]{
  \includegraphics[width=.42\textwidth]{figures/quasi_ransac/Rmean.pdf}
    }
 \subfigure[]{
  \includegraphics[width=.42\textwidth]{figures/quasi_ransac/Tmean.pdf}
    }
  \caption{Average accuracy on synthetic data with outliers. (a)-(b) Accuracy with ordinary 3D cases; (c)-(d) Accuracy with quasi-singular cases.}
\label{fig_outliers}
\end{figure*}

\begin{figure*} [!htb]
\vspace{0.0cm}
\centering
  \includegraphics[width=.42\textwidth]{figures/ordinary_ransac/timeRANSAC.pdf}
  \includegraphics[width=.42\textwidth]{figures/TrialNum.pdf}

  \caption{Average runtime and number of required RANSAC samples with ordinary 3D cases synthetic data.  We do not give the results with quasi-singular cases because they is very close to that with ordinary 3D cases. RANSAC+P3P or P4P needs more than 10 RANSAC trails when $p_{\rm{outliers}}=0$ because the large image noise ($\sigma = 5$ pixels) usually makes P3P or P4P methods unable to find the correct pose with 3 or 4 inliers to satisify the termination condition Eq.\eqref{eq_ransactermination}. In contrast, the required number of RANSAC trials of R1PP$n$P is not sensitive to image noise because all points are taken into account.}
\label{fig_outlierstime}
\end{figure*}

In our accuracy evaluation experiments, the number of points was 100 and we added different levels of Gaussian image noises from 0 to 10 pixels. As shown in Figs. \ref{fig_nooutlers_accuracy_ordinary} and \ref{fig_nooutlers_accuracy_quasi}, for both ordinary 3D and quasi-singular cases, R1PP$n$P gave the most accurate rotation estimation results together with OP$n$P and SDP. For ordinary 3D cases, R1PP$n$P was among the most accurate methods to estimate translation and was only sightly less accurate than OP$n$P. However, for quasi-singular cases, the accuracy of translation estimation of R1PP$n$P was not the state-of-the-art. ASP$n$P became unstable with large image noise hence its mean accuracy decreased significantly compared with that with small image noise. Although sometimes PP$n$P can provide accurate rotation estimation results in ordinary 3D cases, it also suffered from  instability in some random cases, as shown by the jitter in Fig. \ref{fig_nooutlers_accuracy_ordinary}. PP$n$P and LHM cannot handle the quasi-singular cases.

To evaluate runtime, Gaussian image noise with a standard deviation of $\sigma=5$ pixels was added and the number of points increased from 100 to 1000. As shown in Fig. \ref{fig_nooutlers_runtime}, the proposed R1PPnP, together with EPP$n$P, REPP$n$P and ASP$n$P showed superior computational speed. The runtime of R1PP$n$P did not grow significantly with respect to the number of points. We suspect that this results from the intrinsic parallel optimization of the matrix computation of MATLAB 2014a.

Generally speaking, in outlier-free situations, R1PP$n$P was among the state-of-the-art methods in terms of both accuracy and computational speed. One drawback of R1PP$n$P is that the accuracy of translation estimation in quasi-singular cases was not among the best.

\subsubsection{Synthetic Situations with Outliers}

\begin{figure*} [htp]
\vspace{0.0cm}
\centering

  \subfigure[]{
  \includegraphics[width=.45\textwidth]{figures/Rerror_realworld.pdf}
  }
  \subfigure[]{
  \includegraphics[width=.45\textwidth]{figures/Terror_realworld.pdf}
  }
  \subfigure[]{
  \includegraphics[width=.45\textwidth]{figures/runtime.pdf}
  }
  \subfigure[]{
  \includegraphics[width=.45\textwidth]{figures/InliersNptsDetectionError.pdf}
  }
  \caption{Statistical results with real-world data. The $x$-axis is ranges of the percentage of outliers. (a) Rotation error. (b) Translation error. (c) Runtime. (d) The number of detected inliers compared with the maximum, zero suggests this method finds the most inliers.}
\label{fig_realworld}
\end{figure*}

The main advantage of R1PP$n$P is that it is capable of handling a large percentage of outliers with a much faster speed than conventional methods. For demonstrating this, we introduced the following RANSAC-based P$n$P methods for comparison: (RANSAC+P3P \cite{kneip2011novel}); (RANSAC + RP4P + RP$n$P \cite{li2012robust}); (RANSAC + P3P \cite{kneip2011novel} + ASP$n$P \cite{zheng2013aspnp}); and (RANSAC + P3P \cite{kneip2011novel} + OP$n$P \cite{zheng2013revisiting}). According to evaluations in outlier-free situations, OP$n$P is the most accurate P$n$P method and ASP$n$P and RP$n$P are fast. We selected these methods as the final refinement step to fully demonstrate the performance of RANSAC+refinement-like methods. Another important method is REPP$n$P \cite{ferraz2014very}, which is the state-of-the-art P$n$P algorithm that addresses outliers.

The experiments were conducted as follows. $N_{\rm{inlier}}=100$ correct matches (inliers) between 3D object points and 2D image points were generated. $N_{\rm{outlier}}$ mismatches (outliers) were generated by randomly corresponding 3D and 2D points. The true percentage of outliers is $p_{\rm{outlier}} = N_{\rm{outlier}} / (N_{\rm{inlier}}+N_{\rm{outlier}})$. Gaussian image noise with a standard deviation of $\sigma=5$ pixels was added. For R1PP$n$P and other RANSAC-based methods, the reprojection error threshold to distinguish inliers and outliers was $H = 10$ pixels.

As shown in Fig. \ref{fig_outliers}, REPP$n$P began to fail when the percentage of outliers was larger than $50\%$ with ordinary 3D cases, and only $5\%$ with quasi-singular cases. R1PP$n$P and RANSAC-based methods were capable of handling situations with a large percentage of outliers. R1PP$n$P was more accurate than RANSAC-based methods for both rotation and translation estimation. Compared to other RANSAC-based methods, R1PP$n$P was much faster, especially when the percentage of outliers was large.

\subsection{Real-world Image Data}

\begin{figure*} [htp]
\vspace{0.0cm}
\centering
  \includegraphics[width=.95\textwidth]{figures/realworldexp.png}
  \caption{Examples of images and R1P$n$P reprojection results. Green circles are all SURF correspondences and blue stars are the reprojected inliers detected by R1PP$n$P. First row: images with different illumination situations and the 3D point cloud. Second-third row: different data sets.}
\label{fig_realworldexamples}
\end{figure*}

Our real-world experiments were conducted on the DTU robot image data \footnote{http://roboimagedata.imm.dtu.dk/.} \cite{aanaes2012interesting}, which provides images and the related 3D point cloud obtained by structured light scan. The true values of rotations and translations are known. Images have a resolution of $800\times600$. Datasets numbered 1 to 30 were used. In each dataset, images were captured under 19 different illumination situations and from 119 camera positions. We selected 10 out of 19 illumination situations. Hence, a total of $30\times10\times119 = 35700$ images were included in this evaluation. Following the instruction, for each dataset and illumination situation, we used the image numbered 25 as the reference image and performed SURF matching \cite{bay2006surf} between the reference image and other images. The inliers threshold was $H = 5$ pixels for all methods. With each image, we ran all algorithms 5 times and used the average value for the subsequent statistics.

As shown in Fig.\ref{fig_realworldexamples}, the total number of correspondences and the percentage of outliers varied with objects, illumination situations and camera poses. Although clear comparisons require that only one factor is different, this kind of variable-controlling is difficult for P$n$P evaluation on real-world data because SURF matching results are unpredictable. In experiments we found that the performance of P$n$P algorithms were mainly affected by the percentage of outliers, rather than the total number of correspondences. Therefore in this section, we report the evaluation results by comparing the statistical results of P$n$P methods at each percentage of outliers range. Because the true number of inliers was unknown, for each image, algorithms detected inliers and we considered the maximum number of inliers as the ground truth.

As shown in Fig. \ref{fig_realworld}(a), as the percentage of outliers increased, the runtime of R1PP$n$P did not grow significantly compared with conventional RANSAC+P3P or P4P methods. When $p_{\rm{outliers}} < 30\%$, R1PP$n$P was slower than pure RANSAC+P3P, but was much more accurate as shown in Fig. \ref{fig_realworld}(a)(b). To improve accuracy, RANSAC+P3P needs other P$n$P methods, such as OP$n$P or ASP$n$P, as the final refinement step. Compared with other refinement P$n$P methods, R1PP$n$P was slightly less accurate than OP$n$P, which was the most accurate P$n$P method according to both synthetic and real-world experiments, but much faster even when the percentage of outliers was small.

 \begin{figure} [htp]
\vspace{0.0cm}
\centering
 \includegraphics[width=.45\textwidth]{figures/NumberofIterationsHistogram.pdf}
\caption{Histogram of the number of iterations of R1PP$n$P in real-world experiments.}
\label{fig_realworld_iterations}
\end{figure}

Fig. \ref{fig_realworld_iterations} shows the histogram of the number of R1PP$n$P iterations  on all 35700 images. As shown in Fig. \ref{fig_algorithmstep}, the iteration number includes iterations with the re-weighting mechanism that obtained the best results in RANSAC trials, and the subsequent refinement iterations without re-weighting. The average number of required iterations is 51.3.

\section{Conclusions}

We present a fast and robust P$n$P solution named R1PP$n$P for tackling the outliers issue. We integrate a soft re-weighting method into an iterative P$n$P process to distinguish inliers and outliers, and employ the 1-point RANSAC scheme for selecting the control point. The number of trials is greatly reduced compared to conventional RANSAC+P3P or P4P methods; hence, it is much faster. Synthetic and real world experiments demonstrated its feasibility. Except for the good performance, another hidden advantage of R1PP$n$P is that its code implementation is relatively easy because all steps of R1PP$n$P involve only simple calculations. For example, its minima avoidance mechanism only requires to compute the determinant of the rotation matrix and to make $\lambda_{\rm{new}} = 1/\lambda_{\rm{old}}$. The most appropriate situations to replace conventional RANSAC+P3P methods with R1PP$n$P is when the percentage of outliers and/or the image white noise is large. R1PP$n$P is more appropriate for large point clouds because of its low time complexity and the requirement to try control points. Future works involve the development of its extension for planar cases, and applying it in the SLAM system to handle outliers when a new frame is encountered.

\section*{Acknowledgment}
This work is supported by NIH P41EB015898.

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\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


text:
A 'light bulb moment'
By Thomas Goff
Thomas Goff is an instructional assistant at Folsom Lake College who has been trained as an Irlen screener. He is a frequent contributor to SN&R's Poet's Corner.
Recently, a student in the Reading and Writing Center at Folsom Lake College where I work chose one of our "breakout" rooms for study, rather than working in our open area where conversations may distract. He used our optional lamp stand fitted with conventional incandescent light bulbs, rather than the room's fluorescent lighting. Asked about his choice, he replied that the incandescent lights made things "more like home," where he studies successfully with regular bulbs.
I know nothing about this particular student other than his reply. But Helen Irlen, after years as a learning-disabilities specialist in Southern California, has amassed thousands of case studies and much supporting evidence to show that many people, students included, suffer greatly under fluorescent lighting.
About 12 percent of the general population and 46 percent of the "learning-disabled" population may experience, in forms varying from mild to extreme, what's known as Irlen Syndrome. People who have Irlen Syndrome may see the text dance, float, lift off the page, swirl, blur or become degraded by penetrating "rivers" of blank white. This is especially likely to happen when reading black ink on glossy paper illuminated under fluorescents.
Irlen's Syndrome is not an optometrist's problem; it is an eye-brain perception problem. And while the Irlen Institute (www.irlen.com) can provide other solutions to the malady, incandescent light bulbs are of greater help than any other kind yet tried. Moreover, fluorescent bulbs are toxic and serve only to poison our landfills.
Abetted by a spate of recent publicity in the Sacramento Bee—and recently in SN&R, with a full-page editorial—and by exertions around the world from environmentalists (but also from fluorescent-bulb makers), Assemblyman Lloyd Levine, D-Van Nuys, is attempting to have all incandescent bulbs in California snuffed out by 2012.
In view of this ill-considered rush to judgment, it's time for an old-fashioned "light-bulb moment." Any who care to explore the Irlen Web site can contact the Institute and should consider signing a petition to prevent this proposed ban.
The light you save may be your own.
Stop paying for war
Democrats can't oppose the war while they're voting for funds to continue it.
Juvenile diabetes—the 'new normal'
Cure juvenile diabetes and return childhood to normal.
Look beyond Walter Reed
The conditions at Walter Reed are the result of caring for veterans on the cheap.
Health care is breaking our hearts
Our health-care system is like a bad relationship—and it's time to break up.
Veggies aren't 'blight'
Sacramento is considering a ban on <i>some </i>front-yard gardens—the ones that grow food.

redpajama_set_name: RedPajamaCommonCrawl


In Vitrium, click on the Users Tab > Select the User > Under User Info tab, enter the new password in the Password text field provided.
Once completed, click Save & Exit and the new password entered will be applied.
Note: It is your responsibility as the administrator to inform your User about the password (even the username) changes made.


Freshly marinated salmon in a spice mixture made by us matured several steps and thus suitable as a whole or in pieces for the grill. By marinating, the skin becomes particularly crisp and tender during crickets and thus a culinary experience. The salmon can be prepared very well directly on the grill grill as well as in an aluminum dish with some olive oil, pay attention only to the heat so that it does not burn.
Hamburger Fischwerker's Gourmet Tip: Do not grate the salmon completely, so it becomes particularly tender and retains its reddish color in the flesh. Blanched green asparagus with a vinaigrette of olive oil, fresh chopped garden herbs and finely crushed hard-boiled egg.
Durability is done by the Hamburgers only by means of fangfrische slaughter and naturally preserving preparation with salt, sugar and spices. If you want to keep the salmon longer, please freeze it.


Angi Ma Wong, known as the "Feng Shui Lady", has added another book to her Feng Shui Dos and Taboos series—this one focusing on health and well-being. Wong, an internationally recognized Feng Shui expert, practices the Compass School variety of this ancient energetic art. That is, a compass is used to find a space's magnetic North first, and then the 7 other areas of the bagua map fall into place.
Feng Shui is the art of directing chi (life force energy) in the different bagua areas by arranging furniture, adding certain decorations and accessories, using color, removing hindering objects, and utilizing the 5 elements (Metal, Fire, Water, Earth, Air).
Wong also explains the Black Sect School of Feng Shui, which doesn't use a compass. Rather, the 8 sections of the bagua change based upon a room's main entrance. She stresses that these schools do not mix, so when choosing one method over the other, it's important to be consistent. Whether you prefer the Compass School or the Black Sect School (which is what I prefer), Feng Shui Dos and Taboos for Health & Well-Being can be used for either system.
Do position the spines of your books so that they're flush with the edges of open bookcase shelves.
Do wear jewelry with fluorite, tourmaline, onyx, or tiger-eye beads to help you maintain balance while studying or working on your computer.
Do notice that those who sit with their backs to the door in a meeting or conference room have less influence.
Don't give sharp objects as gifts to anyone, as these symbolize the severance of a friendship or a life.
Do prune the leaves of trees and shrubbery so that they don't touch the walls of a house, thus drawing the energy away from it.
Do add more metal in the form of copper, silver, brass, or pewter in your home if your skin is dry and flaky.
Don't design your stairs to lead toward a bathroom or the main entrance door of your home if you're remodeling.
Don't create an imbalance of yellow in your home—too much of any earth color may cause you to worry excessively.
Do add more wood in your home if you're feeling depressed, timid, or shy.
Don't place waterfalls or tabletop fountains in the South area of a room or office—to do so symbolizes water extinguishing fire, which stands for fame and fortune.
2. If you don't see it, it isn't there.
So there's no need to worry if certain elements of your surroundings violate Feng Shui principle. Because "everything is fixable", things can be added or subtracted to promote the balanced flow of the vital life-force energy known as chi.


text:
david doonan
1238.40sc
1 reaction
Response to Trump's "Save America" Rally
The Young Ecosocialists condemn the actions that took place at the Capitol Building today, both those taken by protesters and by a complicit police force. Having clearly lost the election, President Trump has continued to embolden white supremacists, fascists, and other far-right radicals. This is nothing new for President Trump. He has a long pattern of embracing his fascist followers with comments of "very fine people on both sides" after the white supremacist Unite The Right Rally in 2017. He has repeatedly encouraged violence and failed to condemn these groups, famously telling the Proud Boys to "Stand back and stand by" in the first presidential debate of 2020. This behavior has predictably incited right wing violence all across the country.
Young EcoSocialists
By Daniel Bumbarger, Noah Martin, Charlie McVicker, Shannel Pittman, Josh Lorenzo, Manuel Lopez, Avery Seal
Januaury 6, 2021
President Trump is not backing down now. Immediately following the reactionary protest in Washington DC, Donald Trump tweeted the following.
He called for these actions, and he continues to stand by them. But we recognize that this protest, and Trump himself, are just symptoms of the larger problems in this country.
Over the past year, we have seen the feds attack protestors with increasingly violent measures. They have sided with the far-right, and fought back against basic anti-violence and anti-bigotry reforms. In Portland, dozens were killed, wounded, and left permanently disabled by state violence, including several neutral onlookers. In Kenosha, the police aided a radicalized teenager who travelled across two states to shoot protestors and allowed him to go home for the night. In Washington DC, almost 6000 feds were deployed to clamp down on the unrest, at one point gassing protestors near Lafayette Square... So Trump could have a photoshoot with the Bible.
State violence isn't anything new or groundbreaking. Look back at the harsh crackdowns during the Civil Rights Movement, the Los Angeles uprising in the early 90s, the Ferguson protests in 2015, and countless other movements for survival. Police backlash against reforms have made it explicitly clear time and time again: the police state will respond in force to any movement that challenges it.
The police did not have the same violent reaction today. Not only that, but many cops showed solidarity with the revolutionary wannabes. Let's be 100% clear about what happened: in the same city where anti-racist protestors faced a fully militarized police force, an armed mob just strolled in and occupied the single most important federal building in the nation with almost no resistance. After several hours, only thirteen people were arrested before the mob was dispersed. Only one person was fatally shot. Why was the police reaction today so different?
Cops are taking selfies with the terrorists. pic.twitter.com/EjkQ83h1p2
— Timothy Burke (@bubbaprog) January 6, 2021
We don't have to imagine the absolute bloodbath if a Black Lives Matter protest attempted to enter the Capitol. Those of us demanding racial justice are regularly beaten, bruised, and blinded while the state lets down blockades for blatant fascists (View on Twitter). Indigenous activists, Black Lives Matter organizers, and labor strikers have a history of asserting their rights through sit-ins, blockades, and marches. These actions have time and time again been met with state violence.
When we bash the feds for their pathetic response, many respond "but don't you guys want to defund the police?" As the right often does, they ignore the blatant undertones of this incident. They try to turn the argument back on us. They ignore the root issue. Policing exists only to reinforce white supremacy and support the ruling class. No need to let "law and order" get in the way. That's why we saw police siding with terrorists today. Seeing this, our calls for police abolition grow louder and our hatred for the police grows stronger.
Our failed capitalist system and its neoliberal misleaders refuse to confront the multiple crises we face, and organized reactionaries step in with violent "patriotic" fantasies to fill the void. Only an organized, independent working class rooted in democratic practices can overcome these forces. Together we can make that a reality. It's vital that we build leftist trust, solidarity, and unity. Our survival depends on it. In the words of Assata Shakur:
It is our duty to fight for our freedom.
It is our duty to win.
We must love each other and support each other.
We have nothing to lose but our chains.
Edit: As of Jan 7th, 10am Eastern time, there have been four civilian deaths and 26 people have been arrested in relation to the inicident. There have been 52 total arrests including curfew violations.
Background photograph: Evelyn Hockstein for Washington Post
CapitolRiot
david doonan published this page in State & Local News 2021-01-07 08:03:45 -0800


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Home/Candidates 2020, News/Gaskill Announces Re-Election to the Iowa House
State Representative Mary Gaskill announced today she will seek re-election to the Iowa House in District 81, which includes Ottumwa, Agency, Eldon, and the townships of Center, Competine, Dahlonega, Green, Keokuk, Pleasant, and Washington.
"It's a great honor to serve in the Iowa House and I'll keep working hard to improve the lives of families in Wapello County. While I'm proud of the progress we've made, there's more work to do to create new jobs, raise wages, and keep health care both affordable and accessible in our community," said Gaskill.
Prior to her time in the Iowa House, Mary served as the Wapello County Auditor. Mary is the Ranking Member of the House Ethics Committee. She also serves on the Economic Growth, Local Government, Ways and Means, and the Economic Development Budget Appropriations Sub-Committees. Mary is also a member of the Commission on Aging, Iowa Workforce Ex-Offender Reentry Committee, and a Board Member of the Iowa Finance Authority.
"My top priority is listening to the people of Wapello County. Working together, we can build a community where our children
want to stay and start their own families. That means affordable housing and child care; world-class schools; and an opportunity for everyone in our community to get additional training or education after high school," added Gaskill.
Mary is the widow of Jim, a retired Iowa State Trooper. She is currently involved in the Ottumwa Area Chamber of Commerce, the League of Women Voters, American Legion Auxiliary, Veterans of Foreign Wars Auxiliary, a member of the St. Mary of the Visitation Church, and a member of Catholic Daughters of America. Mary is also the mother of four children, who all still live in Iowa, and the proud grandmother of seven grandchildren.
By iowahouse|2019-11-20T11:10:37-06:00November 7th, 2019|Categories: Candidates 2020, News|0 Comments


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Happy Weekend! I'm glad you are here to celebrate Friday night with Best of the Weekend.
It's been a busy time for us without a lot of free time to do projects. It's supposed to rain here this weekend and I'm hoping to spend a lot of time in our basement completing projects to share with you next week.
I look forward to seeing your projects for the week!
Thanks for the party Paula. Like they say, better late than never, whew. Hope you're having a good week so far!


The Iowa Supreme Court heard oral arguments this morning on the Secretary of State's request to remove temporary injunction that has blocked parts of Iowa's new voting law.
The League of United Latin American Citizens challenged the constitutionality of three provisions of the law. One of the provisions is the requirement that a ballot can be rejected if signatures are checked and don't match.
The attorney for the state, Thomas Ogden, says there have always been safeguards in place like this. "The provision at issue that allows the canvassing board to reject a defective ballot has been law for more than 10 years. The only thing that was added to it was this signature provision," Ogden says. Ogden says it only becomes a concern when someone waits until the last minute to vote.
"The fact of the matter is that you have this entire period in which to send it in that you are able to cure. And if you wait until the very end, you are taking the risk that you may not have that chance. And that includes any defect — not just the signature matching," Ogden says.
LULAC attorney Bruce Spiva says the changes hurt the organization as they had to spend more money to get people out to vote. "In order to get its constituency and its membership out to vote and make sure that their vote is counted, they having to expend all kinds of resources and energy, which is diverted from other activities," Spiva says.
Justice Thomas Waterman asked Spiva why the group why the group didn't file a lawsuit as soon as the law changed in January, and says it has caused issues for auditors. "There's a lot of scrambling going on and confusion because of the late nature of this challenge," Waterman says. Spiva replied that waiting to file the lawsuit was not a tactic on the group's part, as he says they would have preferred to be in court earlier. He says having the funds to file the lawsuit was one of the reasons they didn't act sooner.
Spiva was asked if the group would have sued in the early voting period had been 50 days and cut back to 40. He says he wouldn't expect the concern to extend in that case, and says it is more of what voters have been used to for the early voting period. "Iowa's been operating under a system of 40 days since 2003 and a lot of voters have come to rely on that 40-day period. In fact so many, that in 2016, 88,000 people voted in those 11 days," Spiva says. Spiva was asked there was any evidence that the change suppressed the vote in the June primary election.
"No you honor is the direct answer," Spiva says, "buy I think you can't draw any conclusions from aggregate turnout in a single election. We are not really here talking about the aggregate turnout and whether the turnout will go up or down." He says they are arguing that 88,000 people voted in the 11-day period relied on the time and the state pulled it away from them.
Chief Justice Mark Cady says they understand this is an important case that needs a quick answer and they will try to do deliver one.


Polym. Chem., 2015, 6, 2817-2821.
Materials responsive to reactive oxygen species (ROS) at a physiological level are of great significance in diagnostic and therapeutic applications. We have synthesized a water-soluble tellurium-containing hyperbranched polymer and demonstrated that it forms a kind of ROS-responsive aggregate. In aqueous environment, the polymer aggregates can swell under biologically relevant concentration of H2O2, which could be expected to find applications in fields such as elimination of excess ROS.


This work I did for the conference site for the DevFest Siberia.
The illustration created for a short story for kids.
Card invitation to the conference, background.
Here I have drawn the architectural illustration based on the real building.
On this artwork, I will show a typical Russian interer.
Here I created the Phases of the Moon in the style of old engravings.
My work for inktober2017. This time I used digital graphics.
Pixel art. I created for one restaurant landing page.


text:
Маона — средневековая итальянская ассоциация инвесторов, обычно образованная с целью откупа налогов. Этимология, по наиболее популярной версии, происходит от  ma'ūnah, помогать,  mu'āwanah взаимная помощь. По другой версии, происходит от названия турецкого корабля маона. Являлись одними из предшественников современных акционерных обществ, дольщики маон назывались маонеси.

Маоны были наиболее типичны для Генуэзской республики. Первой такой организацией стала Маона Сеуты, образованная в 1234 году для военной экспедиции в этот город, имевший большое торговое значение. Поводом для операции стало нападение правителя Марокко на Сеуту, в ходе чего пострадала местная генуэзская колония.

Наиболее известной является Хиосская Маона, образованная в 1347 году с целью финансирования завоевания острова Хиос и порта Фокея.

На тот момент Венеция контролировала Негропонт и Кандию. Генуя нуждалась в безопасном торговом пути в Константинополь, и приняла решение оккупировать Хиос. В связи с неспособностью государства финансировать военный поход, для покупки кораблей и оплаты услуг наёмников было образовано коммерческое товарищество (маона). Генуя передала маоне откуп на взимание налогов с Хиоса и Фокеи, также дольщики получили монополию на выгодную торговлю мастикой. Хотя формально суверенитет над Хиосом принадлежал Генуэзской республики, присылавшей своего представителя — подеста, финансовая и гражданская администрация относились к ведению маоны, одна из ранних её конституций включала также чеканку монеты.

Вместе с тем Хиос был открыт для атак со всех сторон, и маоне приходилось постоянно содержать на острове гарнизон.

Местные представители генуэзских властей защищали интересы дольщиков маоны, а не местных жителей. Хотя маона обеспечивала большую безопасность и сохранность имущества, чем византийская династия Палеологов или рыцари Родоса, греческое население было практически полностью исключено из управления собственным островом, что усугублялось религиозной враждой (между итальянскими католиками и православными греками). Местный православный епископ также утверждался маоной.

Постепенно доли маоны сконцентрировались в руках восьми человек, сформировавших Новую Маону, получившую управление от Старой. Большинство партнеров Новой маоны образовали на Хиосе такой специфический генуэзский институт, как альберго (клан из нескольких родственных благородных семей). Однако, в отличие от генуэзских альберго, хиосский фактически являлся не кланом, а коммерческой ассоциацией. Все его участники сменили свои фамилии на Джустиниани. В этой связи Новая Маона также упоминается, как Маона Джустиниани.

Маона фактически правила Хиосом вплоть до вторжения в 1566 османов, которым она вынуждена была платить дань с 1415 года. С юридической точки зрения, Генуя передала маоне управление островом вплоть до выплаты её расходов в 203 тыс. генуэзских лир, чего так никогда и не произошло. Первоначально, республика передала маоне откуп на 29 лет, который впоследствии продлевался. По всей видимости, это первый известный в истории случай, когда коммерческая компания исполняла функции государства.

Известны также Маона Корсики, в 1378 году получившая этот остров в связи с арагонским вторжением, и Маона Кипра (см. Кипро-генуэзская война).

Подобные эксперименты Генуи в области сочетания в одном лице коммерческих и государственных функций, оказали огромное влияние на конкурирующую с ней Венецианскую республику. С 1400 года все новые венецианские галеры становились государственной собственностью, был введён целый ряд государственных монополий и ряд ограничений на частные корабли. Также они послужили предтечей гигантских Ост-Индских компаний. Так, Британская Ост-Индская компания сочетала собственно торговые функции с военными акциями и взиманием налогов, причем все эти сферы деятельности были переплетены в одной организации.

Примечания

Средневековая Италия

redpajama_set_name: RedPajamaWikipedia


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Whether you're trying to save money or dealing with a broken air conditioner, sometimes you need to find simple ways to beat the heat without turning on the AC like these!
Nowadays when the summer temperatures start rising, most people turn on their air conditioners without thinking about it. But running the AC all summer long can be pretty pricey, so some people choose to wait until the height of summer to turn their ACs on. And of course, there are some people who wish they could turn their AC on, but are waiting for the AC repair people to get there! Whether you're keeping the AC off for frugal reasons or because it's broken, here's How to Beat the Heat without Turning on the AC!
Perhaps the easiest way to stand the heat without turning on the AC is to fill yourself with cool foods and drinks! Have iced coffees, lemonades, and fruit infused water! And eat lettuce salads, pasta salads, ice pops, and no-bake desserts. Not only do these cool you down by filling your insides with low-temperature foods and drinks, but they also save you from turning on the hot stove top or oven!
If it's a super-hot day and you feel like you can't take the heat much more, step in the shower for a minute and turn just the cold water on. A minute or two under a spray of cold water is all you need to cool yourself down and get rid of that hot, sweaty feeling!
If you have a large freezer or just an especially empty one, consider using it to help you beat the heat without turning on the AC! Fold up your sheets and pillowcases and place them in the freezer for a few hours before going to bed. If you're concerned about freezer food smells leaching into the fabric, wrap them in plastic first. When you take them out and put them on your bed they'll be wonderfully chilled, making it easy to go to sleep on a hot night!
Believe it or not, going outside may actually be a good way to deal with a hot day. Many times the outside of your home will feel cooler than the inside due to breezes, lack of heat-emitting electronics, and the fact that the air isn't stagnant. If you have things to do inside and can't go out to cool off, consider opening the windows or even the doors, provided that they have screens. Getting the air flowing in and out of your house can really help a lot!
If you'd rather not freeze your sheets at night, or are looking for a daytime solution, consider using ice packs! Freeze them ahead of time, and whenever the day starts to get too hot for you, lay them on the back of your neck, your inner wrists, inner elbows, etc. to help cool yourself down. If you don't have actual ice packs, freezing wet washcloths also works.
A simple way to manage the heat without turning on the AC is to make good use of your fans! Run ceiling fans counter-clockwise so that hot air gets pulled up instead of pushed down. Also consider placing fans so that they blow your hot house air out the window, promoting air circulation! You can even place a fan behind a bowl of ice water or frozen water bottles to make a kind of DIY air conditioner!
What do you do to cool down without turning on the AC?
Did you like these 6 Ways to Beat the Heat without Turning on the AC? Find more on my Summer Days board on Pinterest!


KIOC Bangalore conducting 3 days fast bowling master class. Anyone, including non-KIOC people, can join for this fast bowling master class.
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text:
Home >> About Us >> History >> Stats and Surveys
Data to Grow On: The Statistics and Surveys of AAUP
by Regan Colestock
University presses are notable because of their number and variety of sizes and interests. This is one reason why cooperative efforts work so well here: members are as curious about how other university presses operate as they are generous with their own experiences. These cooperative traditions have fostered not only the Association itself, but, over the years, other opportunities to share and educate in the name of good publishing—residencies, workshops, discussion lists, and more.
As a cooperative, one of the most comprehensive informational tools AAUP has provided for its members is data. Statistics and surveys of all shapes and sizes have provided touchstones for press leadership for more than sixty years. The numbers provide a yardstick for where we are (and where we've been), how we relate, and how we continue improving and innovating.
Of course, if such yardsticks are to be useful, the right questions have to be asked. Depending on the decade, the variables in these surveys have taken a variety of forms, inquiring about everything from history to finances to digital publishing.
The first survey that aimed to define and answer a set of critical university publishing questions was the comprehensive, membership-wide Kerr Report, commissioned in 1948—about a decade after AAUP's founding—and completed in time for the 1949 Annual Meeting in Princeton.
The Kerr Report adopted its name from its lead investigator Chester Kerr, an experienced publisher. AAUP received funding from the Rockefeller Foundation, a grant administered through the American Council of Learned Societies (ACLS), to commission a report with three broad goals. These were: to investigate and describe university press organization and operating procedures; to evaluate the relationship of university press publishing to education, scholarship, and to American publishing in general; and to "arrive at conclusions and make recommendations."
While these questions may seem broad today, it must be noted that the Kerr Report was the first to document the collective history of university presses, to measure basic business statistics such as net sales, backlist sales, and rate of publication, and to explore the composition of editorial lists. Kerr also compiled the average profiles of a university press director—largely (though not entirely) male and middle-aged, "these thirty-five university press heads could not in general be described as well paid"—and a scholarly author—"in regard to his publishing problems, he was still inclined to maintain his sense of snobbery about the imprint of a commercial publisher.")
The response to the Kerr report, particularly from the AAUP membership, was very positive, as was recorded in the thank-you letters to the Rockefeller Foundation. "I doubt if any among us had previously known the real role the presses are playing in the dissemination of scholarship, or the importance of their effort in relation to publishing in the U.S. as a whole," wrote Savoie Lottinville, AAUP's incoming president and director of the University of Oklahoma Press. "The value of this undertaking is almost self-evident: it is bound to produce a clearer understanding and a broader basis for cooperation between scholars and the publishers of scholarship, between universities and their presses, and between the public, which is essential to all our efforts, and all of the university presses in and out of the association."
Datus Smith (of Princeton University Press), the outgoing President at the time, outlined the lasting effects he expected the report to have as a guide for AAUP. The report encouraged uniform, and thus easily comparable, account keeping among the presses. It led to the proposal that the Association create membership requirements, because it provided the first yardstick to compare individual press's performances. The yardstick would also become an important tool for the foundation of new university presses. Finally, the solid data encouraged more respect for, and perhaps faith in, university presses from the broader publishing community, as well as scholars and university administrators, and provided some handy public relations ammunition.
But most importantly, the Kerr Report set a precedent for AAUP, its success encouraging a variety of future inquiries.
From then on, whenever new questions arose about scholarly publishing practices, the board would answer them by setting up short-term committees (or enlisting existing ones) to conduct surveys and generate reports. The Committee on Foreign Review Media surveyed the book review policies of member presses and published a list of resources in 1949. In 1955, the Committee on Manufacturing Economies reported on best practices, tips, money and time savers, new processes, and new products for book manufacturing. Surveys of both "endangered disciplines" and press internships and fellowships were conducted by committee in the late 1980s.
And so the practice of inquiry-driven committee work, of surveying members and generating a report from that data for the benefit of all member presses, became a pattern ingrained into AAUP, up to the most recent Q&A iteration, the Digital Publishing Report, begun in 2009. But these evolving, committee or question-driven, topical surveys, which come and go over the years as needed, producing dozens of contextually useful reports, were joined by another type of survey in 1969.
Forty-three years ago, the first annual operating statistics survey was undertaken. As Harry Van Ierssel, then at the University of Toronto Press, remembers it, the only comparable non-AAUP surveys at the time were relatively useless. One day when the AAUP President was visiting the Toronto offices, Van Ierssel voiced his complaints, which unexpectedly led him to a meeting with the AAUP Board. Van Ierssel pitched his idea for an AAUP survey that would improve on the status quo, and the first survey was soon commissioned.
Later, in the mid-1980s, Van Ierssel himself took over the survey, transforming it by breaking the presses down into groups based on net sales, expanding it with new appendices, and issuing the reports into contextualized four-year analyses rather than one-year snapshots. (Contributions that would later be recognized with an AAUP Constituency Award.)
Over the years, under the guidance of the Business Systems Committee, the annual operating survey has nearly doubled in size, now including statistics from an average of more than 60 university presses. The detail and depth of reporting has consistently expanded to provide clearer representations of our niche of the publishing industry, with the accompanying commentary growing as well, thanks to the professional interpretation of consultant Kimberly Maselli Schmelzinger.
Unknowingly echoing Datus Smith's predictions, Van Ierssel observes, "I think what the report has done over the years—and one of the best benefits that has come out of it—is a standardization of reporting. You're comparing apples to apples. In a sense, I think even the [financial] handbook has built on this and made the survey a stand-up kind of reporting—especially for small presses." AAUP surveys, from Kerr to the Operating Statistics, have created real guides and markers for growth and progress. And, as they each show, we have come a long way as an Association.
History of the Annual Meeting
Stats and Surveys
Women in Scholarly Publishing


Set in the high-stakes world of the financial industry, Margin Call is an entangling thriller involving the key players at an investment firm during one perilous 24-hour period in the early stages of the 2008 financial crisis. When an entry-level analyst unlocks information that could prove to be the downfall of the firm, a roller-coaster ride ensues as decisions both financial and moral catapult the lives of all involved to the brink of disaster.
Critics Consensus: Smart, tightly wound, and solidly acted, Margin Call turns the convoluted financial meltdown of '08 into gripping, thought-provoking drama.
Thoughtful Wall Street drama has drinking, language.


Germany needs more ethnic minorities in its political system, the police and its courts, and has to do more to tackle racism in daily life, a UN special rapporteur said on Wednesday.
"My visit has convinced me that much remains to be done," Githu Muigai, UN special rapporteur for racism, said after a 10-day fact-finding trip across the country.
People with a migrant background "are under-represented in important institutions, including the political system, the police and the courts," Muigai said.
Last November, the Greens became the first major party to elect a Turkish-German as leader, Cem Ozdemir, but ethnic minorities are generally a rarity in German politics, making up fewer than 15 national MPs.
Muigai, who was paying a routine visit to Germany, also said that due to the historical experience of Germany with Nazism, there is a "tendency to equate racism with extremist politics."
"I think that this great country needs to turn its attention to the problems of daily racism and discrimination, that is the racism and discrimination to be found in daily life in schools, public places, in housing, in employment etcetera," he said.
He added however that he was "encouraged by the open recognition by authorities that Germany is nowadays a country of migrants and that migrants make a positive contribution to society."
Kenyan-born Muigai, special rapporteur since August, also said that far-right groups in Germany "demand constant vigilance" and should be banned "within the constitutional legal mechanism provided by German law."
There are regular calls for a ban on Germany's biggest far-right party, the NPD, which has no seats in the Bundestag national parliament but has representatives in two of Germany's powerful regional assemblies.
The previous centre-left government had sought to ban it, but the case was thrown out in 2003 by the Constitutional Court.
Germany also needs to do more to speed up the processing of asylum-seekers, Muigai said.
Muigai said that his full report, due to be presented at the Human Rights Council in 2010, will also focus on the plight of Muslims in Germany following the increase in security measures aimed at tackling Islamic extremism.
"The Muslim community does have very special concerns, particularly in the aftermath of 9/11 and in the manner in which the security apparatus have responded to ... the challenge of the fight against terrorism," he said.
A government study published in June found that Germany had between 3.8 and 4.3 million Muslims - between 4.6 and 5.2 percent of the population – much higher than the previous estimates of 3.1-3.4 million.


text:
Q: Convert PDF to PDF/A-2u using Ghostscript/itextsharp i need to convert a existing PDF into PDF/A-2u using Ghostscript or itextsharp. i am searching in stackoverflow, not able to get exact resolution. Let me know is there any way to achieve this requirement
In Ghostscript, i have used the below command,
gs -dPDFA -dBATCH -dNOPAUSE -sProcessColorModel=DeviceRGB -sDEVICE=pdfwrite -sPDFACompatibilityPolicy=2 -sOutputFile="path/to/output_File.pdf" "/path/to/input_file"
In iTextSharp, i am trying to create a new PDF with PDF/A-2u, tried to load the existing or available pdf and save the document. Expected result of PDF/A-2u is not reflecting in the output pdf file

redpajama_set_name: RedPajamaStackExchange


text:
Q: Get Parent Size SwiftUI Is there any way of finding the parent view size using SwiftUI, I have had a look through the documentation and examples and it seems most (if not all) are hard coding sizes, ideally I want to find the size of the parent and then set the sub view size based on a percentage of the parents size (probably in some swift helper class or something) e.g.
func getSizeFromParent(fractionHeight: Int, fractionWidth: Int) -> Size
{
    var parentSize = // is there a way to get parent size somehow

    var newHeight = parentSize.height * fractionHeight
    var newWidth = parentSize.width * fractionWidth

    return Size(newHeight, newWidth)
}

Note the above code is not meant to be a working example just pseudo code

A: In SwiftUI parents suggest a size to their children, but children decide what to do with it. They can ignore it, use it partially, or be completely obedient.
As Radagast commented in your question, GeometryReader is the way SwiftUI uses to communicate sizes down the view tree hierarchy.
I've written a detailed article about how you can use GeometryReader and GeometryProxy and I included some examples of use cases. GeometryReader is also very useful in combination with the .background() and .overlay() modifiers, as it let you "steal" the geometry of another view.
For more information, check: https://swiftui-lab.com/geometryreader-to-the-rescue/


text:
Pakistan on the verge of becoming World's number one ODI team
by Zainab Shafiq | 9 Jan 2023
The ongoing One Day International (ODI) series between New Zealand and Pakistan is an important one as it could potentially see the men in green become the number one ranked ODI side in the world. If they are able to defeat the Kiwis in a clean sweep, they will replace the current top-ranked team, New Zealand on the board.
However, things may not be easy for Babar Azam and co as Pakistan are experimenting with a new management and selection committee. In the Test series preceding this ODI series, both teams were unable to secure a victory, with the matches ending in a draw.
Currently, Pakistan sit in fifth place in the ODI rankings with a rating of 107, while New Zealand are in first place with a rating of 116. It is uncertain if Pakistan will be able to win all of the matches in the series, which would change the current ranking scenario.
In the first match of the series, Pakistan won the toss and elected to bowl first. They were able to concede 255 runs and take nine wickets, making things difficult for New Zealand. However, Pakistan struggled while chasing the runs, and it seemed like the match was slipping out of their control. Fortunately, they were able to secure a victory with 258 runs on the loss of four wickets and 11 balls left in the inning.
Also, see:
Analyzing the Suitability of Pakistan Cricket Players for Captaincy
Rivalry of the Dangerous Bowlers: Bumrah vs Afridi
The rivalry of the Dangerous Bowlers: Bumrah vs Afridi
Pakistan will play better than India in India in World Cup 2023
Pakistan will play better than India in India in World Cup 2023, claims ex bowling coach....
Azharuddin Weighs in on Kohli vs Babar Debate
Azharuddin Weighs in on Kohli vs Babar Debate. Here is whom he rates better....
Is Babar Azam 'Greatest Test cricketer'? Tells ex-Pakistani player
Shadab does not match Babar's calibre, says Rashid Latif
Karachi Kings: A New Season, A New Beginning: PSL 8 Training Commences on T...
Karachi Kings: A New Season, A New Beginning: PSL 8 Training Commences on This Date...
Lahore Qalandars's PSL 8 Anthem Ready to be Released
Babar Azam talks after getting numerous ICC Awards
Out or Not Out? MCC Clarifies Nida Dar's controversy
What ICC record Babar Azam has made?