You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Over four decades, the majority addresses the problem of optical flow estimation using variational methods. With the advance of machine learning, some recent works have attempted to address the problem using convolutional neural network (CNN) and have showed promising results. FlowNet2, the state-of-the-art CNN, requires over 160M parameters to achieve accurate flow estimation. Our LiteFlowNet2 outperforms FlowNet2 on Sintel and KITTI benchmarks, while being 25.3 times smaller in the footprint and 3.1 times faster in the running speed. LiteFlowNet2 which is built on the foundation laid by conventional methods has marked a milestone to achieve the corresponding roles as data fidelity and regularization in variational methods. We present an effective flow inference approach at each pyramid level through a novel lightweight cascaded network. It provides high flow estimation accuracy through early correction with seamless incorporation of descriptor matching. A novel flow regularization layer is used to ameliorate the issue of outliers and vague flow boundaries through a novel feature-driven local convolution. Our network also owns an effective structure for pyramidal feature extraction and embraces feature warping rather than image warping as practiced in FlowNet2. Comparing to our earlier work, LiteFlowNet2 improves the optical flow accuracy on Sintel clean pass by 24 , Sintel final pass by 8.9 , KITTI 2012 by 16.8 , and KITTI 2015 by 17.5 . Our network protocol and trained models will be made publicly available on this https URL .

Cited Abstract(s):
[1]: A framework for learning parameterized models of optical flow from image sequences is presented. A class of motions is represented by a set of orthogonal basis flow fields that are computed from a training set using principal component analysis. Many complex image motions can be represented by a linear combination of a small number of these basis flows. The learned motion models may be used for optical flow estimation and for model-based recognition. For optical flow estimation we describe a robust, multi-resolution scheme for directly computing the parameters of the learned flow models from image derivatives. As examples we consider learning motion discontinuities, non-rigid motion of human mouths, and articulated human motion.

[2]: We address the elusive goal of estimating optical flow both accurately and efficiently by adopting a sparse-to-dense approach. Given a set of sparse matches, we regress to dense optical flow using a learned set of full-frame basis flow fields. We learn the principal components of natural flow fields using flow computed from four Hollywood movies. Optical flow fields are then compactly approximated as a weighted sum of the basis flow fields. Our new PCA-Flow algorithm robustly estimates these weights from sparse feature matches. The method runs in under 200ms frame on the MPI-Sintel dataset using a single CPU and is more accurate and significantly faster than popular methods such as LDOF and Classic+NL. For some applications, however, the results are too smooth. Consequently, we develop a novel sparse layered flow method in which each layer is represented by PCA-Flow. Unlike existing layered methods, estimation is fast because it uses only sparse matches. We combine information from different layers into a dense flow field using an image-aware MRF. The resulting PCA-Layers method runs in 3.2s frame, is significantly more accurate than PCA-Flow, and achieves state-of-the-art performance in occluded regions on MPI-Sintel.

[3]: Motivated by recent progress in natural image statistics, we use newly available datasets with ground truth optical flow to learn the local statistics of optical flow and compare the learned models to prior models assumed by computer vision researchers. We find that a Gaussian mixture model (GMM) with 64 components provides a significantly better model for local flow statistics when compared to commonly used models. We investigate the source of the GMM's success and show it is related to an explicit representation of flow boundaries. We also learn a model that jointly models the local intensity pattern and the local optical flow. In accordance with the assumptions often made in computer vision, the model learns that flow boundaries are more likely at intensity boundaries. However, when evaluated on a large dataset, this dependency is very weak and the benefit of conditioning flow estimation on the local intensity pattern is marginal.

[4]: We develop a method for learning the spatial statistics of optical flow fields from a novel training database. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from handheld and car-mounted video sequences. A detailed analysis of optical flow statistics in natural scenes is presented and machine learning methods are developed to learn a Markov random field model of optical flow. The prior probability of a flow field is formulated as a field-of-experts model that captures the higher order spatial statistics in overlapping patches and is trained using contrastive divergence. This new optical flow prior is compared with previous robust priors and is incorporated into a recent, accurate algorithm for dense optical flow computation. Experiments with natural and synthetic sequences illustrate how the learned optical flow prior quantitatively improves flow accuracy and how it captures the rich spatial structure found in natural scene motion.

[5]: Assumptions of brightness constancy and spatial smoothness underlie most optical flow estimation methods. In contrast to standard heuristic formulations, we learn a statistical model of both brightness constancy error and the spatial properties of optical flow using image sequences with associated ground truth flow fields. The result is a complete probabilistic model of optical flow. Specifically, the ground truth enables us to model how the assumption of brightness constancy is violated in naturalistic sequences, resulting in a probabilistic model of "brightness inconstancy". We also generalize previous high-order constancy assumptions, such as gradient constancy, by modeling the constancy of responses to various linear filters in a high-order random field framework. These filters are free variables that can be learned from training data. Additionally we study the spatial structure of the optical flow and how motion boundaries are related to image intensity boundaries. Spatial smoothness is modeled using a Steerable Random Field, where spatial derivatives of the optical flow are steered by the image brightness structure. These models provide a statistical motivation for previous methods and enable the learning of all parameters from training data. All proposed models are quantitatively compared on the Middlebury flow dataset.

[6]: 

[7]: We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov random field (MRF) models by learning potential functions over extended pixel neighborhoods. Field potentials are modeled using a Products-of-Experts framework that exploits nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field of Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with and even outperform specialized techniques.

[8]: 

[9]: A novel optical flow estimation process based on a spatio-temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced. Previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill-posed even without introducing any additional parameters: Neighborhood based methods of the Lucas---Kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods. Modern variational methods represent the optic flow directly via the flow field components at each pixel. The benefit of over-parametrization becomes evident in the smoothness term, which instead of directly penalizing for changes in the optic flow, accumulates a cost of deviating from the assumed optic flow model. Our proposed method is very general and the classical variational optical flow techniques are special cases of it, when used in conjunction with constant basis functions. Experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far.
Black al propose to represent complex image motion as a linear combination of the learned basis vectors [1] . Roth al formulates the prior probability of flow field as Field-of-Experts model [7] that captures higher order spatial statistics [4] . Sun al study the probabilistic model of brightness inconstancy in a high-order random field framework [5] . Nir al represent image motion using the over-parameterization model [4]7 . Rosenbaum al model the local statistics of optical flow using Gaussian mixtures [3] . Given a set of sparse matches, Wulff al propose to regress them to a dense flow field using a set of basis flow fields (PCA-Flow) [2] . It can be shown that the parameterized model [1] [8] [6] can be efficiently implemented in a CNN.