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:
Although Faster R-CNN and its variants have shown promising performance in object detection, they only exploit simple first-order representation of object proposals for final classification and regression. Recent classification methods demonstrate that the integration of high-order statistics into deep convolutional neural networks can achieve impressive improvement, but their goal is to model whole images by discarding location information so that they cannot be directly adopted to object detection. In this paper, we make an attempt to exploit high-order statistics in object detection, aiming at generating more discriminative representations for proposals to enhance the performance of detectors. To this end, we propose a novel Multi-scale Location-aware Kernel Representation (MLKP) to capture high-order statistics of deep features in proposals. Our MLKP can be efficiently computed on a modified multi-scale feature map using a low-dimensional polynomial kernel approximation. Moreover, different from existing orderless global representations based on high-order statistics, our proposed MLKP is location retentive and sensitive so that it can be flexibly adopted to object detection. Through integrating into Faster R-CNN schema, the proposed MLKP achieves very competitive performance with state-of-the-art methods, and improves Faster R-CNN by 4.9 (mAP), 4.7 (mAP) and 5.0 (AP at IOU=[0.5:0.05:0.95]) on PASCAL VOC 2007, VOC 2012 and MS COCO benchmarks, respectively. Code is available at: https: github.com Hwang64 MLKP.

Cited Abstract(s):
[1]: Convolutional Neural Networks (CNNs) with Bilinear Pooling, initially in their full form and later using compact representations, have yielded impressive performance gains on a wide range of visual tasks, including fine-grained visual categorization, visual question answering, face recognition, and description of texture and style. The key to their success lies in the spatially invariant modeling of pairwise (2nd order) feature interactions. In this work, we propose a general pooling framework that captures higher order interactions of features in the form of kernels. We demonstrate how to approximate kernels such as Gaussian RBF up to a given order using compact explicit feature maps in a parameter-free manner. Combined with CNNs, the composition of the kernel can be learned from data in an end-to-end fashion via error back-propagation. The proposed kernel pooling scheme is evaluated in terms of both kernel approximation error and visual recognition accuracy. Experimental evaluations demonstrate state-of-the-art performance on commonly used fine-grained recognition datasets.

[2]: We propose bilinear models, a recognition architecture that consists of two feature extractors whose outputs are multiplied using outer product at each location of the image and pooled to obtain an image descriptor. This architecture can model local pairwise feature interactions in a translationally invariant manner which is particularly useful for fine-grained categorization. It also generalizes various orderless texture descriptors such as the Fisher vector, VLAD and O2P. We present experiments with bilinear models where the feature extractors are based on convolutional neural networks. The bilinear form simplifies gradient computation and allows end-to-end training of both networks using image labels only. Using networks initialized from the ImageNet dataset followed by domain specific fine-tuning we obtain 84.1 accuracy of the CUB-200-2011 dataset requiring only category labels at training time. We present experiments and visualizations that analyze the effects of fine-tuning and the choice two networks on the speed and accuracy of the models. Results show that the architecture compares favorably to the existing state of the art on a number of fine-grained datasets while being substantially simpler and easier to train. Moreover, our most accurate model is fairly efficient running at 8 frames sec on a NVIDIA Tesla K40 GPU. The source code for the complete system will be made available at http: vis-www.cs.umass.edu bcnn.

[3]: Recently, plugging trainable structural layers into deep convolutional neural networks (CNNs) as image representations has made promising progress. However, there has been little work on inserting parametric probability distributions, which can effectively model feature statistics, into deep CNNs in an end-to-end manner. This paper proposes a Global Gaussian Distribution embedding Network (G2DeNet) to take a step towards addressing this problem. The core of G2DeNet is a novel trainable layer of a global Gaussian as an image representation plugged into deep CNNs for end-to-end learning. The challenge is that the proposed layer involves Gaussian distributions whose space is not a linear space, which makes its forward and backward propagations be non-intuitive and non-trivial. To tackle this issue, we employ a Gaussian embedding strategy which respects the structures of both Riemannian manifold and smooth group of Gaussians. Based on this strategy, we construct the proposed global Gaussian embedding layer and decompose it into two sub-layers: the matrix partition sub-layer decoupling the mean vector and covariance matrix entangled in the embedding matrix, and the square-rooted, symmetric positive definite matrix sub-layer. In this way, we can derive the partial derivatives associated with the proposed structural layer and thus allow backpropagation of gradients. Experimental results on large scale region classification and fine-grained recognition tasks show that G2DeNet is superior to its counterparts, capable of achieving state-of-the-art performance.

[4]: The success of fine-grained visual categorization (FGVC) extremely relies on the modeling of appearance and interactions of various semantic parts. This makes FGVC very challenging because: (i) part annotation and detection require expert guidance and are very expensive; (ii) parts are of different sizes; and (iii) the part interactions are complex and of higher-order. To address these issues, we propose an end-to-end framework based on higherorder integration of hierarchical convolutional activations for FGVC. By treating the convolutional activations as local descriptors, hierarchical convolutional activations can serve as a representation of local parts from different scales. A polynomial kernel based predictor is proposed to capture higher-order statistics of convolutional activations for modeling part interaction. To model inter-layer part interactions, we extend polynomial predictor to integrate hierarchical activations via kernel fusion. Our work also provides a new perspective for combining convolutional activations from multiple layers. While hypercolumns simply concatenate maps from different layers, and holistically-nested network uses weighted fusion to combine side-outputs, our approach exploits higher-order intra-layer and inter-layer relations for better integration of hierarchical convolutional features. The proposed framework yields more discriminative representation and achieves competitive results on the widely used FGVC datasets.

[5]: By stacking layers of convolution and nonlinearity, convolutional networks (ConvNets) effectively learn from lowlevel to high-level features and discriminative representations. Since the end goal of large-scale recognition is to delineate complex boundaries of thousands of classes, adequate exploration of feature distributions is important for realizing full potentials of ConvNets. However, state-of-theart works concentrate only on deeper or wider architecture design, while rarely exploring feature statistics higher than first-order. We take a step towards addressing this problem. Our method consists in covariance pooling, instead of the most commonly used first-order pooling, of highlevel convolutional features. The main challenges involved are robust covariance estimation given a small sample of large-dimensional features and usage of the manifold structure of covariance matrices. To address these challenges, we present a Matrix Power Normalized Covariance (MPNCOV) method. We develop forward and backward propagation formulas regarding the nonlinear matrix functions such that MPN-COV can be trained end-to-end. In addition, we analyze both qualitatively and quantitatively its advantage over the well-known Log-Euclidean metric. On the ImageNet 2012 validation set, by combining MPN-COV we achieve over 4 , 3 and 2.5 gains for AlexNet, VGG-M and VGG-16, respectively; integration of MPN-COV into 50-layer ResNet outperforms ResNet-101 and is comparable to ResNet-152. The source code will be available on the project page: http: www.peihuali.org MPN-COV.

[6]: Deep neural network architectures have recently produced excellent results in a variety of areas in artificial intelligence and visual recognition, well surpassing traditional shallow architectures trained using hand-designed features. The power of deep networks stems both from their ability to perform local computations followed by pointwise non-linearities over increasingly larger receptive fields, and from the simplicity and scalability of the gradient-descent training procedure based on backpropagation. An open problem is the inclusion of layers that perform global, structured matrix computations like segmentation (e.g. normalized cuts) or higher-order pooling (e.g. log-tangent space metrics defined over the manifold of symmetric positive definite matrices) while preserving the validity and efficiency of an end-to-end deep training framework. In this paper we propose a sound mathematical apparatus to formally integrate global structured computation into deep computation architectures. At the heart of our methodology is the development of the theory and practice of backpropagation that generalizes to the calculus of adjoint matrix variations. We perform segmentation experiments using the BSDS and MSCOCO benchmarks and demonstrate that deep networks relying on second-order pooling and normalized cuts layers, trained end-to-end using matrix backpropagation, outperform counterparts that do not take advantage of such global layers.
Recent works have shown that the integration of high-order statistics with deep CNNs can improve classification performance [4] [1] [6] [2] [5] [3] . Thereinto, the global second-order pooling methods [6] [5] [2] are plugged into deep CNNs to represent whole images, in which the sum of outer product of convolutional features is firstly computed, then element-wise power normalization [2] , matrix logarithm normalization [6] and matrix power normalization [5] are performed, respectively. Wang al. [3] embed a trainable global Gaussian distribution into deep CNNs, which exploits first-order and second-order statistics of deep convolutional features. However, all these methods generate very high dimensional orderless representations, which can not be directly adopted to object detection. The methods in [4] [1] adopt polynomial and Gaussian RBF kernel functions to approximate high-order statistics, respectively. Such methods can efficiently generate low-dimensional high-order representations. However, different from methods that are designed for whole image classification, our MLKP is location retentive and sensitive to guarantee that it can be flexibly adopted to object detection.