Beyond Covariance: Feature Representation with Nonlinear Kernel Matrices

Wang, Lei; Zhang, Jianjia; Zhou, Luping; Tang, Chang; Li, Wanqing

doi:10.1109/iccv.2015.519

Cited by 85 publications

(118 citation statements)

References 24 publications

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“…Representations based directly on raw joint positions are widely used due to the simple acquisition from sensors. Although normalization procedures can make human representations partially invariant to view and scale variations, more [210] Moving Pose BoW Lowlv Dict Bloom et al [211] Dynamic Features Conc Lowlv Hand Vemulapalli et al [212] Lie Group Manifold Conc Manif Hand Zhang and Parker [213] BIPOD Stat Body Hand Lv and Nevatia [214] HMM/Adaboost Conc Lowlv Hand Herda et al [215] Quaternions Conc Body Hand Negin et al [216] RDF Kinematic Features Conc Lowlv Unsup Masood et al [217] Logistic Regression Conc Lowlv Hand Meshry et al [218] Angle & Moving Pose BoW Lowlv Unsup Tao and Vidal [219] Moving Poselets BoW Body Dict Eweiwi et al [220] Discriminative Action Features Conc Lowlv Unsup Wang et al [221] Ker-RP Stat Lowlv Hand Salakhutdinov et al [222] HD Models Conc Lowlv Deep sophisticated construction techniques (e.g., deep learning) are typically needed to develop robust human representations. Representations without involving temporal information are suitable to address problems such as pose and gesture recognition.…”

Section: Discussionmentioning

confidence: 99%

“…An advantage of this statistics-based encoding approach is that the size of the final feature vector is independent of the number of frames. Moreover, Wang et al [221] proposed an open framework by using the kernel matrix over feature dimensions as a generic representation and elevated the covariance representation to the unlimited opportunities.…”

Section: Statistics-based Encodingmentioning

confidence: 99%

“…The representations with open-source implementations include Ker-RP [221], lie group manifold [212], orientation matrix [126], temporal relational features [154], node feature map [119]. We provide the web link to these open-source packages in the reference [229,230,231,232,233,234].…”

Section: Performance Analysis Of the Current State Of The Artmentioning

confidence: 99%

See 2 more Smart Citations

Space-time representation of people based on 3D skeletal data: A review

Han

Reily

Hoff

et al. 2017

Computer Vision and Image Understanding

273

192

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Spatiotemporal human representation based on 3D visual perception data is a rapidly growing research area. Representations can be broadly categorized into two groups, depending on whether they use RGB-D information or 3D skeleton data. Recently, skeletonbased human representations have been intensively studied and kept attracting an increasing attention, due to their robustness to variations of viewpoint, human body scale and motion speed as well as the realtime, online performance. This paper presents a comprehensive survey of existing space-time representations of people based on 3D skeletal data, and provides an informative categorization and analysis of these methods from the perspectives, including information modality, representation encoding, structure and transition, and feature engineering. We also provide a brief overview of skeleton acquisition devices and construction methods, enlist a number of benchmark datasets with skeleton data, and discuss potential future research directions.

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Section: Discussionmentioning

confidence: 99%

Section: Statistics-based Encodingmentioning

confidence: 99%

See 1 more Smart Citation

Space-time representation of people based on 3D skeletal data: A review

Han

Reily

Hoff

et al. 2017

Computer Vision and Image Understanding

273

192

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show abstract

“…Wang et al [30] proposed an open framework 2 to use the kernel matrix over feature dimensions as a generic representation. This work uses a non-linear kernel matrix as the representation, but the kernel functions are defined in the Euclidean space and the resulting representation describes similarities between pixels at different locations, as the traditional CovDs [30]. Our work proposes to capture the similarities between sub-image sets that contain more useful information.…”

Section: Comparison With Other Improved Versions Of Traditional Covdsmentioning

confidence: 99%

“…For the comparative experiments with existing descriptors [4,20,30], we first resize all images to 24 × 24 and then use the intensity values to generate their corresponding representations. For our proposed framework, the sub-image sets are obtained by 6 × 6 sliding window with spatial step of 2 pixels for the CG, ETH-80 and MDSD datasets, and spatial step of 3 pixels for the Virus dataset.…”

Section: A Comparison With Existing Descriptorsmentioning

confidence: 99%

More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework Based Kernel Matrix Representation

Chen

Ren

et al. 2019

2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW)

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We consider a family of structural descriptors for visual data, namely covariance descriptors (CovDs) that lie on a non-linear symmetric positive definite (SPD) manifold, a special type of Riemannian manifolds. We propose an improved version of CovDs for image set coding by extending the traditional CovDs from Euclidean space to the SPD manifold. Specifically, the manifold of SPD matrices is a complete inner product space with the operations of logarithmic multiplication and scalar logarithmic multiplication defined in the Log-Euclidean framework. In this framework, we characterise covariance structure in terms of the arc-cosine kernel which satisfies Mercer's condition and propose the operation of mean centralization on SPD matrices. Furthermore, we combine arc-cosine kernels of different orders using mixing parameters learnt by kernel alignment in a supervised manner. Our proposed framework provides a lower-dimensional and more discriminative data representation for the task of image set classification. The experimental results demonstrate its superior performance, measured in terms of recognition accuracy, as compared with the state-of-the-art methods.

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DeepKSPD: Learning Kernel-Matrix-Based SPD Representation For Fine-Grained Image Recognition

Engin

Wang

Zhou

et al. 2018

Computer Vision – ECCV 2018

Self Cite

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Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via an end-to-end training process. We derive the derivatives for the mapping from a local descriptor set to the SPD representation to carry out backpropagation. Also, we exploit the Daleckiǐ-Kreǐn formula in operator theory to give a concise and unified result on differentiating SPD matrix functions, including the matrix logarithm to handle the Riemannian geometry of kernel matrix. Experiments not only show the superiority of kernel-matrixbased SPD representation with deep local descriptors, but also verify the advantage of the proposed deep network in pursuing better SPD representations for fine-grained image recognition tasks.

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Beyond Covariance: Feature Representation with Nonlinear Kernel Matrices

Cited by 85 publications

References 24 publications

Space-time representation of people based on 3D skeletal data: A review

Space-time representation of people based on 3D skeletal data: A review

More About Covariance Descriptors for Image Set Coding: Log-Euclidean Framework Based Kernel Matrix Representation

DeepKSPD: Learning Kernel-Matrix-Based SPD Representation For Fine-Grained Image Recognition

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