Covariance descriptors on a Gaussian manifold and their application to image set classification

Chen, Kai-Xuan; Ren, Jie-Yi; Wu, Xiao-Jun; Kittler, Josef

doi:10.1016/j.patcog.2020.107463

Cited by 25 publications

(13 citation statements)

References 15 publications

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“…III, our proposed MSNet-MS ourperforms all the other competitors on Method CG UCF-sub GDA [2] 88.68 43.67 CDL [3] 90.56 41.53 PML [49] 84.32 50.60 LEML [21] 71.15 44.67 SPDML-Stein [6] 82.62 51.40 SPDML-AIM [6] 88. 61 51.13 HERML [7] 88.94 NA MMML [4] 89.92 NA GrNet [48] 85.69 35.80 SPDNet [33] 89.03 59.93 SymNet [35] 89 three datasets. Note that in relatively large dataset, some shallow learning methods, such as MMML and HERML, is barely feasible in view of its time-consuming optimization.…”

Section: Discussionmentioning

confidence: 99%

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MSNet: A Deep Multi-scale Submanifold Network for Visual Classification

Chen¹,

Wu²,

Xu³

et al. 2022

Preprint

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The Symmetric Positive Definite (SPD) matrix has received wide attention as a tool for visual data representation in computer vision. Although there are many different attempts to develop effective deep architectures for data processing on the Riemannian manifold of SPD matrices, a very few solutions explicitly mine the local geometrical information in deep SPD feature representations.While CNNs have demonstrated the potential of hierarchical local pattern extraction even for SPD represented data, we argue that it is of utmost importance to ensure the preservation of local geometric information in the SPD networks. Accordingly, in this work we propose an SPD network designed with this objective in mind. In particular, we propose an architecture, referred to as MSNet, which fuses geometrical multi-scale information. We first analyse the convolution operator commonly used for mapping the local information in Euclidean deep networks from the perspective of a higher level of abstraction afforded by the Category Theory. Based on this analysis, we postulate a submanifold selection principle to guide the design of our MSNet. In particular, we use it to design a submanifold fusion block to take advantage of the rich local geometry encoded in the network layers. The experiments involving multiple visual tasks show that our algorithm outperforms most Riemannian SOTA competitors.

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Section: Discussionmentioning

confidence: 99%

“…It consists of 900 video sequences covering nine kinds of hand gesture. For this dataset, following the criteria in [61], we randomly select 20 and 80 clips for training and testing per class, respectively. For evaluation, we resize each frame into 20 × 20 and obtain the grey scale feature.…”

Section: B Datasets and Settingsmentioning

confidence: 99%

MSNet: A Deep Multi-scale Submanifold Network for Visual Classification

Chen¹,

Wu²,

Xu³

et al. 2022

Preprint

Self Cite

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“…Gaussian-based representation methods In statistics, Gaussian distribution is a very important term and is generally used to represent real-valued random variables. By considering two main parameters of Gaussians, the Gaussian-based representation methods [13], [15]- [22] have been shown to offer powerful representations for various tasks. Nakayama et al [15] embedded Gaussians in a flat manifold by taking an affine coordinate system and applied them to scene categorization.…”

Section: Graph Pooling Methodsmentioning

confidence: 99%

“…Lovrić et al [22] embedded Gaussians in the Riemannian symmetric space [16] with a slightly different metric on the space of multivariate Gaussians. Chen et al [13] considered the structure of the Riemannian manifold of Gaussians and generated the final representations via Riemannian local difference vectors for image set classification. Wang et al [19] proposed robust estimation of approximate infinite dimensional Gaussian based on von Neumann divergence and applied them to material recognition.…”

Section: Graph Pooling Methodsmentioning

confidence: 99%

“…Our pooling goal is to learn a vector outlining the entire node distribution, which is used for following task predictions. Specially, we formulate the graph as a multivariate Gaussian distribution, and thus the distribution space is a special type of Riemannian manifold [13] that is more informative to outline the non-Euclidean geometry information of graphs.…”

Section: Introductionmentioning

confidence: 99%

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Distribution Knowledge Embedding for Graph Pooling

Chen¹,

Song²,

Liu³

et al. 2021

Preprint

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Graph-level representation learning is the pivotal step for downstream tasks that operate on the whole graph. The most common approach to this problem heretofore is graph pooling, where node features are typically averaged or summed to obtain the graph representations. However, pooling operations like averaging or summing inevitably cause massive information missing, which may severely downgrade the final performance. In this paper, we argue what is crucial to graphlevel downstream tasks includes not only the topological structure but also the distribution from which nodes are sampled. Therefore, powered by existing Graph Neural Networks (GNN), we propose a new plug-and-play pooling module, termed as Distribution Knowledge Embedding (DKEPool), where graphs are rephrased as distributions on top of GNNs and the pooling goal is to summarize the entire distribution information instead of retaining a certain feature vector by simple predefined pooling operations. A DKEPool network de facto disassembles representation learning into two stages, structure learning and distribution learning. Structure learning follows a recursive neighborhood aggregation scheme to update node features where structure information is obtained. Distribution learning, on the other hand, omits node interconnections and focuses more on the distribution depicted by all the nodes. Extensive experiments demonstrate that the proposed DKEPool significantly and consistently outperforms the state-of-the-art methods.

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A CNN-based methodology for cow heat analysis from endoscopic images

Benhabiles

Windal

et al. 2021

Appl Intell

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Covariance descriptors on a Gaussian manifold and their application to image set classification

Cited by 25 publications

References 15 publications

MSNet: A Deep Multi-scale Submanifold Network for Visual Classification

MSNet: A Deep Multi-scale Submanifold Network for Visual Classification

Distribution Knowledge Embedding for Graph Pooling

A CNN-based methodology for cow heat analysis from endoscopic images

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