Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

Harandi, Mehrtash; Salzmann, Mathieu; Baktashmotlagh, Mahsa

doi:10.1109/iccv.2015.468

Cited by 37 publications

(13 citation statements)

References 37 publications

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“…For example, Wang et al [44] represented image sets with the more flexible Gaussian mixture models (GMM) and proposed discriminant analysis on the Riemannian manifold of Gaussian distributions for classification. Harandi et al [9] modelled the set structure with probability distribution functions (PDFs) via kernel density estimation. The models are then matched using the Csiszar f-divergences.…”

Section: Related Workmentioning

confidence: 99%

Representation learning with deep extreme learning machines for efficient image set classification

Uzair

Ghanem

Mian

2016

Neural Comput & Applic

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Efficient and accurate representation of a collection of images, that belong to the same class, is a major research challenge for practical image set classification. Existing methods either make prior assumptions about the data structure, or perform heavy computations to learn structure from the data itself. In this paper, we propose an efficient image set representation that does not make any prior assumptions about the structure of the underlying data. We learn the nonlinear structure of image sets with deep extreme learning machines that are very efficient and generalize well even on a limited number of training samples. Extensive experiments on a broad range of public datasets for image set classification show that the proposed algorithm consistently outperforms state-of-the-art image set classification methods both in terms of speed and accuracy.

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Section: Related Workmentioning

confidence: 99%

Representation learning with deep extreme learning machines for efficient image set classification

Uzair

Ghanem

Mian

2016

Neural Comput & Applic

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“…Recently, image set classification has provided a new direction to address this task. In this paper, we report the classification performance of our method on the MDSD [37], [56] dataset. This dataset is comprised of 13 different categories of dynamic scenes with each has 10 video sequences.…”

Section: E Dynamic Scene Classificationmentioning

confidence: 99%

Multiple Riemannian Manifold-Valued Descriptors Based Image Set Classification With Multi-Kernel Metric Learning

Wang

Chen

et al. 2022

IEEE Trans. Big Data

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The importance of wild video based image set recognition is becoming monotonically increasing due to the large amount of video resources obtained by diversified video collection approaches, like surveillance, drive recorders, smart phones, and internet. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a big challenge for set-based classification algorithms. In recent years, some proposed image set classification methods have made a considerable advance by modeling the original image set with covariance matrix, linear subspace, or Gaussian distribution. Moreover, the distinctive geometry spanned by them are Symmetric Positive Definite (SPD) manifold, Grassmann manifold, and Gaussian embedded Riemannian manifold, respectively. As a matter of fact, most of them just adopt a single geometric model to describe each given image set, which may lose some other useful information for classification. To tackle this problem, we propose a novel algorithm to model each image set from a multi-geometric perspective. Specifically, the covariance matrix, linear subspace, and Gaussian distribution are applied for set representation simultaneously. In order to fuse these multiple heterogeneous Riemannian manifoldvalued features, the well-equipped Riemannian kernel functions are first utilized to map them into high dimensional Hilbert spaces. Then, a multi-kernel metric learning framework is devised to embed the learned hybrid kernels into a lower dimensional common subspace for classification. We conduct experiments on four widely used datasets corresponding to four different classification tasks: video-based face recognition, set-based object categorization, video-based emotion recognition, and dynamic scene classification, to evaluate the classification performance of the proposed algorithm. Extensive experimental results justify its superiority over the state-of-the-art.

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“…In order to estimate the PDF on the manifold of SPD matrices, we can map them to the tangent space and transform them into vectors. Since KDE may produce less reliable and very sparse PDFs [22], we can learn a lowdimensional representation of these vectors through PCA. However, this solution is inconsistent with the aim of performing discriminative manifold-to-manifold dimensionality reduction for SPD matrices.…”

Section: B Affinity Matrixmentioning

confidence: 99%

“…The original-sized color images are used as the input to CNN and the dimensionality of the CNN output is reduced by PCA to 400. Following the same settings as in [22], we adopt a seventy-thirty-ratio (STR) protocol which randomly selects 7 videos for training and the remaining 3 videos for testing. We set m = 40 and λ b = 7 on this dataset.…”

Section: E Scene Classificationmentioning

confidence: 99%

Probability Distribution-Based Dimensionality Reduction on Riemannian Manifold of SPD Matrices

Ren

2020

IEEE Access

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Representing images and videos with Symmetric Positive Definite (SPD) matrices and utilizing the intrinsic Riemannian geometry of the resulting manifold has proved successful in many computer vision tasks. Since SPD matrices lie in a nonlinear space known as a Riemannian manifold, researchers have recently shown a growing interest in learning discriminative SPD matrices with appropriate Riemannian metrics. However, the computational complexity of analyzing high-dimensional SPD matrices is nonnegligible in practical applications. Inspired by the theory of nonparametric estimation, we propose a probability distribution-based approach to overcome this drawback by learning a mapping from the manifold of high-dimensional SPD matrices to a manifold of lower-dimension, which can be expressed as an optimization problem on the Grassmann manifold. Specifically, we perform the dimensionality reduction for high-dimensional SPD matrices with popular Riemannian metrics and an affinity matrix constructed using an estimated probability distribution function (PDF) to achieve maximum class separability. The evaluation of several classification tasks shows the competitiveness of the proposed approach compared with state-ofthe-art methods.

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Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

Cited by 37 publications

References 37 publications

Representation learning with deep extreme learning machines for efficient image set classification

Representation learning with deep extreme learning machines for efficient image set classification

Multiple Riemannian Manifold-Valued Descriptors Based Image Set Classification With Multi-Kernel Metric Learning

Probability Distribution-Based Dimensionality Reduction on Riemannian Manifold of SPD Matrices

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