The importance of wild video based image set recognition is becoming monotonically increasing. 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. 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.
In image set classification, the covariance matrix, linear subspace and Gaussian distribution are three commonly used Riemannian manifold-valued descriptors for image set description. For covariance matrix, its advantages are the simplicity and flexibility to capture the variations within the set @cite_1 @cite_50 @cite_24 , and for linear subspace, its preponderance stem both from the lower computational cost and from the ability to accommodate the effects of various intra-set variations @cite_37 @cite_19 . In comparison, the strength of Gaussian distribution is that it can describe the set data variations by estimating their first-order statistics and second order statistics simultaneously @cite_44 @cite_3 . The increasing attention and promotion of these three descriptors based image set classification problems manifests in three main factors, which are presented as follows.
@cite_37 @cite_1 @cite_3 @cite_24 @cite_19 @cite_44 @cite_50
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We propose a novel discriminative learning approach to image set classification by modeling the image set with its natural second-order statistic, i.e. covariance matrix. Since nonsingular covariance matrices, a.k.a. symmetric positive definite (SPD) matrices, lie on a Riemannian manifold, classical learning algorithms cannot be directly utilized to classify points on the manifold. By exploring an efficient metric for the SPD matrices, i.e., Log-Euclidean Distance (LED), we derive a kernel function that explicitly maps the covariance matrix from the Riemannian manifold to a Euclidean space. With this explicit mapping, any learning method devoted to vector space can be exploited in either its linear or kernel formulation. Linear Discriminant Analysis (LDA) and Partial Least Squares (PLS) are considered in this paper for their feasibility for our specific problem. We further investigate the conventional linear subspace based set modeling technique and cast it in a unified framework with our covariance matrix based modeling. The proposed method is evaluated on two tasks: face recognition and object categorization. Extensive experimental results show not only the superiority of our method over state-of-the-art ones in both accuracy and efficiency, but also its stability to two real challenges: noisy set data and varying set size. We describe a new region descriptor and apply it to two problems, object detection and texture classification. The covariance of d-features, e.g., the three-dimensional color vector, the norm of first and second derivatives of intensity with respect to x and y, etc., characterizes a region of interest. We describe a fast method for computation of covariances based on integral images. The idea presented here is more general than the image sums or histograms, which were already published before, and with a series of integral images the covariances are obtained by a few arithmetic operations. Covariance matrices do not lie on Euclidean space, therefore we use a distance metric involving generalized eigenvalues which also follows from the Lie group structure of positive definite matrices. Feature matching is a simple nearest neighbor search under the distance metric and performed extremely rapidly using the integral images. The performance of the covariance features is superior to other methods, as it is shown, and large rotations and illumination changes are also absorbed by the covariance matrix. We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data are typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing pixel intensities with gradient orientations and the l2 norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Within this framework, which we coin Image Gradient Orientations (IGO) subspace learning, we first formulate and study the properties of Principal Component Analysis of image gradient orientations (IGO-PCA). We then show its connection to previously proposed robust PCA techniques both theoretically and experimentally. Finally, we derive a number of other popular subspace learning techniques, namely, Linear Discriminant Analysis (LDA), Locally Linear Embedding (LLE), and Laplacian Eigenmaps (LE). Experimental results show that our algorithms significantly outperform popular methods such as Gabor features and Local Binary Patterns and achieve state-of-the-art performance for difficult problems such as illumination and occlusion-robust face recognition. In addition to this, the proposed IGO-methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding l2 norm intensity-based counterparts. Matlab code for the methods presented in this paper can be found at http: ibug.doc.ic.ac.uk resources. Describing the color and textural information of a person image is one of the most crucial aspects of person re-identification. In this paper, we present a novel descriptor based on a hierarchical distribution of pixel features. A hierarchical covariance descriptor has been successfully applied for image classification. However, the mean information of pixel features, which is absent in covariance, tends to be major discriminative information of person images. To solve this problem, we describe a local region in an image via hierarchical Gaussian distribution in which both means and covariances are included in their parameters. More specifically, we model the region as a set of multiple Gaussian distributions in which each Gaussian represents the appearance of a local patch. The characteristics of the set of Gaussians are again described by another Gaussian distribution. In both steps, unlike the hierarchical covariance descriptor, the proposed descriptor can model both the mean and the covariance information of pixel features properly. The results of experiments conducted on five databases indicate that the proposed descriptor exhibits re-markably high performance which outperforms the state-of-the-art descriptors for person re-identification.