Xuelong Li

General Tensor Discriminant Analysis and Gabor Features for Gait Recognition

Traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis (LDA) because of the undersample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two-dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA, compared with existing preprocessing methods such as the principal components analysis (PCA) and 2DLDA, include the following: 1) the USP is reduced in subsequent classification by, for example, LDA, 2) the discriminative information in the training tensors is preserved, and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, whereas that of 2DLDA does not. We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor-function-based image decompositions for image understanding and object recognition, we develop three different Gabor-function-based image representations: 1) GaborD is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS, and GaborSD representations are applied to the problem of recognizing people from their averaged gait images. A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS, or GaborSD image representation, then using GDTA to extract features and, finally, using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the University of South Florida (USF) HumanID Database. Experimental comparisons are made with nine state-of-the-art classification methods in gait recognition.

Geometric Mean for Subspace Selection

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fishers linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

Patch Alignment for Dimensionality Reduction

Spectral analysis-based dimensionality reduction algorithms are important and have been popularly applied in data mining and computer vision applications. To date many algorithms have been develope...Spectral analysis-based dimensionality reduction algorithms are important and have been popularly applied in data mining and computer vision applications. To date many algorithms have been developed, e.g., principal component analysis, locally linear embedding, Laplacian eigenmaps, and local tangent space alignment. All of these algorithms have been designed intuitively and pragmatically, i.e., on the basis of the experience and knowledge of experts for their own purposes. Therefore, it will be more informative to provide a systematic framework for understanding the common properties and intrinsic difference in different algorithms. In this paper, we propose such a framework, named patch alignment,rdquo which consists of two stages: part optimization and whole alignment. The framework reveals that (1) algorithms are intrinsically different in the patch optimization stage and (2) all algorithms share an almost identical whole alignment stage. As an application of this framework, we develop a new dimensionality reduction algorithm, termed discriminative locality alignment (DLA), by imposing discriminative information in the part optimization stage. DLA can (1) attack the distribution nonlinearity of measurements; (2) preserve the discriminative ability; and (3) avoid the small-sample-size problem. Thorough empirical studies demonstrate the effectiveness of DLA compared with representative dimensionality reduction algorithms.

A survey of graph edit distance

Inexact graph matching has been one of the significant research foci in the area of pattern analysis. As an important way to measure the similarity between pairwise graphs error-tolerantly, graph edit distance (GED) is the base of inexact graph matching. The research advance of GED is surveyed in order to provide a review of the existing literatures and offer some insights into the studies of GED. Since graphs may be attributed or non-attributed and the definition of costs for edit operations is various, the existing GED algorithms are categorized according to these two factors and described in detail. After these algorithms are analyzed and their limitations are identified, several promising directions for further research are proposed.

Supervised tensor learning

This paper aims to take general tensors as inputs for supervised learning. A supervised tensor learning (STL) framework is established for convex optimization based learning techniques such as support vector machines (SVM) and minimax probability machines (MPM). Within the STL framework, many conventional learning machines can be generalized to take n/sup th/-order tensors as inputs. We also study the applications of tensors to learning machine design and feature extraction by linear discriminant analysis (LDA). Our method for tensor based feature extraction is named the tenor rank-one discriminant analysis (TR1DA). These generalized algorithms have several advantages: 1) reduce the curse of dimension problem in machine learning and data mining; 2) avoid the failure to converge; and 3) achieve better separation between the different categories of samples. As an example, we generalize MPM to its STL version, which is named the tensor MPM (TMPM). TMPM learns a series of tensor projections iteratively. It is then evaluated against the original MPM. Our experiments on a binary classification problem show that TMPM significantly outperforms the original MPM.

Discriminant Locally Linear Embedding With High-Order Tensor Data

Graph-embedding along with its linearization and kernelization provides a general framework that unifies most traditional dimensionality reduction algorithms. From this framework, we propose a new manifold learning technique called discriminant locally linear embedding (DLLE), in which the local geometric properties within each class are preserved according to the locally linear embedding (LLE) criterion, and the separability between different classes is enforced by maximizing margins between point pairs on different classes. To deal with the out-of-sample problem in visual recognition with vector input, the linear version of DLLE, i.e., linearization of DLLE (DLLE/L), is directly proposed through the graph-embedding framework. Moreover, we propose its multilinear version, i.e., tensorization of DLLE, for the out-of-sample problem with high-order tensor input. Based on DLLE, a procedure for gait recognition is described. We conduct comprehensive experiments on both gait and face recognition, and observe that: 1) DLLE along its linearization and tensorization outperforms the related versions of linear discriminant analysis, and DLLE/L demonstrates greater effectiveness than the linearization of LLE; 2) algorithms based on tensor representations are generally superior to linear algorithms when dealing with intrinsically high-order data; and 3) for human gait recognition, DLLE/L generally obtains higher accuracy than state-of-the-art gait recognition algorithms on the standard University of South Florida gait database.

Gait Components and Their Application to Gender Recognition

Human gait is a promising biometrics resource. In this paper, the information about gait is obtained from the motions of the different parts of the silhouette. The human silhouette is segmented into seven components, namely head, arm, trunk, thigh, front-leg, back-leg, and feet. The leg silhouettes for the front-leg and the back-leg are considered separately because, during walking, the left leg and the right leg are in front or at the back by turns. Each of the seven components and a number of combinations of the components are then studied with regard to two useful applications: human identification (ID) recognition and gender recognition. More than 500 different experiments on human ID and gender recognition are carried out under a wide range of circumstances. The effectiveness of the seven human gait components for ID and gender recognition is analyzed.

Image Quality Assessment Based on Multiscale Geometric Analysis

Reduced-reference (RR) image quality assessment (IQA) has been recognized as an effective and efficient way to predict the visual quality of distorted images. The current standard is the wavelet-domain natural image statistics model (WNISM), which applies the Kullback-Leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion. However, WNISM fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells. In addition, wavelet transforms are optimal greedy approximations to extract singularity structures, so they fail to explicitly extract the image geometric information, e.g., lines and curves. Finally, wavelet coefficients are dense for smooth image edge contours. In this paper, to target the aforementioned problems in IQA, we develop a novel framework for IQA to mimic the human visual system (HVS) by incorporating the merits from multiscale geometric analysis (MGA), contrast sensitivity function (CSF), and the Webers law of just noticeable difference (JND). In the proposed framework, MGA is utilized to decompose images and then extract features to mimic the multichannel structure of HVS. Additionally, MGA offers a series of transforms including wavelet, curvelet, bandelet, contourlet, wavelet-based contourlet transform (WBCT), and hybrid wavelets and directional filter banks (HWD), and different transforms capture different types of image geometric information. CSF is applied to weight coefficients obtained by MGA to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in HVS. JND is finally introduced to produce a noticeable variation in sensory experience. Thorough empirical studies are carried out upon the LIVE database against subjective mean opinion score (MOS) and demonstrate that 1) the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images, 2) different transforms in MGA under the new framework perform better than the standard WNISM and some of them even perform better than the standard full-reference IQA model, i.e., the mean structural similarity index, and 3) HWD performs best among all transforms in MGA under the framework.

Direct kernel biased discriminant analysis: a new content-based image retrieval relevance feedback algorithm

In recent years, a variety of relevance feedback (RF) schemes have been developed to improve the performance of content-based image retrieval (CBIR). Given user feedback information, the key to a RF scheme is how to select a subset of image features to construct a suitable dissimilarity measure. Among various RF schemes, biased discriminant analysis (BDA) based RF is one of the most promising. It is based on the observation that all positive samples are alike, while in general each negative sample is negative in its own way. However, to use BDA, the small sample size (SSS) problem is a big challenge, as users tend to give a small number of feedback samples. To explore solutions to this issue, this paper proposes a direct kernel BDA (DKBDA), which is less sensitive to SSS. An incremental DKBDA (IDKBDA) is also developed to speed up the analysis. Experimental results are reported on a real-world image collection to demonstrate that the proposed methods outperform the traditional kernel BDA (KBDA) and the support vector machine (SVM) based RF algorithms

A local Tchebichef moments-based robust image watermarking

Protection against geometric distortions and common image processing operations with blind detection becomes a much challenging task in image watermarking. To achieve this, in this paper we propose a content-based watermarking scheme that combines the invariant feature extraction with watermark embedding by using Tchebichef moments. Harris-Laplace detector is first adopted to extract feature points, and then non-overlapped disks centered at feature points are generated. These disks are invariant to scaling and translation distortions. For each disk, orientation alignment is then performed to achieve rotation invariant. Finally, the watermark is embedded in magnitudes of Tchebichef moments of each disk via dither modulation to realize the robustness to common image processing operations and the blind detection. Thorough simulation results obtained by using the standard benchmark, Stirmark, demonstrate that the proposed method is robust against various geometric distortions as well as common image processing operations and outperforms representative image watermarking schemes.