Dong Xu

Mesh editing with poisson-based gradient field manipulation

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.

Graph embedding: a general framework for dimensionality reduction

In the last decades, a large family of algorithms - supervised or unsupervised; stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA.

Discriminant analysis with tensor representation

In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a discriminant tensor criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode cluster-based discriminant analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm discriminant analysis with tensor representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes; 2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem; and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases.

Human Gait Recognition With Matrix Representation

Human gait is an important biometric feature. It can be perceived from a great distance and has recently attracted greater attention in video-surveillance-related applications, such as closed-circuit television. We explore gait recognition based on a matrix representation in this paper. First, binary silhouettes over one gait cycle are averaged. As a result, each gait video sequence, containing a number of gait cycles, is represented by a series of gray-level averaged images. Then, a matrix-based unsupervised algorithm, namely coupled subspace analysis (CSA), is employed as a preprocessing step to remove noise and retain the most representative information. Finally, a supervised algorithm, namely discriminant analysis with tensor representation, is applied to further improve classification ability. This matrix-based scheme demonstrates a much better gait recognition performance than state-of-the-art algorithms on the standard USF HumanID Gait database

Concurrent subspaces analysis

A representative subspace is significant for image analysis, while the corresponding techniques often suffer from the curse of dimensionality dilemma. In this paper, we propose a new algorithm, called concurrent subspaces analysis (CSA), to derive representative subspaces by encoding image objects as 2/sup nd/ or even higher order tensors. In CSA, an original higher dimensional tensor is transformed into a lower dimensional one using multiple concurrent subspaces that characterize the most representative information of different dimensions, respectively. Moreover, an efficient procedure is provided to learn these subspaces in an iterative manner. As analyzed in this paper, each sub-step of CSA takes the column vectors of the matrices, which are acquired from the k-mode unfolding of the tensors, as the new objects to be analyzed, thus the curse of dimensionality dilemma can be effectively avoided. The extensive experiments on the 3/sup rd/ order tensor data, simulated video sequences and Gabor filtered digital number image database show that CSA outperforms principal component analysis in terms of both reconstruction and classification capability.

Cast shadow detection in video segmentation

In video segmentation, an intrinsic problem is that the moving cast shadows are always misclassified as part of the moving objects. This paper presents a novel moving cast shadow detection algorithm. The experiments demonstrate shadow region can be removed quite well and thus good video segmentation results can be obtained.

Insignificant shadow detection for video segmentation

To prevent moving cast shadows from being misunderstood as part of moving objects in change detection based video segmentation, this paper proposes a novel approach to the cast shadow detection based on the edge and region information in multiple frames. First, an initial change detection mask containing moving objects and cast shadows is obtained. Then a Canny edge map is generated. After that, the shadow region is detected and removed through multiframe integration, edge matching, and region growing. Finally, a post processing procedure is used to eliminate noise and tune the boundaries of the objects. Our approach can be used for video segmentation in indoor environment. The experimental results demonstrate its good performance.

Rank-one Projections with Adaptive Margins for Face Recognition

In supervised dimensionality reduction, tensor representations of images have recently been employed to enhance classification of high-dimensional data with small training sets. To handle tensor data, this approach has been formulated with tight restrictions on projection directions that, along with convergence issues and the assumption of Gaussian distributed class data, limits its face recognition performance. To overcome these problems, we propose a method of rank-one projections with adaptive margins (RPAM) that gives a provably convergent solution for tensor data over a more general class of projections, while accounting for margins between samples of different classes. In contrast to previous margin based works which determine margin sample pairs within the original high dimensional space, RPAM instead aims to maximize the margins defined in the expected lower dimensional feature subspace by progressive margin refinement after each rank-one projection. In addition to handling tensor data, vector-based variants of RPAM are presented for linear mappings and for nonlinear mappings using kernel tricks. Comprehensive experimental results demonstrate that RPAM brings significant improvement in face recognition over previous subspace learning techniques.

Coupled kernel-based subspace learning

It was prescriptive that an image matrix was transformed into a vector before the kernel-based subspace learning. In this paper, we take the kernel discriminant analysis (KDA) algorithm as an example to perform kernel analysis on 2D image matrices directly. First, each image matrix is decomposed as the product of two orthogonal matrices and a diagonal one by using singular value decomposition; then an image matrix is expanded to be of higher or even infinite dimensions by applying the kernel trick on the column vectors of the two orthogonal matrices; finally, two coupled discriminative kernel subspaces are iteratively learned for dimensionality reduction by optimizing the Fisher criterion measured by Frobenius norm. The derived algorithm, called coupled kernel discriminant analysis (CKDA), effectively utilizes the underlying spatial structure of objects and the discriminating information is encoded in two coupled kernel subspaces respectively. The experiments on real face databases compared with KDA and Fisherface validate the effectiveness of CKDA.

Indoor shadow detection for video segmentation

To prevent moving cast shadows from being misunderstood as part of moving objects in change detection based video segmentation, this paper proposes a novel approach to cast shadow detection based on the edge and region information in multiple frames. First, an initial change detection mask containing moving objects and cast shadows is obtained. Then, a Canny edge map is generated. After that, the shadow region is detected and removed through multi-frame integration, edge matching and region growing. Finally, a post-processing procedure is used to eliminate noise and tune the boundaries of the objects. Our approach can be used for removing moving cast shadows in indoor environments for better video segmentation. The experimental results demonstrate the good performance of our algorithm.