Allen Y. Yang

Robust Face Recognition via Sparse Representation

We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

Unsupervised segmentation of natural images via lossy data compression

In this paper, we cast natural-image segmentation as a problem of clustering texture features as multivariate mixed data. We model the distribution of the texture features using a mixture of Gaussian distributions. Unlike most existing clustering methods, we allow the mixture components to be degenerate or nearly-degenerate. We contend that this assumption is particularly important for mid-level image segmentation, where degeneracy is typically introduced by using a common feature representation for different textures in an image. We show that such a mixture distribution can be effectively segmented by a simple agglomerative clustering algorithm derived from a lossy data compression approach. Using either 2D texture filter banks or simple fixed-size windows to obtain texture features, the algorithm effectively segments an image by minimizing the overall coding length of the feature vectors. We conduct comprehensive experiments to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for image segmentation. The algorithm compares favorably against other well-known image-segmentation methods on the Berkeley image database.

Fast ℓ 1 -minimization algorithms and an application in robust face recognition: A review

We provide a comprehensive review of five representative ℓ1-minimization methods, i.e., gradient projection, homotopy, iterative shrinkage-thresholding, proximal gradient, and augmented Lagrange multiplier. The repository is intended to fill in a gap in the existing literature to systematically benchmark the performance of these algorithms using a consistent experimental setting. The experiment will be focused on the application of face recognition, where a sparse representation framework has recently been developed to recover human identities from facial images that may be affected by illumination change, occlusion, and facial disguise. The paper also provides useful guidelines to practitioners working in similar fields.

CITRIC: A low-bandwidth wireless camera network platform

In this paper, we propose and demonstrate a novel wireless camera network system, called CITRIC. The core component of this system is a new hardware platform that integrates a camera, a frequency-scalable (up to 624 MHz) CPU, 16MB FLASH, and 64MB RAM onto a single device. The device then connects with a standard sensor network mote to form a camera mote. The design enables in-network processing of images to reduce communication requirements, which has traditionally been high in existing camera networks with centralized processing. We also propose a back-end client/server architecture to provide a user interface to the system and support further centralized processing for higher-level applications. Our camera mote enables a wider variety of distributed pattern recognition applications than traditional platforms because it provides more computing power and tighter integration of physical components while still consuming relatively little power. Furthermore, the mote easily integrates with existing low-bandwidth sensor networks because it can communicate over the IEEE 802.15.4 protocol with other sensor network platforms. We demonstrate our system on three applications: image compression, target tracking, and camera localization.

Fast

l 1-minimization refers to finding the minimum l1-norm solution to an underdetermined linear system \mbib=A\mbix. Under certain conditions as described in compressive sensing theory, the minimum l1-norm solution is also the sparsest solution. In this paper, we study the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as augmented Lagrangian methods. We conduct extensive experiments to validate and compare its performance against several popular l1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing, and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

\ell_{1}

Recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high-dimensional data that have very complicated structures. From both geometric and statistical points of view, such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model. In this paper we propose to use subspace arrangements—a union of multiple subspaces—for modeling mixed data: each subspace in the arrangement is used to model just a homogeneous subset of the data. Thus, multiple subspaces together can capture the heterogeneous structures within the data set. In this paper, we give a comprehensive introduction to a new approach for the estimation of subspace arrangements. This is known as generalized principal component analysis (GPCA). In particular, we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust, even when the given data are corrupted by noise or contaminated with outliers. This new method in many ways improves and generalizes extant methods for modeling or clustering mixed data. There have been successful applications of this new method to many real-world problems in computer vision, image processing, and system identification. In this paper, we will examine several of those representative applications. This paper is intended to be expository in nature. However, in order that this may serve as a more complete reference for both theoreticians and practitioners, we take the liberty of filling in several gaps between the theory and the practice in the existing literature.

-Minimization Algorithms for Robust Face Recognition

We propose a distributed recognition framework to classify continuous human actions using a low-bandwidth wearable motion sensor network, called distributed sparsity classifier (DSC). The algorithm classifies human actions using a set of training motion sequences as prior examples. It is also capable of rejecting outlying actions that are not in the training categories. The classification is operated in a distributed fashion on individual sensor nodes and a base station computer. We model the distribution of multiple action classes as a mixture subspace model, one subspace for each action class. Given a new test sample, we seek the sparsest linear representation of the sample w.r.t. all training examples. We show that the dominant coefficients in the representation only correspond to the action class of the test sample, and hence its membership is encoded in the sparse representation. Fast linear solvers are provided to compute such representation via e 1-minimization. To validate the accuracy of the framework, a public wearable action recognition database is constructed, called wearable action recognition database (WARD). The database is comprised of 20 human subjects in 13 action categories. Using up to five motion sensors in the WARD database, DSC achieves state-of-the-art performance. We further show that the recognition precision only decreases gracefully using smaller subsets of active sensors. It validates the robustness of the distributed recognition framework on an unreliable wireless network. It also demonstrates the ability of DSC to conserve sensor energy for communication while preserve accurate global classification. (This work was partially supported by ARO MURI W911NF-06-1-0076, NSF TRUST Center, and the startup funding from the University of Texas and Texas Instruments.)

Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment.

Distributed recognition of human actions using wearable motion sensor networks

We present a novel algorithm for segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region boundary can be effectively coded by an adaptive chain code. The optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image, and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes as multi-scale texture features. The optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image. We test our algorithm on the publicly available Berkeley Segmentation Dataset. It achieves state-of-the-art segmentation results compared to other existing methods.

Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming

We present a novel algorithm for unsupervised segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region boundary can be effectively coded by an adaptive chain code. The optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image, and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes. The optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image. Our algorithm achieves state-of-the-art results on the Berkeley Segmentation Dataset compared to other popular methods.