Hanxi Li

Real-time visual tracking using compressive sensing

The ℓ1 tracker obtains robustness by seeking a sparse representation of the tracking object via ℓ1 norm minimization. However, the high computational complexity involved in the ℓ1 tracker may hamper its applications in real-time processing scenarios. Here we propose Real-time Com-pressive Sensing Tracking (RTCST) by exploiting the signal recovery power of Compressive Sensing (CS). Dimensionality reduction and a customized Orthogonal Matching Pursuit (OMP) algorithm are adopted to accelerate the CS tracking. As a result, our algorithm achieves a realtime speed that is up to 5,000 times faster than that of the ℓ1 tracker. Meanwhile, RTCST still produces competitive (sometimes even superior) tracking accuracy compared to the ℓ1 tracker. Furthermore, for a stationary camera, a refined tracker is designed by integrating a CS-based background model (CSBM) into tracking. This CSBM-equipped tracker, termed RTCST-B, outperforms most state-of-the-art trackers in terms of both accuracy and robustness. Finally, our experimental results on various video sequences, which are verified by a new metric — Tracking Success Probability (TSP), demonstrate the excellence of the proposed algorithms.

On the Dual Formulation of Boosting Algorithms

We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of ℓ1-norm-regularized AdaBoost, LogitBoost, and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems of these boosting algorithms, we show that the success of boosting algorithms can be understood in terms of maintaining a better margin distribution by maximizing margins and at the same time controlling the margin variance. We also theoretically prove that approximately, ℓ1-norm-regularized AdaBoost maximizes the average margin, instead of the minimum margin. The duality formulation also enables us to develop column-generation-based optimization algorithms, which are totally corrective. We show that they exhibit almost identical classification results to that of standard stagewise additive boosting algorithms but with much faster convergence rates. Therefore, fewer weak classifiers are needed to build the ensemble using our proposed optimization technique.

Boosting Through Optimization of Margin Distributions

Boosting has been of great interest recently in the machine learning community because of the impressive performance for classification and regression problems. The success of boosting algorithms may be interpreted in terms of the margin theory. Recently, it has been shown that generalization error of classifiers can be obtained by explicitly taking the margin distribution of the training data into account. Most of the current boosting algorithms in practice usually optimize a convex loss function and do not make use of the margin distribution. In this brief, we design a new boosting algorithm, termed margin-distribution boosting (MDBoost), which directly maximizes the average margin and minimizes the margin variance at the same time. This way the margin distribution is optimized. A totally corrective optimization algorithm based on column generation is proposed to implement MDBoost. Experiments on various data sets show that MDBoost outperforms AdaBoost and LPBoost in most cases.

Robust Discrete Spectral Hashing for Large-Scale Image Semantic Indexing

In big data era, the ever-increasing image data has posed significant challenge on modern image retrieval. It is of great importance to index images with semantic keywords efficiently and effectively, especially confronted with fast-evolving property of the web. Learning-based hashing has shown its power in handling large-scale high-dimensional applications, such as image retrieval. Existing solutions normally separate the process of learning binary codes and hash functions into two independent stages to bypass challenge of the discrete constraints on binary codes. In this work, we propose a novel unsupervised hashing approach, namely robust discrete hashing (RDSH), to facilitate large-scale semantic indexing of image data. Specifically, RDSH simultaneously learns discrete binary codes as well as robust hash functions within a unified model. In order to suppress the influence of unreliable binary codes and learn robust hash functions, we also integrate a flexible `2;p loss with nonlinear kernel embedding to adapt to different noise levels. Finally, we devise an alternating algorithm to efficiently optimize RDSH model. Given a test image, we first conduct r-nearest-neighbor search based on Hamming distance of binary codes, and then propagate semantic keywords of neighbors to the test image. Extensive experiments have been conducted on various real-world image datasets to show its superiority to the state-of-the-arts in large-scale semantic indexing.

Rapid face recognition using hashing

We propose a face recognition approach based on hashing. The approach yields comparable recognition rates with the random ℓ1 approach [18], which is considered the state-of-the-art. But our method is much faster: it is up to 150 times faster than [18] on the YaleB dataset. We show that with hashing, the sparse representation can be recovered with a high probability because hashing preserves the restrictive isometry property. Moreover, we present a theoretical analysis on the recognition rate of the proposed hashing approach. Experiments show a very competitive recognition rate and significant speedup compared with the state-of-the-art.

LACBoost and FisherBoost: optimally building cascade classifiers

Object detection is one of the key tasks in computer vision. The cascade framework of Viola and Jones has become the de facto standard. A classifier in each node of the cascade is required to achieve extremely high detection rates, instead of low overall classification error. Although there are a few reported methods addressing this requirement in the context of object detection, there is no a principled feature selection method that explicitly takes into account this asymmetric node learning objective. We provide such a boosting algorithm in this work. It is inspired by the linear asymmetric classifier (LAC) of [1] in that our boosting algorithm optimizes a similar cost function. The new totallycorrective boosting algorithm is implemented by the column generation technique in convex optimization. Experimental results on face detection suggest that our proposed boosting algorithms can improve the state-of the art methods in detection performance.

Fast Kernel Sparse Representation

Two efficient algorithms are proposed to seek the sparse representation on high-dimensional Hilbert space. By proving that all the calculations in Orthogonal Match Pursuit (OMP) are essentially inner-product combinations, we modify the OMP algorithm to apply the kernel-trick. The proposed Kernel OMP (KOMP) is much faster than the existing methods, and illustrates higher accuracy in some scenarios. Furthermore, inspired by the success of group-sparsity, we enforce a rigid group-sparsity constraint on KOMP which leads to a noniterative variation. The constrained cousin of KOMP, dubbed as Single-Step KOMP (S-KOMP), merely takes one step to achieve the sparse coefficients. A remarkable improvement (up to 2,750 times) in efficiency is reported for S-KOMP, with only a negligible loss of accuracy.

Robust regression based face recognition with fast outlier removal

In this paper, we propose a new robust face recognition method through pixel selection. The method is based on the subspace assumption that a face can be represented by a linear combination in terms of the samples from the same subject. In order to obtain a reliable representation, only a subset of pixels with respect to smallest residuals are taken into the estimation. Outlying pixels which deviate from the linear model of the majority are removed using a robust estimation technique — least trimmed squares regression (LTS). By this method, the representation residual with each class is computed from only the clean data, which gives a more discriminant classification rule. The proposed algorithm provides a novel way to tackle the crucial occlusion problem in face recognition. Evaluation of the proposed algorithm is conducted on several public databases for the cases of both artificial and nature occlusions. The promising results show its efficacy.

Polygonal Approximation Using Integer Particle Swarm Optimization

Polygonal approximation is an effective yet challenging digital curve representation for image analysis, pattern recognition and computer vision. This paper proposes a novel approach, integer particle swarm optimization (iPSO), for polygonal approximation. When compared to the traditional binary version of particle swarm optimization (bPSO), the new iPSO directly uses an integer vector to represent the candidate solution and provides a more efficient and convenient means for solution processing. The velocity and position updating mechanisms in iPSO not only have clear physical meaning, but also guarantee the optimality of the solutions. The method is suitable for polygonal approximation which could otherwise be an intractable optimization problem. The proposed method has been tested on commonly used synthesized shapes and lake contours extracted from the maps of four famous lakes in the world. The experimental results show that the proposed iPSO has better solution quality and computational efficiency than the bPSO-based methods and better solution quality than the other state-of-the-art methods.

Fully corrective boosting with arbitrary loss and regularization

We propose a general framework for analyzing and developing fully corrective boosting-based classifiers. The framework accepts any convex objective function, and allows any convex (for example, ℓp-norm, p ≥ 1) regularization term. By placing the wide variety of existing fully corrective boosting-based classifiers on a common footing, and considering the primal and dual problems together, the framework allows a direct comparison between apparently disparate methods. By solving the primal rather than the dual the framework is capable of generating efficient fully-corrective boosting algorithms without recourse to sophisticated convex optimization processes. We show that a range of additional boosting-based algorithms can be incorporated into the framework despite not being fully corrective. Finally, we provide an empirical analysis of the performance of a variety of the most significant boosting-based classifiers on a few machine learning benchmark datasets.