Robust Subspace Estimation Using Low-Rank Optimization

Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book, the authors discuss fundamental formulations and extensions for low-rank optimization-based subspace estimation and representation. By minimizing the rank of the matrix containing observations drawn from images, the authors demonstrate how to solve four fundamental computer vision problems, including video denosing, background subtraction, motion estimation, and activity recognition.

Provides a comprehensive summary of the state-of-the-art methods and applications of Low-Rank Optimization Reviews the latest approaches in a wide range of computer vision problems, including: Scene Reconstruction, Video Denoising, Activity Recognition, and Background Subtraction Involves a self-complete and detailed description of the methods and theories which makes it ideal for graduate students looking for a comprehensive resource in this area Includes supplementary material: sn.pub/extras

Klappentext

pRecovering the low-rank structure of a linear subspace using a small set of corrupted examples has recently been made feasible through substantial advances in the area of matrix completion and nuclear-norm minimization. Such low-rank structures appear in certain conditions heavily in computer vision, for instance, in the frames of a video, the camera motion, and a picture of a building façade. In this book, we discuss several formulations and extensions of low-rank optimization, and demonstrate how recovering the underlying basis and detecting the corresponding outliers allow us to solve fundamental computer vision problems, including video denoising, background subtraction, action detection, and complex event recognition./p

Inhalt
Introduction.- Background and Literature Review.- Seeing Through Water: Underwater Scene Reconstruction.- Simultaneous Turbulence Mitigation and Moving Object Detection.- Action Recognition by Motion Trajectory Decomposition.- Complex Event Recognition Using Constrained Rank Optimization.- Concluding Remarks.- Extended Derivations for Chapter 4.