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.

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 authorsdiscuss 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."

Over the last several years there has been a growing interest in developing computational methodologies for modeling and analyzing movements and behaviors of 'crowds' of people. This interest spans several scientific areas that includes Computer Vision, Computer Graphics, and Pedestrian Evacuation Dynamics. Despite the fact that these different scientific fields are trying to model the same physical entity (i.e. a crowd of people), research ideas have evolved independently. As a result each discipline has developed techniques and perspectives that are characteristically their own. The goal of this book is to provide the readers a comprehensive map towards the common goal of better analyzing and synthesizing the pedestrian movement in dense, heterogeneous crowds. The book is organized into different parts that consolidate various aspects of research towards this common goal, namely the modeling, simulation, and visual analysis of crowds. Through this book, readers will see the common ideas and vision as well as the different challenges and techniques, that will stimulate novel approaches to fully grasping "crowds."

Traditionally, scientific fields have defined boundaries, and scientists work on research problems within those boundaries. However, from time to time those boundaries get shifted or blurred to evolve new fields. For instance, the original goal of computer vision was to understand a single image of a scene, by identifying objects, their structure, and spatial arrangements. This has been referred to as image understanding. Recently, computer vision has gradually been making the transition away from understanding single images to analyz ing image sequences, or video understanding. Video understanding deals with understanding of video sequences, e. g. , recognition of gestures, activities, fa cial expressions, etc. The main shift in the classic paradigm has been from the recognition of static objects in the scene to motion-based recognition of actions and events. Video understanding has overlapping research problems with other fields, therefore blurring the fixed boundaries. Computer graphics, image processing, and video databases have obvious overlap with computer vision. The main goal of computer graphics is to gener ate and animate realistic looking images, and videos. Researchers in computer graphics are increasingly employing techniques from computer vision to gener ate the synthetic imagery. A good example of this is image-based rendering and modeling techniques, in which geometry, appearance, and lighting is de rived from real images using computer vision techniques. Here the shift is from synthesis to analysis followed by synthesis.

Motion-based recognition deals with the recognition of an object and/or its motion, based on motion in a series of images. In this approach, a sequence containing a large number of frames is used to extract motion information. The advantage is that a longer sequence leads to recognition of higher level motions, like walking or running, which consist of a complex and coordinated series of events. Unlike much previous research in motion, this approach does not require explicit reconstruction of shape from the images prior to recognition. This book provides the state-of-the-art in this rapidly developing discipline. It consists of a collection of invited chapters by leading researchers in the world covering various aspects of motion-based recognition including lipreading, gesture recognition, facial expression recognition, gait analysis, cyclic motion detection, and activity recognition. Audience: This volume will be of interest to researchers and post- graduate students whose work involves computer vision, robotics and image processing.

The recent development of intelligent surveillance systems has captured the interest of both academic research labs and industry. Automated Multi-Camera Surveillance addresses monitoring of people and vehicles, and detection of threatening objects and events in a variety of scenarios. In this book, techniques for development of an automated multi-camera surveillance system are discussed and proposed. The state-of-the-art in the automated surveillance systems is reviewed as well. Detailed explanation of sub-components of surveillance systems are provided, and enhancements to each of these components are proposed. The authors identify important challenges that such a system must address, and propose solutions. Development of a specific surveillance system called "KNIGHT" is described, along with the authors' experience using it. This book enables the reader to understand the mathematical models and algorithms underlying automated surveillance as well as the benefits and limitations of using such methods.

The deployment of surveillance systems has captured the interest of both the research and the industrial worlds in recent years. The aim of this effort is to increase security and safety in several application domains such as national security, home and bank safety, traffic monitoring and navigation, tourism, and military applications. The video surveillance systems currently in use share one feature: A human operator must monitor them at all times, thus limiting the number of cameras and the area under surveillance and increasing cost. A more advantageous system would have continuous active warning capabilities, able to alert security officials during or even before the happening of a crime.

Existing automated surveillance systems can be classified into categories according to:

• The environment they are primarily designed to observe;
• The number of sensors that the automated surveillance system can handle;
• The mobility of sensor.

The primary concern of this book is surveillance in an outdoor urban setting, where it is not possible for a single camera to observe the complete area of interest. Multiple cameras are required to observe such large environments. This book discusses and proposes techniques for development of an automated multi-camera surveillance system for outdoor environments, while identifying the important issues that a system needs to cope with in realistic surveillance scenarios. The goal of the research presented in this book is to build systems that can deal effectively with these realistic surveillance needs.

Traditionally, scientific fields have defined boundaries, and scientists work on research problems within those boundaries. However, from time to time those boundaries get shifted or blurred to evolve new fields. For instance, the original goal of computer vision was to understand a single image of a scene, by identifying objects, their structure, and spatial arrangements. This has been referred to as image understanding. Recently, computer vision has gradually been making the transition away from understanding single images to analyz ing image sequences, or video understanding. Video understanding deals with understanding of video sequences, e. g., recognition of gestures, activities, fa cial expressions, etc. The main shift in the classic paradigm has been from the recognition of static objects in the scene to motion-based recognition of actions and events. Video understanding has overlapping research problems with other fields, therefore blurring the fixed boundaries. Computer graphics, image processing, and video databases have obvious overlap with computer vision. The main goal of computer graphics is to gener ate and animate realistic looking images, and videos. Researchers in computer graphics are increasingly employing techniques from computer vision to gener ate the synthetic imagery. A good example of this is image-based rendering and modeling techniques, in which geometry, appearance, and lighting is de rived from real images using computer vision techniques. Here the shift is from synthesis to analysis followed by synthesis."

Motion-based recognition deals with the recognition of an object and/or its motion, based on motion in a series of images. In this approach, a sequence containing a large number of frames is used to extract motion information. The advantage is that a longer sequence leads to recognition of higher level motions, like walking or running, which consist of a complex and coordinated series of events. Unlike much previous research in motion, this approach does not require explicit reconstruction of shape from the images prior to recognition. This book provides the state-of-the-art in this rapidly developing discipline. It consists of a collection of invited chapters by leading researchers in the world covering various aspects of motion-based recognition including lipreading, gesture recognition, facial expression recognition, gait analysis, cyclic motion detection, and activity recognition. Audience: This volume will be of interest to researchers and post- graduate students whose work involves computer vision, robotics and image processing.