This book presents a unified view of image motion analysis under the variational framework. Variational methods, rooted in physics and mechanics, but appearing in many other domains, such as statistics, control, and computer vision, address a problem from an optimization standpoint, i.e., they formulate it as the optimization of an objective function or functional. The methods of image motion analysis described in this book use the calculus of variations to minimize (or maximize) an objective functional which transcribes all of the constraints that characterize the desired motion variables. The book addresses the four core subjects of motion analysis: Motion estimation, detection, tracking, and three-dimensional interpretation. Each topic is covered in a dedicated chapter. The presentation is prefaced by an introductory chapter which discusses the purpose of motion analysis. Further, a chapter is included which gives the basic tools and formulae related to curvature, Euler Lagrange equations, unconstrained descent optimization, and level sets, that the variational image motion processing methods use repeatedly in the book.

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.

The four-volume set comprising LNCS volumes 3021/3022/3023/3024 constitutes the refereed proceedings of the 8th European Conference on Computer Vision, ECCV 2004, held in Prague, Czech Republic, in May 2004. The 190 revised papers presented were carefully reviewed and selected from a total of 555 papers submitted. The four books span the entire range of current issues in computer vision. The papers are organized in topical sections on tracking; feature-based object detection and recognition; geometry; texture; learning and recognition; information-based image processing; scale space, flow, and restoration; 2D shape detection and recognition; and 3D shape representation and reconstruction.

Abstract Biological vision is a rather fascinating domain of research. Scientists of various origins like biology, medicine, neurophysiology, engineering, math ematics, etc. aim to understand the processes leading to visual perception process and at reproducing such systems. Understanding the environment is most of the time done through visual perception which appears to be one of the most fundamental sensory abilities in humans and therefore a significant amount of research effort has been dedicated towards modelling and repro ducing human visual abilities. Mathematical methods play a central role in this endeavour. Introduction David Marr's theory v^as a pioneering step tov^ards understanding visual percep tion. In his view human vision was based on a complete surface reconstruction of the environment that was then used to address visual subtasks. This approach was proven to be insufficient by neuro-biologists and complementary ideas from statistical pattern recognition and artificial intelligence were introduced to bet ter address the visual perception problem. In this framework visual perception is represented by a set of actions and rules connecting these actions. The emerg ing concept of active vision consists of a selective visual perception paradigm that is basically equivalent to recovering from the environment the minimal piece information required to address a particular task of interest.

This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.

Image segmentation consists of dividing an image domain into disjoint regions according to a characterization of the image within or in-between the regions. Therefore, segmenting an image is to divide its domain into relevant components. The efficient solution of the key problems in image segmentation promises to enable a rich array of useful applications. The current major application areas include robotics, medical image analysis, remote sensing, scene understanding, and image database retrieval. The subject of this book is image segmentation by variational methods with a focus on formulations which use closed regular plane curves to define the segmentation regions and on a level set implementation of the corresponding active curve evolution algorithms. Each method is developed from an objective functional which embeds constraints on both the image domain partition of the segmentation and the image data within or in-between the partition regions. The necessary conditions to optimize the objective functional are then derived and solved numerically. The book covers, within the active curve and level set formalism, the basic two-region segmentation methods, multiregion extensions, region merging, image modeling, and motion based segmentation. To treat various important classes of images, modeling investigates several parametric distributions such as the Gaussian, Gamma, Weibull, and Wishart. It also investigates non-parametric models. In motion segmentation, both optical flow and the movement of real three-dimensional objects are studied.

This book constitutes the refereed proceedings of the First International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2007, emanated from the joint edition of the 4th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2007 and the 6th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2007, held in Ischia Italy, May/June 2007.