Visual perception refers to the ability of understanding the visual information that is provided by the environment. Such a mechanism integrates several human abilities and was studied by many researchers with different scientific origins including philosophy, physiology, biology, neurobiology, mathematics and engineering. In particular in the recent years an effort to understand, formalize and finally reproduce mechanical visual perception systems able to see and understand the environment using computational theories was made by mathematicians, statisticians and engineers. Such a task connects visual tasks with optimization processes and the answer to the visual perception task corresponds to the lowest potential of a task-driven objective function. In this edited volume we present the most prominent mathematical models that are considered in computational vision. To this end, tasks of increasing complexity are considered and we present the state-of-the-art methods to cope with such tasks. The volume consists of six thematic areas that provide answers to the most dominant questions of computational vision:

Image reconstruction,

Segmentation and object extraction,

Shape modeling and registration,

Motion analysis and tracking,

3D from images, geometry and reconstruction

Applications in medical image analysis

Résumé
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.

Contenu
Image Reconstruction.- Diffusion Filters and Wavelets: What Can They Learn from Each Other?.- Total Variation Image Restoration: Overview and Recent Developments.- PDE-Based Image and Surface Inpainting.- Boundary Exraction, Segmentation and Grouping.- Levelings: Theory and Practice.- Graph Cuts in Vision and Graphics: Theories and Applications.- Minimal Paths and Fast Marching Methods for Image Analysis.- Integrating Shape and Texture in DeformabIe Models: from Hybrid Methods to Metamorphs.- Variational Segmentation with Shape Priors.- Curve Propagation, Level Set Methods and Grouping.- On a Stochastic Model of Geometric Snakes.- Shape Modeling & Registration.- Invariant Processing and Occlusion Resistant Recognition of Planar Shapes.- Planar Shape Analysis and Its Applications in Image-Based Inferences.- Diffeomorphic Point Matching.- Uncertainty-Driven, Point-Based Image Registration.- Motion Analysis, Optical Flow & Tracking.- Optical Flow Estimation.- From Bayes to PDEs in Image Warping.- Image Alignment and Stitching.- Visual Tracking: A Short Research Roadmap.- Shape Gradient for Image and Video Segmentation.- Model-Based Human Motion Capture.- Modeling Dynamic Scenes: An Overview of Dynamic Textures.- 3D from Images, Projective Geometry & Stereo Reconstruction.- Differential Geometry from the Frenet Point of View: Boundary Detection, Stereo, Texture and Color.- Shape From Shading.- 3D from Image Sequences: Calibration, Motion and Shape Recovery.- Multi-view Reconstruction of Static and Dynamic Scenes.- Graph Cut Algorithms for Binocular Stereo with Occlusions.- Modelling Non-Rigid Dynamic Scenes from Multi-View Image Sequences.- Applications: Medical Image Analysis.- Interactive Graph-Based Segmentation Methods in Cardiovascular Imaging.- 3D Active Shape and Appearance Models in Cardiac Image Analysis.- Characterization of Diffusion Anisotropy in DWI.- Segmentation of Diffusion Tensor Images.- Variational Approaches to the Estimation, Regularizatinn and Segmentation of Diffusion Tensor Images.- An Introduction to Statistical Methods of Medical Image Registration.