Shape reconstruction from apparent contours : theory and algorithms / Giovanni Bellettini...[et al.].

Includes bibliographical references and index.

1.A Variational Model on Labelled Graphs with Cusps and Crossings.-
2.Stable Maps and Morse Descriptions of an Apparent Contour.- 3.Apparent Contours of Embedded Surfaces.-
4.Solving the Completion Problem.-
5.Topological Reconstruction of a Three-dimensional Scene.- 6.Completeness of Reidemeister-type Moves on Labelled Apparent Contours.-
7.Invariants of an Apparent Contour.-
8.Elimination of Cusps.-
9.The Program "Visible".-
10.The Program "Appcontour": User's Guide.-
11.Variational Analysis of the Model on Labelled Graphs.

This book investigates one of the central problems of computer vision: the℗ℓ topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the℗ℓ algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.