Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: thetopological 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...