Using the Shape Gradient for Active Contour Segmentation: from the Continuous to the Discrete Formulation

A variational approach to image or video segmentation consists in defining an energy depending on local or global image characteristics, the minimum of which being reached for objects of interest. This study focuses on energies written as an integral on a domain of a function which can depend on this domain. The derivative of the energy with respect to the domain, the so-called shape derivative, is a function of a velocity field applied to the domain boundary. For a given, non-optimal domain, the velocity should be chosen such that the shape derivative is negative, thus indicating a way to deform the domain in order to decrease its energy. Minimizing the energy through an iterative deformation process is known as the active contour method. In the continuous framework, setting the velocity to the opposite of the gradient associated with the L2 inner product is a common practice. In this paper, it is noted that the negativity of the shape derivative is not preserved, in general, by th...

• Type: Journal
• Year: 2007
• Where: JMIV
• Authors: Eric Debreuve, Muriel Gastaud, Michel Barlaud, Gilles Aubert
• Keywords: Global Image Characteristics, JMIV 2007, So-called Shape Derivative, Velocity