RESUMEN

We introduce a nove implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as posible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potencial that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial defferential equation and use its solution for segmentation. We show that the zero level seto of this solution contains the constraining curves as well as a seto f paths joining them. We present a fase implementation that has been successfully applied to 3D medicla and synthetic images.

We give a necessary and sufficient condition for an -dimensional Riemannian manifold to be isometrically immersed in or in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in or , obtained by rotating the shape operator