Large deformable splines, crest lines and matching

Abstract

The author presents new deformable spline surfaces for segmentation of 3-D medical images. He explores parametric surfaces with two different topologies, planar and cylindrical, that permit segmentation of fine anatomical structures. The surface deformation process is seen as a sequence of least squares approximations of dense data. When the deformation process stops, a smooth differentiable surface results where principle curvatures and directions are measured. An original algorithm is described that extracts lines of extremal curvature on the surface. These lines can be matched from different views with an algorithm. Experimental evidence is presented with real medical images that illustrate these points. The spherical topology for spline surfaces is outlined. Ostrogradsky's formula is used to compute the exact volume bounded by such a surface.