Abstract

A geometric approach for 3D object segmentation and representation is presented. The segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3D image. The model is based on curvature motion and the computation of surfaces with minimal areas, better known as minimal surfaces. The space where the surfaces are computed is induced from the 3D image (volumetric data) in which the objects are to be detected. The model links between classical deformable surfaces obtained via energy minimization, and intrinsic ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation. Index Terms---3D segmentation, minimal surfaces, deformable models, mean curvature motion, medical images. ------------------------ F ------------------------ 1I NTRODUCTION ONE of the basic problems in image analysis is object detection. It can be associated with the problem of boundary detection, when boundaries are defined as curves or surfaces separating homogeneous regions. "Snakes," or active contours, were proposed by Kass et al. in [16] to solve this problem, and were later extended to 3D surfaces. The classical snakes and 3D deformable surfaces approach are based on deforming an initial contour or surface towards the boundary of the object to be detected. The deformation is obtained by minimizing a functional designed so that its (local) minima is at the boundary of the object [3], [33]. The energy usually involves two terms, one that controls the smoothness of the surface and the other that attracts it to the object's boundary. The topology of the final surface is, in general, as that of the initial one, unless special procedures are used to detect possible spli...

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