Geometric segmentation of 3D structures

Segmentation in volumetric images deals with separating ‘objects’ from their ‘background’ in a given 3D data. Usually, one starts with ‘edge detectors’ that give binary clues on the locations of the objects boundaries. Classical edge detectors that can be adopted from 2D are the Marr–Hildreth, and Haralick or Canny edge detectors. Next, usually one integrates these clues into meaningful contours or surfaces that indicate the boundaries of the objects. We use our recent variational explanation for the Marr– Hildreth and the Haralick–Canny like edge detectors to extend these classical operators. We combine these operators with a minimal deviation measure that can be tuned to the problem at hand. Finally, an improved ‘geometric active surface model’ is defined.