Globally optimal surface segmentation using regional properties of segmented objects

Efficient segmentation of globally optimal surfaces in volumetric images is a central problem in many medical image analysis applications. Intra-class variance has been successfully utilized, for instance, in the Chan-Vese model especially for images without prominent edges. In this paper, we study the optimization problem of detecting a region (volume) between two coupled smooth surfaces by minimizing the intra-class variance using an efficient polynomial-time algorithm. Our algorithm is based on the shape probing technique in computational geometry and computes a sequence of minimum-cost closed sets in a derived parametric graph. The method has been validated on computer-synthetic volumetric images and in X-ray CT-scanned datasets of plexiglas tubes of known sizes. Its applicability to clinical data sets was demonstrated in human CT image data. The achieved results were highly accurate with mean signed surface positioning errors of the inner and outer walls of the tubes of +0.013 mm and 0.012 mm, respectively, given a voxel size of 0.39 times 0.39 times 0.6 mm³. Comparing with the original Chan-Vese method [8], our algorithm expressed higher robustness. With its polynomialtime efficiency, our algorithm is ready to be extended to higher-dimensional image segmentation. In addition, the developed technique is of its own interest. We expect that it can shed some light on solving other important optimization problems arising in computer vision. To the best of our knowledge, the shape probing technique is for the first time introduced into the field of computer vision.