Mutual information in coupled multi-shape model for medical image segmentation

This paper presents extensions which improve the performance of the shape-based deformable active contour model presented earlier in [IEEE Conf. Comput. Vision Pattern Recog. 1 (2001) 463] for medical image segmentation. In contrast to that previous work, the segmentation framework that we present in this paper allows multiple shapes to be segmented simultaneously in a seamless fashion. To achieve this, multiple signed distance functions are employed as the implicit representations of the multiple shape classes within the image. A parametric model for this new representation is derived by applying principal component analysis to the collection of these multiple signed distance functions. By deriving a parametric model in this manner, we obtain a coupling between the multiple shapes within the image and hence effectively capture the co-variations among the different shapes. The parameters of the multi-shape model are then calculated to minimize a single mutual information-based cost criterion for image segmentation. The use of a single cost criterion further enhances the coupling between the multiple shapes as the deformation of any given shape depends, at all times, upon every other shape, regardless of their proximity. We found that this resulting algorithm is able to effectively utilize the co-dependencies among the different shapes to aid in the segmentation process. It is able to capture a wide range of shape variability despite being a parametric shape-model. And finally, the algorithm is robust to large amounts of additive noise. We demonstrate the utility of this segmentation framework by applying it to a medical application: the segmentation of the prostate gland, the rectum, and the internal obturator muscles for MR-guided prostate brachytherapy.