Nonparametric Shape Priors for Active Contour-based Image Segmentation
Junmo Kim, Müjdat Çetin, Alan S. Willsky
Signal Processing, vol. 87, no. 12, pp. 3021-3044, December 2007.
When segmenting images of low quality or with missing data, statistical prior information about the shapes of the objects to be segmented can signiﬁcantly aid the segmentation process. However, deﬁning probability densities in the space of shapes is an open and challenging problem. In this paper, we propose a nonparametric shape prior model for image segmentation problems. In particular, given example training shapes, we estimate the underlying shape distribution by extending a Parzen density estimator to the space of shapes. Such density estimates are expressed in terms of distances between shapes, and we consider the L2 distance between signed distance functions for shape density estimation, in addition to a distance measure based on the template metric. In particular, we consider the case in which the space of shapes is interpreted as a manifold embedded in a Hilbert space. We then incorporate the learned shape prior distribution into a maximum a posteriori (MAP) estimation framework for segmentation. This results in an optimization problem, which we solve using active contours. We demonstrate the effectiveness of the resulting algorithm in segmenting images that involve low-quality data and occlusions. The proposed framework is especially powerful in handling "multimodal" shape densities.