Markov surfaces: A probabilistic framework for user-assisted three-dimensional image segmentation

Abstract

This paper presents Markov surfaces, a probabilistic algorithm for user-assisted segmentation of elongated structures in 3D images. The 3D segmentation problem is formulated as a path-finding problem, where path probabilities are described by Markov chains. Users define points, curves, or regions on 2D image slices, and the algorithm connects these user-defined features in a way that respects the underlying elongated structure in data. Transition probabilities in the Markov model are derived from intensity matches and interslice correspondences, which are generated from a slice-to-slice registration algorithm. Bézier interpolations between paths are applied to generate smooth surfaces. Subgrid accuracy is achieved by linear interpolations of image intensities and the interslice correspondences. Experimental results on synthetic and real data demonstrate that Markov surfaces can segment regions that are defined by texture, nearby context, and motion. A parallel implementation on a streaming parallel computer architecture, a graphics processor, makes the method interactive for 3D data.