IMAGE SEGMENTATION WITH ASTEROIDALITY/TUBULARITY AND SMOOTHNESS CONSTRAINTS

Abstract

Image segmentation with specific constraints has found applications in several areas such as biomedical image analysis and data mining. In this paper, we study the problem of segmenting star-shaped and smooth objects in 2-D and tubular objects in 3-D images. Image objects of these shapes are often studied in medical applications. For the 2-D case of the problem, we present an O(IJ log J) time algorithm, improving the previously best known O(IJ2M) time algorithm by a factor of [Formula: see text] time, where the size of the input 2-D image is I × J and M is the smoothness parameter with 1 ≤ M ≤ J. Our 2-D algorithm is based on a combination of dynamic programming and divide-and-conquer strategy, and on computing an optimal path in an implicitly represented graph. We also prove that a generalized version of the 3-D case of the problem is NP-hard.