Abstract
Image segmentation with monotonicity and smoothness constraints has found applications in several areas such as biomedical image analysis and data mining. In this paper, we study the problem of segmenting monotone and smooth objects in 2-D and 3-D images. 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 \( O\left( {\frac{{JM}} {{\log J}}} \right) \) time, where the size of the input 2-D image is I×J and M is the smoothness parameter with 1≤M ≤J. Our algorithm is based on a combination of dynamic programming and divide-and-conquer strategy, and computes 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.
The research of the first and the third authors was supported in part by the National Science Foundation under Grants CCR-9623585 and CCR-9988468 and by the 21st Century Research and Technology Fund from the State of Indiana. The work of the second author was supported in part by the National Science Foundation under Grant CCR-9820611.
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Chen, D.Z., Wang, J., Wu, X. (2001). Image Segmentation with Monotonicity and Smoothness Constraints. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_40
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DOI: https://doi.org/10.1007/3-540-45678-3_40
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