Polynomial-time solutions to image segmentation
- Osaka Electro-Communication Univ., Neyagawa (Japan)
- Notre Dame, South Bend, IN (United States)
- Kobe Univ. of Commerce (Japan)
Separating an object in an image from its background is a central problem (called segmentation) in pattern recognition and computer vision. In this paper, we study the complexity of the segmentation problem, assuming that the object forms a connected region in an intensity image. We show that the optimization problem of separating a connected region in an n-pixel grid is NP-hard under the interclass variance, a criterion that is used in discriminant analysis. More importantly, we consider the basic case in which the object is separated by two x-monotone curves (i.e., the object itself is x-monotone), and present polynomial-time algorithms for computing exact and approximate optimal segmentation. Our main algorithm for exact optimal segmentation by two x-monotone curves runs in O(n{sup 2}) time; this algorithm is based on several techniques such as a parametric optimization formulation, a hand-probing algorithm for the convex hull of an unknown point set, and dynamic programming using fast matrix searching. Our efficient approximation scheme obtains an {epsilon}-approximate solution in O({epsilon}{sup -1} n log L) time, where {epsilon} is any fixed constant with 1 > {epsilon} > 0, and L is the total sum of the absolute values of brightness levels of the image.
- OSTI ID:
- 416791
- Report Number(s):
- CONF-960121--
- Country of Publication:
- United States
- Language:
- English
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