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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/4925

Title: Efficient Algorithms for Optimization-based Image Segmentation
Authors: Asano, Tetsuo
Chen, Danny Z.
Katoh, Naoki
Tokuyama, Takeshi
Issue Date: 2001-04
Publisher: World Scientific Publishing
Magazine name: International Journal of Computational Geometry & Applications
Volume: 11
Number: 2
Start page: 145
End page: 166
DOI: 10.1142/S0218195901000420
Abstract: 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^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 ε-approximate solution in O(ε^<-1>n log L) time, whereεis any fixed constant with 1>ε>0, and L is the total sum of the absolute values of brightness levels of the image.
Rights: Electronic version of an article published as International Journal of Computational Geometry & Applications, 11(2), 2001, 145-166. DOI:10.1142/S0218195901000420. Copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218195901000420
URI: http://hdl.handle.net/10119/4925
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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