Interactive color image segmentation with linear programming |
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Authors: | Hongdong Li Chunhua Shen |
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Affiliation: | 1. Australian National University, Canberra, ACT, 0200, Australia 2. NICTA (National ICT Australia), Canberra Research Lab, Canberra, ACT, 2601, Australia
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Abstract: | Image segmentation is an important and fundamental task for image and vision understanding. This paper describes a linear programming (LP) approach for segmenting a color image into multiple regions. Compared with the recently proposed semi-definite programming (SDP)-based approach, our approach has a simpler mathematical formulation, and a far lower computational complexity. In particular, to segment an image of M × N pixels into k classes, our method requires only O((M N k) m ) complexity—a sharp contrast to the complexity of O((M N k)2n ) if the SDP method is adopted, where m and n are the polynomial complexity of the corresponding LP solver and SDP solver, respectively (in general we have m≪ n). Such a significant reduction in computation readily enables our algorithm to process color images of reasonable sizes. For example, while the existing SDP relaxation algorithm is only able to segment a toy-size image of, e.g., 10 × 10 to 30 × 30 pixels in hours time, our algorithm can process larger color image of, say, 100 × 100 to 500 × 500 image in much shorter time. |
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