Interactive color image segmentation with linear programming

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 x 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 ma parts per thousand(a) 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 x 10 to 30 x 30 pixels in hours time, our algorithm can process larger color image of, say, 100 x 100 to 500 x 500 image in much shorter time.