We introduce a fast, multiscale algorithm for image segmentation. Our algorithm uses modern numeric techniques to nd an approximate solution to normalized cut measures in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into segments. The algorithm detects the segments by applying a process of recursive coarsening in which the same minimization problem is represented with fewer and fewer variables producing an irregular pyramid. During this coarsening process we may compute additional internal statistics of the emerging segments and use these statistics to facilitate the segmentation process. Once the pyramid is completed it is scanned from the top down to associate pixels close to the boundaries of segments with the appropriate segment. The algorithm is inspired by algebraic multigrid (AMG) solvers of minimization problems of heat or electric networks. We demonstrate the algorithm by applying it to real images.

Image segmentation is very essential and critical to image processing and pattern recognition. This survey provides a summary of color image segmentation techniques available now. Basically, color segmentation approaches are based on monochrome segmentation approaches operating in di erent color spaces. Therefore, we rst discuss the major segmentation approaches for segmenting monochrome images: histogram thresholding, characteristic feature clustering, edge detection, region-based methods, fuzzy techniques, neural networks, etc. � then review some major color representation methods and their advantages/disadvantages� nally summarize the color image segmentation techniques using di erent color representations. The usage of color models for image segmentation is also discussed. Some novel approaches such as fuzzy method and physics based method are investigated as well.