A new algorithm named dynamic graph merging (DGM) for automatic image segmentation is explored. Firstly a novel variational model for multi-section cut is introduced by decomposing the traditional cut into two parts, the harmonic cut and the elastic energy of the boundary. The new energy is called the continuous combined cut. Secondly a new algorithm that removes those edges with higher energy and synchronously merges their starting and ending vertices in an ordered manner is proposed. The continual merging process would iteratively contract the graph, merge those homogeneous vertices into bigger and bigger super-pixels, and fuse the remainder edges into longer and longer boundaries. So we call this algorithm dynamic graph merging. Merging criterions based on the continuous combined cut model are also discussed, which will be used to determine whether a given edge should collapse. Since the merging condition should be highly related to the image content, we present different predicates for structure images and texture images respectively. This algorithm whose efficiency is showed by experiments has a linear time/space complexity, and can efficiently segment gray/color and 2D/3D images.
Time-space complexity and the opening hours of commerce: a study of four European cities
