Fast Region Merging Algorithms for Image Segmentation

One of the more successful approaches to image segmentation involves formulating the problem as the minimisation of a Mumford-Shah functional and then using region merging algorithms to approximate the minimiser. Recent work by Redding et al. presented such an algorithm and demonstrated the quality of the segmentations it produces. Here, we extend that work in two ways. First, we describe a variation of the algorithm which leads to the same segmentations but which is an order of magnitude faster to compute. This gain is made by introducing the concept of a locally best merge. Second, and as a natural consequence of considering locally best merges, we describe a new algorithm. While the new algorithm is no longer optimal, it is faster and has other desirable properties. In particular, in the case where the functional to be minimised takes account of region variances as well as means, the new algorithm overcomes the problem of unreliable variance estimates for small regions.