Digital image thresholding, based on topological stable-state

A new approach for image segmentation for scenes that contain distinct objects is presented. A sequence of graphs N-s(t) is defined, where N-s(t) is the number of connected objects composed of at least s pixels, for the image thresholded at t. The sequence of graphs is built in almost linear time complexity, namely at O(alpha(n, n). n), where alpha(n, n) is the inverse of the Ackermann function, and n is the number of pixels in the image. Stable states on the graph in the appropriate ''resolution'' s* correspond to threshold values that yield a segmentation similar to a human observer. The relevance of a Percolation model to the graphs N-s(t) is discussed.