This paper addresses the problem of segmenting an image into regions. We de¯ ne

a predicate for measuring the evidence for a boundary between two regions using a

graph-based representation of the image. We then develop an e±cient segmentation

algorithm based on this predicate, and show that although this algorithm makes greedy

decisions it produces segmentations that satisfy global properties. We apply the algorithm

to image segmentation using two di® erent kinds of local neighborhoods in

constructing the graph, and illustrate the results with both real and synthetic images.

The algorithm runs in time nearly linear in the number of graph edges and is also fast

in practice. An important characteristic of the method is its ability to preserve detail

in low-variability image regions while ignoring detail in high-variability regions.