Quantitative evaluation and comparison of image segmentation algorithms is now feasible owing to the recent availability of collections of hand-labeled images. However, little attention has been paid to the design of measures to compare one segmentation result to one or more manual segmentations of the same image. Existing measures in statistics and computer vision literature suffer either from intolerance to labeling refinement, making them unsuitable for image segmentation, or from the existence of degenerate cases, making the process of training algorithms using the measures to be prone to failure. This paper surveys previous work on measures of similarity and illustrates scenarios where they are applicable for performance evaluation in computer vision. For the image segmentation problem, we propose a measure that addresses the above concerns and has desirable properties such as accommodation of labeling errors at segment boundaries, region sensitive refinement, and compensation for differences in segment ambiguity between images.