An Information-Based Measure for Grouping Quality

Grouping is an essential process of computer vision. However, measurement of grouping results is not straightforward and is often heuristic. We propose here a method for measuring grouping quality which is based on the following observation: the grouping result provides some information about the true, unknown grouping and reduces its uncertainty. This uncertainty is evaluated by the number of queries required to specify the true grouping. An automatic procedure which generates queries about a given hypothesized grouping, and answers them using the ground truth, is used. The queries are homogeneity queries which specify some region in the image and ask whether it all belongs to the same group/object. The process terminates once the queries su ce to specify the ground truth. The number of queries is returned as a measure of hypothesis non-informativeness. Following a probabilistic characterization and considering the given grouping result to be a random variable gives a precise meaning to the uncertainty of the true grouping, using common information theory terms such as surprise and entropy. The uncertainty based measure does not rely on arbitrary preferences, and, as our experiments show, is also consistent with human judgment more than the common set di erence method. The utility of the proposed method is demonstrated by its usage as a bene t function in the optimization of a grouping algorithm.