Summary: We consider the problem of finding the best match for a given query shape among candidate shapes stored in a shape base. This is central to a wide range of applications, such as, digital libraries, digital film databases, environmental sciences, and satellite image repositories. We present an efficient matching algorithm built around a novel similarity criterion and based on shape normalization about the shape’s diameter, which reduces the effects of noise or limited accuracy during the shape extraction procedure. Our matching algorithm works by gradually “fattening” the query shape until the best match is discovered. The algorithm exhibits poly-logarithmic time behavior assuming uniform distribution of the shape vertices in the locus of their normalized positions.