Recognition of shapes in images is an important problem in computer vision with application in various medical problems, including robotic surgery and cell analysis. The similarity measures for such purpose must be robust to various transformations and modest occlusions. Transformations, such as scaling and translation can be handled easily by techniques through data representations or similarity measures. Rotation invariance is an inherently more difficult problem and can be handled through data representation, but at the expense of poor discrimination. Approaches which provide excellent discrimination require a complexity of O(n3) for each shape comparison. In this paper, we present a framework that provides a speedup over the slow but accurate approaches. The algorithm is inspired by the iterative deepening framework in artificial intelligence, by examining the data at increasingly fine levels of approximation until it is either considered irrelevant or submits to the full calculations. Although we examine the data several times at different levels of abstractions, because the time required for the last iteration dwarfs all others, this apparent redundancy is inconsequential. We will show that our method provides at least a 3-4 orders of magnitude in speedup without generating any false dismissals.