In this paper, we study the reorientation of 2D shapes. We describe an algorithm that removes orientational ambiguity from arbitrarily oriented 2D shapes. The algorithm is robust to error in pixel locations as well as in the presence of occluded or added pixels. After reorientation, the resulting shape is in a normalized orientation and can then be used effectively in post-processing stages of such applications as pattern detection, recognition, and registration. The algorithm combines a new measure of shape orientation, the variable-size window orientation indicator index (/spl Delta/-OII), and the point-based reorientation algorithm (PRA) that we presented before. We test the new algorithm against an extensive database of complex 2D shapes.