In this paper, we propose a descriptor as a shape signature and the projective refinement as a verification method for recognizing 2D curved objects with occlusions from their partial views. For an extracted curve segment, we compute a series of the geometric invariance of equally spaced five co-planar points on the curve. Thus the resulting descriptor is invariant only under rotation, translation, and scale, but sufficient similarity is preserved even under large distortions. It is more stable and robust since it does not need derivatives. We use this transformation-invariant descriptor to index a hash table. We show the efficiency of the method through experiments using seriously distorted images of 2-D curved objects with occlusions.