The shape matching problem is concerned with fitting an input shape, represented by a set of discrete boundary data, to a defect-free reference shape. Two aspects of the problem must be considered: (1) shape modeling, and (2) matching algorithm. In this paper, two shape modeling schemes are proposed to represent the reference shape by a set of primitives, in which the object geometric configuration is encoded. The primitives uniquely define the pose and dimension of a given polygonal object. Based on these models, optimization matching procedures that use the least-squares criterion to find the best fitting between the set of scene data and the reference shape are developed. The complexity analysis and computational results show our shape matching approaches to be extremely fast.