In this paper, an efficient algorithm for recognizing and positioning occuluded objects in a two-dimensional plane is presented. Model objects and unknown input image are approximated by polygonal boundaries, which are compactly represented by shape functions of the polygons. The input image is partitioned into measningful segments whose end points are at the locations of possible occlusion - i.e. at concave vertices. Each segment is matched against known model objects by calculating a matching measure, which is defined as the minimum euclidean distance between the shape functions. An O(mm(n+m) algorithm for computing the measure is presentd, where n and m are the number of veritces for a model and an unknown object, respectively. Match results from aprtial segments are combined based on mutual compatibility, then are verified using distance transformation and translation vector to produce the final recognition. The proposed algorithm is invariant under translation and rotation of objects, which has been shown by experimental results.