The problem of distinguishing shapes from a compound contour, which is formed by overlapping more than one distinct object, is considered. The algorithm exploits the fact that planar shapes can be completely described by contour segments, and that they can be decomposed at their maximum concavity into simpler objects. To reduce spurious decomposition, the decomposed segments are merged hypotheses. The algorithm calculates the linking possibility by weighting the angular differentiation which measures against k-curvature consistency. The techniques were implemented and applied to other partial shape matching problems for clustering purposes.