2-D shape boundary segmentation is required as a fundamental and important stage in the recognition of partially occluded objects. We introduce here a new segmentation method capable of extracting a controlled number of segments along a smooth boundary curve. This new approach is invariant to similarity transformation, and partial occlusion has only marginal influence on the segmentation of the visible part. The basic concept is to transform the curve into another one which intersects itself. Points of intersection of the new curve are re-transformed to the original curve and serve as endpoints of segments. Properties of the transform are discussed, and conditions for existence of intersection points are given. Simulation results of gray level images are presented, and advantages of our method over conventional approaches relying on singular points of the curvature are discussed.< >