Separating Parts from 2D Shapes using Relatability

It´s often important to analyze shapes as made up of parts. But there are two ways to think of how parts fit together. We can characterize the remainder of a shape after apart is removed; here we want to cut the shape so what remains has the simplest possible structure. Alternatively, we can cut out the part so that the part itself takes on a simple shape. These cuts do not directly give rise to a segmentation of the shape; a point inside the shape may associate with the part, the remainder, neither, or both. We present a new model for reconstructing these cuts based on the differential geometry of smoothed local symmetries. The model takes into account relatability (which characterizes clean cuts) to determine part boundaries. Our approach complements and unifies existing work on part- based segmentation of shape, and can be used to construct interesting simplifications of shapes.