Shape interpolating on closed curves space with stretching channels

Shapes are the outline of objects, which are expressed by closed curves. Since we usually extract the shape from the binary image, the shapes are a kind of grid-based data in engineering practice. In this paper, we firstly propose a discrete curve model for the grid-based data. Based on this model, the curves are represented by their direction functions in discrete form. Furthermore, we propose stretching and bending indications to describe the structure of curves. Geometrically, all the closed curves reside on the closed curves space (CCS), which is defined by the stretching indication. In addition, we also construct the stretching channels using the stretching indication. The process of shape interpolating is the shortest path on the CCS, which is achieved by two procedures: 1) to find a straight line between two curves; 2) to project the straight line onto CCS depending on the channels. Several comparison experiments demonstrate the advantages of our method in accuracy and efficiency.