Nested Pictorial Structures

We propose a theoretical construct coined nested pictorial structure to represent an object by parts that are recursively nested. Three innovative ideas are proposed: First, the nested pictorial structure finds a part configuration that is allowed to be deformed in geometric arrangement, while being confined to be topologically nested. Second, we define nested features which lend themselves to better, more detailed accounting of pixel data cost and describe occlusion in a principled way. Third, we develop the concept of constrained distance transform, a variation of the generalized distance transform, to guarantee the topological nesting relations and to further enforce that parts have no overlap with each other. We show that matching an optimal nested pictorial structure of K parts on an image of N pixels takes O(NK) time using dynamic programming and constrained distance transform. In our MATLAB/C++ implementation, it takes less than 0.1 seconds to do the global optimal matching when K = 10 and N = 400× 400. We demonstrate the usefulness of nested pictorial structures in the matching of objects of nested patterns, objects in occlusion, and objects that live in a context.