Manifold Clustering of Shapes

Shape clustering can significantly facilitate the automatic labeling of objects present in image collections. For example, it could outline the existing groups of pathological cells in a bank of cyto-images; the groups of species on photographs collected from certain aerials; or the groups of objects observed on surveillance scenes from an office building. Here we demonstrate that a nonlinear projection algorithm such as Isomap can attract together shapes of similar objects, suggesting the existence of isometry between the shape space and a low dimensional nonlinear embedding. Whenever there is a relatively small amount of noise in the data, the projection forms compact, convex clusters that can easily be learned by a subsequent partitioning scheme. We further propose a modification of the Isomap projection based on the concept of degree-bounded minimum spanning trees. The proposed approach is demonstrated to move apart bridged clusters and to alleviate the effect of noise in the data.