Dynamics Based Robust Motion Segmentation

In this paper we consider the problem of segmenting multiple rigid motions using multi-frame point correspondence data. The main idea of the method is to group points according to the complexity of the model required to explain their relative motion. Intuitively, this formalizes the idea that points on the same rigid share more modes of motion (for instance a common translation or rotation) than points on different objects, leading to less complex models. By exploiting results from systems theory, the problem of estimating the complexity of the underlying model is reduced to simply computing the rank of a matrix constructed from the correspondence data. This leads to a simple segmentation algorithm, computationally no more expensive than a sequence of SVDs. Since the proposed method exploits both spatial and temporal constraints, is less sensitive to the effect of noise or outliers than approaches that rely solely on factorizations of the measurements matrix. In addition, the method can also naturally handle "degenerate cases", e.g. cases where the objects partially share motion modes. These results are illustrated using several examples involving both degenerate and non-degenerate cases.