Hierarchical Motion Detection

This thesis presents algorithms for the efficient computation of image motions using hierarchical multiresolution methods operating on image data pyramids in the processing cone architecture. Three topics are addressed: (1) fast construction of image pyramids; (2) hierarchical motion detection algorithms: correlation-based and gradient-based; and (3) multilevel relaxation algorithms. Pyramid building is the first step in hierarchical motion detection. A family of discrete Gaussian low pass filters for building low pass pyramids is presented that provide good anti-aliasing characteristics, efficient computation, and a good hierarchical Gaussian approximation. Frequency space analysis, using Fourier Transform theory, is used to compare alternative filters. Hierarchical correlation overcomes two disadvantages of correlation matching: large search areas which require expensive searches, and repeating features which cause incorrect matches. Coarse-to-fine control provides speed and efficiency when search spaces are large, and accuracy when repeating details can be confused. Hierarchical gradient-based algorithms extend single level gradient-based algorithms to the computation of large disparities. They use a coarse-to-fine method in which approximate disparities are refined at each level by computing relatively small updates. This allows the gradient-based method's assumption of local linearity to apply in spite of the large total disparities. Experiments show the failure of single level methods (for large disparities) and the success of hierarchical methods. The two hierarchical algorithms are shown to have comparable accuracy. Comparison of the computational costs, both arithmetic and data transfer, show that the gradient-based algorithm are, in general, less costly. Multilevel relaxation algorithms for the computation of optic flow are developed and experiments show the expected increased convergence rate over single level relaxation, although some experiments present a problem of divergence at coarse levels. A local mode analysis of the relaxation equations shows that convergence is at least as fast as simple smoothing, and that, with strong gradients, convergence is accelerated towards the constraint line. The local mode analysis does not account for coarse level divergence. Divergence is then shown to be due to spatial variation in the image data. Fixed up/down cycling schemes are used to overcome the divergence problem.