Tensor-based Image Sequence Processing Techniques for the Study of Dynamical Processes

Quantitative analysis of dynamical processes requires a precise estimation of the optical ow eld from image sequences. Most articles evaluating the performance of optical ow techniques focus on the initial formulation of the minimization problem to solve the ill posed brightness change constraint equation. Performance di erences are attributed to slight di erences in the formulation of the minimization and the numerical solution is taken for granted. It can be shown, however, that most di erential techniques can be formulated in a generalized way and be solved by two major numerical estimation techniques: least squares and total least squares. We will conclude that the least squares technique does only vary two of three parameters of the spatiotemporal optical ow vector while the latter varies all three parameters which leads to a more precise solution. Total least squares estimation of optical ow is equivalent to a tensor representation of the spatiotemporal image structure. In addition to the optical ow, measures of certainty and type of motion, quantifying the presence of an aperture problem are directly obtained by analyzing the eigenvalues of the so called structure tensor. These measures give a uni ed perspective of common quality measures proposed by various techniques. Another crucial factor in uencing the accuracy of any di erential technique is the choice of appropriate di erential kernels. With optimized di erential lters, errors can be reduced by more than one order of magnitude.