Abstract. Scale variation commonly arises in images/videos, which cannot be naturally dealt with by optical flow. Invariant feature matching, on the contrary, provides sparse matching and could fail for regions without conspicuous structures. We aim to establish dense correspondence between frames containing objects in different scales and contribute a new framework taking pixel-wise scales into consideration in optical flow estimation. We propose an effective numerical scheme, which iteratively optimizes discrete scale variables and continuous flow ones. This scheme notably expands the practicality of optical flow in natural scenes containing various types of object motion.

The Schwarz alternating algorithm, which is based on natural boundary element method, is constructed for solving the exterior anisotropic problem in the three-dimension domain. The anisotropic problem is transformed into harmonic problem by using the coordinate transformation. Correspondingly, the algorithm is also changed. Continually, we analysis the convergence and the error estimate of the algorithm. Meanwhile, we give the contraction factor for the convergence. Finally, some numerical examples are computed to show the efficiency of this algorithm.

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