Analysis of Differential and Matching Methods for Optical Flow
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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Several algorithms for optical flow are studied theoretically and experimentally. Differential and matching methods are examined these two methods have differing domains of application - differential methods are best when displacements in the image are small 2 pixels while matching methods work well for moderate displacements but do not handle sub-pixel motions. Both types of optical flow algorithm can use either local or global constraints, such as spatial smoothness. Local matching and differential techniques will be examined. Most algorithms for optical flow utilize weak assumptions on the local variation of the flow and on the variation of image brightness. Strengthening these assumptions improves the flow computation. The computational consequence of this is a need for larger spatial and temporal support. Global differential approaches can be extended to local patchwise differential methods and local differential methods using higher derivatives. Using larger support is valid when constraints on the local shape of the flow are satisfied. A simple constraint on the local shape of the optical flow, that there is slow spatial variation in the image plane, is often satisfied. Local differential methods imply the constraints for related methods using higher derivatives. Experiments show the behavior of these optical flow methods on velocity fields which do not obey the assumptions. Implementation of these methods highlights the importance of numerical differentiation.