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Multiple light source optical flow for translations and rotations in the image plane Takagi, Shingo Jason

Abstract

The classic optical flow constraint equation is accurate under conditions of translation and distant light sources, but becomes inaccurate under conditions where the object may rotate or deform. The inaccuracies are generally a result of the changing intensities at points under rotation or deformation. The changing intensities of these points are associated with the changing surface gradients. We investigate a novel approach to multiple light source optical flow under known reflectance properties. This novel approach is specialized for translation and for rotation around axes which are parallel to the optical axis. The assumption that the object is moving under translation, rotation, or a combination of translation androtation in the image plane allows us to introduce a physical surface area constraint. Even with this additional constraint, however, the problem still remains locally underdetermined. At each time frame, our multiple light source optical flow approach assumes that three images are acquired from the same viewpoint, but under three different illumination conditions. Photometric stereo determines many of the coefficients in our underdetermined system, which has six equations in seven unknowns at each pixel in the image. Two of the unknowns are the optical flow components. Another three of the unknowns are the total derivatives of the three intensities with respect to time. The last two are the total derivatives of the surface gradients with respect to time. A variety of local regularization methods were investigated to select optical flow estimates which best matched the known motion fields. All the experimental results for this approach were obtained from synthetic data, in which the motion fields were known.

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