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On the Fourier Properties of Discontinuous Motion

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Abstract

Retinal image motion and optical flow as its approximation are fundamental concepts in the field of vision, perceptual and computational. However, the computation of optical flow remains a challenging problem as image motion includes discontinuities and multiple values mostly due to scene geometry, surface translucency and various photometric effects such as reflectance. In this contribution, we analyze image motion in the frequency space with respect to motion discontinuities and translucence. We derive the frequency structure of motion discontinuities due to occlusion and we demonstrate its various geometrical properties. The aperture problem is investigated and we show that the information content of an occlusion almost always disambiguates the velocity of an occluding signal suffering from the aperture problem. In addition, the theoretical framework can describe the exact frequency structure of Non-Fourier motion and bridges the gap between Non-Fourier visual phenomena and their understanding in the frequency domain.

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Authors and Affiliations

  1. GRASP Laboratory, University of Pennsylvania, Philadelphia, PA, 19104-6228, USA

    Steven S. Beauchemin

  2. The University of Western Ontario, London, Canada, N6A 5B7

    John L. Barron

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  1. Steven S. Beauchemin
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  2. John L. Barron
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Beauchemin, S.S., Barron, J.L. On the Fourier Properties of Discontinuous Motion. Journal of Mathematical Imaging and Vision 13, 155–172 (2000). https://doi.org/10.1023/A:1011220130307

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