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Shape from Lambertian Photometric Flow Fields

Wolff, Lawrence B.

A new idea for the analysis of shape from reflectance maps is introduced in this paper. It is shown that local surface orientation and curvature constraints can be obtained at points on a smooth surface by computing the instantaneous rate of change of reflected scene radiance caused by angular variations in illumination geometry. The resulting instantaneous changes in image irradiance values across an optic sensing array of pixels constitute what is termed a photometric flow field. Unlike optic flow fields which are instantaneous changes in position across an optic array of pixels caused by relative motion, there is no correspondence problem with respect to obtaining the instantaneous change in image irradiance values between successive image frames. This is because the object and camera remain static relative to one another as the illumination geometry changes. There are a number of advantages to using photometric flow fields. One advantage is that local surface orientation and curvature at a point on a smooth surface can be uniquely determined by only slightly varying the incident orientation of an illuminator within a small local neighborhood about a specific incident orientation. Robot manipulators and rotation/positioning jigs can be accurately varied within small ranges of motion. Conventional implementation of photometric stereo requires the use of three vastly different incident orientations of an illuminator requiring either much calibration and/or gross and inaccurate robot arm motions. Another advantage of using photometric flow fields is the duality that exists between determining unknown local surface orientation from a known incident illuminator orientation and determining an unknown incident illuminator orientation from a known local surface orientation. The equations for photometric flow fields allow the quantitative determination of the incident orientation of an illuminator from an object having a known calibrated surface orientation. Computer simulations will be shown depicting photometric flow fields on a Lambertian sphere. Simulations will be shown depicting how photometric flow fields quantitatively determine local surface orientation from a known incident orientation of an illuminator as well as determining incident illuminator orientation from a known local surface orientation.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-396-88
Published Here
December 21, 2011
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