Color and Grassmann-Cayley coordinates of shape

Alexander P. Petrov

doi:10.1117/12.44368

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1 June 1991 Color and Grassmann-Cayley coordinates of shape

Alexander P. Petrov

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Proceedings Volume 1453, Human Vision, Visual Processing, and Digital Display II; (1991) https://doi.org/10.1117/12.44368
Event: Electronic Imaging '91, 1991, San Jose, CA, United States

Abstract

A new concept of surface color is developed and the variety of all perceived colors is proved to be a 9-D set of 3 X 3 matrices corresponding to different surface colors. We consider the Grassmann manifold Q of orbits Q equals {B (DOT) h + c; detBdoes not equal 0} where c is an arbitrary vector of colorimetric space, B is a 3 X 3 matrix, and h(x,y) is a color image of a Lambertian surface assumed to be a linear vector-function of the normal vectors. Different orbits Q(n) correspond to different shapes but they are invariant under color and illuminant transformation. Coordinates of an orbit Q in Q can be computed as 3 X 3 (2 X 2, sometimes) determinants the elements of which are values of some linear functionals (receptive fields) of h(x,y). Based on the approach, a shape-from-shading algorithm was developed and successfully tested on the three-color images of various real objects (an egg, cylinders and cones made of paper, etc.).

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Alexander P. Petrov "Color and Grassmann-Cayley coordinates of shape", Proc. SPIE 1453, Human Vision, Visual Processing, and Digital Display II, (1 June 1991); https://doi.org/10.1117/12.44368

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