Color Constancy Using a Dichromatic Reflection Model

8 Color Constancy Using a Dichromatic Reflection Model 

Assuming narrow-band camera sensors that only respond to wavelength X, with i e r, g, b, we obtain 

When we now compute chromaticities, the three-dimensional data points are projected onto the plane r + g + b = 1. The linear combination results in a two-dimensional line in chromaticity space. Let Cm be the chromaticity of the matte color and let cs be the chromaticity of the specular color. Then, the dichromatic line on the plane r + g + b = 1 

Alternatively, we can also compute the covariance matrix for the pixel colors of the region in XYZ color space and then determine the eigenvector that corresponds to the largest eigenvalue. Let cj with j e 1. n] be the pixel colors of an image region that contains n pixels. Let xyy = [x, y]T be the xy-coordinates of the pixel colors cj in XYZ color space. Then the (2 x 2) covariance matrix C is given by 

The illuminant is located at the position where all the lines Cj intersect. 

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Color constancy using a dichromatic reflection model. 

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