Fisher Information and the Combination of RGB Channels

We introduce a method to combine the color channels of an image to a scalar valued image. Linear combinations of the RGB channels are constructed using the Fisher-Trace-Information (FTI), defined as the trace of the Fisher information matrix of the Weibull distribution, as a cost function. The FTI characterizes the local geometry of the Weibull manifold independent of the parametrization of the distribution. We show that minimizing the FTI leads to contrast enhanced images, suitable for segmentation processes. The Riemann structure of the manifold of Weibull distributions is used to design optimization methods for finding optimal weight RGB vectors. Using a threshold procedure we find good solutions even for images with limited content variation. Experiments show how the method adapts to images with widely varying visual content. Using these image dependent de-colorizations one can obtain substantially improved segmentation results compared to a mapping with pre-defined coefficients.