RGB Filter design using the properties of the Weibull Manifold

摘要

Combining the channels of a multi-band image with the help of a pixelwise weighted sum is one of the basic operations in color and multispectral image processing. A typical example is the conversion of RGB- to intensity images. Usually the weights are given by some standard values or chosen heuristically. This does not take into account neither the statistical nature of the image source nor the intended further processing of the scalar image. In this paper we will present a framework in which we specify the statistical properties of the input data with the help of a representative collection of image patches. On the output side we specify the intended processing of the scalar image with the help of a filter kernel with zero-mean filter coefficients. Given the image patches and the filter kernel we use the Fisher information of the manifold of two-parameter Weibull distributions to introduce the trace of the Fisher information matrix as a cost function on the space of weight vectors of unit length. We will illustrate the properties of the method with the help of a database of scanned leaves and some color images from the internet. For the green leaves we find that the result of the mapping is similar to standard mappings like Matlab's RGB2Gray weights. We then change the colour of the leaf using a global shift in the HSV representation of the original image and show how the proposed mapping adapts to this color change. This is also confirmed with other natural images where the new mapping reveals much more subtle details in the processed image. In the last experiment we show that the mapping emphasizes visually salient points in the image whereas the standard mapping only emphasizes global intensity changes. The proposed approach to RGB filter design provides thus a new methodology based only on the properties of the image statistics and the intended post-processing. It adapts to color changes of the input images and, due to its foundation in the statistics of extreme-value distributions, it is suitable for detecting salient regions in an image.