Advancement in Color Image Processing using Geometric Algebra

Abstract

This paper describes an advancement in color image processing, using geometric algebra. This is achieved using a compact representation of vectors within $n$ dimensional space. Geometric Algebra (GA) is a preferred framework for signal representation and image representation. In this context the R, G, B color channels are not defined separately but as a single entity. As GA provides a rich set of operations, the signal and image processing operations becomes straightforward and the algorithms intuitive. From the experiments described in this paper, it is also possible to conclude that the convolution operation with the rotor masks within GA belong to a class of linear vector filters and can be applied to image or speech signals. The usefulness of the introduced approach has been demonstrated by analyzing and implementing two different types of edge detection schemes.

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