A Metric and Multiscale Color Segmentation Using the Color Monogenic Signal

In this paper; we use the formalism of Clifford algebras to extend the so-called Monogenic Signal to color images. This extension consists in a. function with values in the Clifford algebra R-5,R-0 that encodes color as well as geometric structure information. Using geometric calculus, such a mathematical object can be used to extend classical concepts of signal processing (filtering, Fourier Transform...) to color images in a consistent manner. Regarding this paper; a local color phase is introduced, which generalizes the one for grayscale image. As an example of application, we provide a new method for color segmentation. Based on our please definition and the multiscale aspect of the Color Monogenic Signal, we provide a metric approach using differential geometry which reveals relevant on the Berkeley Image Dataset.