Color Morphological Image Segmentation on a New Opponent Color Space Based on the Notion of Critical Functions

In the present paper color image segmentation, based on the notion of critical functions, is investigated. The notion of critical functions is derived from the well-known waterfall transformation. In the one-dimensional case the critical functions and the waterfall transformation provide similar results. However, in the two-dimensional case, the critical functions give better results for segmenting images than the waterfall transformation, since they take into account the fusion of regional minima (or maxima) to transform the image, providing a good control of the regions merging process. Moreover, contrary to the waterfall transformation which is non-parametric, critical functions allow the introduction of image segmentation criteria to compute an optimal partition. To carry out our study, a color space based on the opponent colors is proposed that we call YO₁O₂ model. The main reason to propose a new color space is that despite the numerous perceptually color spaces (HSV,HSL, HSI, among others) proposed in the literature, they have several drawbacks for color image processing. The performance in image segmentation of both proposals, the color model and critical functions, is illustrated with several examples. Also, some interesting properties of the color model YO₁O₂ and the critical functions are shown.