Introducing a new metric for automatic true color images granulometry

Mathematical morphology (MM) is a powerful tool for automatic extraction of grain-sized data from digital images. In many cases, color information can be quite useful for the enhancement of the results obtained. Nevertheless, the definition of color MM, as simple extension of gray level MM, does not work appropriately for granulometry applications. The problem is that fake colors arise in the results obtained by applying morphological granulometry separately for each color component in the recombination stage. In order to solve this problem it is necessary to define an ordering in an appropriate color space. This work proposes a new metric defined in the HSV color space. We named this chromaticity constant. The validity of this is shown by the experimental results obtained by the application of the metric to synthetic and real images.