Color ordering strategy based on Loewner order applied to the mathematical morphology

Morphological mathematics applied to color images requires a color space and an ordering method to be able to define a complete lattice. Among the drawbacks in the methods proposed in the current literature we find some that produce false colors, or are inefficient at computation time. False colors are undesirable in the process of transformation as they alter original colors of the image, turning them into noise. On the other hand, any vector sorting method must be efficient enough to meet the requirements of procedures that do not allow for lengthy response times. In this work we propose a method of order based on Loewners order, using a transformation of the colors associated with the pixels of an image in the RGB space to symmetric matrices. In order to bring about a comparison of the results obtained through the proposed method and the others, we tested on a consistent basis, measuring the computation time in the process of basic operations, such as dilation and erosion, checked the generation of no false colors, removal of noise (smoothing), brightness reduction and local contrast enhancement, all in the same computing environment. The results demonstrate the validity of the method, resulting in efficiency of time and quality results, as well as producing no false colors.