Mathematical Morphology in the L*a*b* Colour Space

The use of mathematical morphology in the L*a*b* colour space is discussed. Initially, a description of the characteristics of the L*a*b* space and a comparison to the HLS space are given. This is followed by a theoretical demonstration of the use of weighting functions to impose a complete order on a vector space. Various colour weighting functions are considered, and one based on a model of an electrostatic potential is chosen for further development. A lexicographical order using this weighting function allows one to simulate a complete order by colour saturation, a notion absent from the definition of the L*a*b* space. Demonstrations of the basic morphological operators and of the top-hat operator making use of the proposed colour order are shown.