The morphological top-hat operator generalised to multi-channel images

The morphological top-hat operator for grayscale images is part of the basic toolbox of mathematical morphology operators. We discuss two ways of generalising the top-hat operator to multi-channel images, such as colour images. The first method presented is the use of a vectorial order in the relevant vector space. The second is based on the demonstration that the top-hat operator can be rewritten in terms of increments. These increments can be replaced by any vectorial distance function, removing the requirement to first impose an order on the vectors. We present examples of the use of the suggested top-hat operators in feature detection in colour images and defect detection in texture.