Geodesic Transformations

All morphological transformations discussed so far involved combinations of one input image with specific structuring elements. The approach taken with geodesic transformations is to consider two input images. A morphological transformation is applied to the first image and it is then forced to remain either greater or lower to the second image. Authorised morphological transformations are restricted to elementary erosions and dilations. The choice of specific structuring elements is therefore eluded. In practice, geodesic transformations are iterated until stability making the choice of a size unnecessary. It is actually the combination of appropriate pairs of input images which produces new morphological primitives. These primitives are at the basis of formal definitions of many important image structures for both binary and grey scale images.