Monday, June 29th 2015
Title: Elementary Morphology for Color Images and Orientation Fields
In this talk we discuss two recent extensions of classical (elementary)morphology.First we propose an extension to morphology for color images that relies onthe existing order based morphology for matrix fields ofsymmetric 2 × 2-matrices.An RGB-image is embedded into a field of those 2 × 2-matrices by exploitingthe geometrical properties of the order cone associated with theLoewner order. To this end a modification of the HSL-color model anda relativistic addition of matrices is introduced.\\Secondly, we extend morphological techniques to process fieldsof special orthogonal matrices (SO(n)-matrices).Since the group structure of SO(2)- resp. SO(3)-fields does not lend itselfto establish useful notions of infimum and supremum, they are transformedinto scalar images resp. fields of symmetric 2 x 2 matricesutilising a matrix-valued version of the Cayley transform. \\Several examples and numerical results are presented to show the meritsand the limitations of these approaches.
Colloquium coordinators are Prof.dr. M. Aiello (e-mail :
Prof.dr. M. Biehl (e-mail:
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