of research which is a particular case of the processing of multichannel images defined by a vector of scalar values é No natural ordering on a set of color vectors and more generally of multivariate data é several possible types of multidimensional vector ordering: ò marginal ordering, ò reduced ordering, ò partial ordering, ò conditional ordering, ò total ordering.
dilatation operations can be defined by : What is essential is to determine the two extreme values corresponding to the Ç and the Æ which are respectively higher and lower than all the other colors of the lattice
? é Consider the structuring element B as a Region Adjacency Graph G0 where each pixel of B is a node of the graph é Total ordering : path from Æ to Ç é Solution :Prune the RAG to obtain such a path é The Minimum Spanning Tree (MST) of the RAG G0 is a good approximation
to the wanted solution é Internal nodes cannot be potential Æ ot Ç é Only external nodes are potential candidates é This assumption can be used to build another graph from the leaves of the MST é The MST of this new graph can be again computed and so on until finding a two-node path é Æ : closest to a reference color
on graph decimation for determining the inf and the sup of a set of colors : better results than lexicographic ordering é The traditional morphological definition of morphological gradient has been extended and new waterfall hierarchies can be obtained é Perspectives : ò Use the cascade of MSTs to find an ordering of colors ò Compare the proposed method with lexicographic and bit-mixing on different color spaces Conclusion
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