Towards a New Approach for Modeling Volume Datasets Based on Orthogonal Polytopes in Four-Dimensional Color Space

This work is devoted to describe some results for a new approach intended to represent volume datasets in a concise way. The main idea is to specify voxelizations as orthogonal polytopes whose fourth dimension corresponds to color. Then, the 4D representation is expressed via the Extreme Vertices Model in the n-Dimensional Space (nD-EVM). There will be presented some examples that show how the proposed methodology leads to a representation whose storing requirements are lesser than those demanded by the original datasets. Moreover, it will be described the way the properties and algorithms behind the nD-EVM can be applied in order to interrogate the 4D-EVM associated to a dataset with the purpose of obtaining, in efficient way and working directly and only with the EVM, useful geometrical and topological information. Also, there will be described EVM-based algorithms for morphological erosion and dilation and the way they can be useful in aspects such as the removal of "Salt and Pepper" noise under the context of our 4D representation.