Similarity between volumetric scalar fields
Some recent research work, attempts to determine several methods of comparing scalar volumetric functions  . In these endeavours, an effective strategy was formulated for matching 3D volumetric functions based on multi-resolution dual contour trees which does not varies under affine transformation. A finest level dual contour tree had been constructed from a pre-computed contour tree of a volumetric scalar field by dividing its functional range into some segments such that the connected contour tree edges within a segment become a node in the dual tree. For each node of the dual contour tree, geometric, functional and topological attributes such as functional volume, range and Betti numbers  were computed and used to match two multi-resolution dual contour trees , which were computed by merging the adjacent functional segments of dual contour trees. Two multi-resolution dual contour trees were matched by computing their similarity score using a similarity metric. In this project, a new code for computing the initial contour tree is presented, together with a detailed revision. The main goal of my project is to understand the approach described in the paper and to improve its algorithm.
Keywords: dual contour trees, multi-resolution dual contour trees, attributes, volumetric scalar fileds matching