Similarity between volumetric scalar fields
Abstract
Some recent research work, attempts to determine several methods of comparing scalar volumetric functions[1] [2] [3]. 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[3]. A finest level dual contour tree had been constructed from a pre-computed contour tree of a volumetric scalar field[4] 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[5] [6] were computed and used to match two multi-resolution dual contour trees[7] [8], 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[3] and to improve its algorithm.
Keywords: dual contour trees, multi-resolution dual contour trees, attributes, volumetric scalar fileds matching
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