The Weighted Euler Curve Transform for Shape and Image Analysis

Autor:	Jiang, Qitong, Kurtek, Sebastian, Needham, Tom
Rok vydání:	2020
Předmět:	Computer Science - Computational Geometry Mathematics - Algebraic Topology Statistics - Applications
Druh dokumentu:	Working Paper
Popis:	The Euler Curve Transform (ECT) of Turner et al.\ is a complete invariant of an embedded simplicial complex, which is amenable to statistical analysis. We generalize the ECT to provide a similarly convenient representation for weighted simplicial complexes, objects which arise naturally, for example, in certain medical imaging applications. We leverage work of Ghrist et al.\ on Euler integral calculus to prove that this invariant---dubbed the Weighted Euler Curve Transform (WECT)---is also complete. We explain how to transform a segmented region of interest in a grayscale image into a weighted simplicial complex and then into a WECT representation. This WECT representation is applied to study Glioblastoma Multiforme brain tumor shape and texture data. We show that the WECT representation is effective at clustering tumors based on qualitative shape and texture features and that this clustering correlates with patient survival time. Comment: To appear in CVPR conference workshop proceedings for DIFF-CVML 2020
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.11128 Zobrazit plný text záznamu View this record from Arxiv