Visual analysis of Multi-valued function data via classification of singular fibers

2014 Fiscal Year Final Research Report

• Project/Area Number: 25540041
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: High performance computing
• Research Institution: The University of Tokyo
• Principal Investigator: TAKAHASHI Shigeo 東京大学, 情報理工学(系)研究科, 准教授 (40292619)
• Co-Investigator(Kenkyū-buntansha): SAEKI Osamu 九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)
• Project Period (FY): 2013-04-01 – 2015-03-31
• Keywords: 多値関数 / 微分トポロジー / 特異ファイバー / joint contour nets / 可視化 / 特徴解析 / 数理可視化

Outline of Final Research Achievements

This study aims at visually analyzing features of data samples taken from multi-valued functions, by tracking the topological changes in mathematical fibers that are defined to be inverse images of such multi-valued function values. The proposed approach also allows us to identify the topological types of singular fibers, which has topological changes in the corresponding inverse images. The study specifically focus on the case f: R3 -> R2 and then the case f: R2 -> R2 where the inverse image is shrunk to a single point. The computation algorithms developed in this study have been applied to several problems including mathematical visualisation that facilitates mathematicians to explore further research insights in the area of differential topology, 3D shape retreival that takes into account two scalar attribute functions, and multiple geographical field analysis through interactive visual analytics.

Free Research Field

可視化学