Geometric integration of crystal theory and vision theory by singularity theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 26610035
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yokohama National University
• Principal Investigator: NISHIMURA Takashi 横浜国立大学, 環境情報研究科(研究院), 教授 (80189307)
• Co-Investigator(Kenkyū-buntansha): HONDA Atsufumi 都城工業高等専門学校, 講師 (90708611)
• Research Collaborator: HAN Huhe 横浜国立大学, 大学院環境情報学府, 大学院生
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: no-silhouette / ウルフ図形 / convex integrand / 球面極変換 / 自己双対ウルフ図形 / 安定 convex integrand / 双対 convex integrand / 可微分写像の特異点論

Outline of Final Research Achievements

(1) We succeeded to obtain a new relation between a Wulff shape, which are known as the geometric model of a crystal at equilibrium, and the perspective projection by using Singularity Theory of Smooth Mappings.
(2) In the last half of this research period, from various viewpoint we studied close relationships between a Wulff shape and its convex integrand which is the best efficient continuous function generating the Wulff shape. We have obtained many results on these topics. As of the beginning of June 2016, these results are still under submission.

Free Research Field

可微分写像の特異点論