Application of sub-Riemannian geometry to vision model

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13431
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: Ishikawa Goo 北海道大学, 理学研究院, 教授 (50176161)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: グルサ系 / 接触構造 / エンゲル構造 / G_2 構造 / ルジャンドル特異点 / (2,3,5)-分布 / 異常測地線 / 零測地線

Outline of Final Research Achievements

We have developed the geometric vision theory by contact structures. In particular the basic theory on Goursat controls of higher degree is established and is applied to models. Moreover, related to singularity theory of mappings on sub-Riemannian geometry, we have investigated the problems, as a feedback of the research project, on Legendre singularities, abnormal geodesics, null geodesics, Engel structures,
G_2 structures and on (2,3,5)-distributions. As consequences of results obtained by the research project, we published articles in international academic journals and gave lectures on them in international conferences.

Free Research Field

微分式系の特異点論