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Characteristic spaces of images

Research Project

Project/Area Number 26610026
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

Ochiai Hiroyuki  九州大学, マス・フォア・インダストリ研究所, 教授 (90214163)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords映像数学 / リー群 / アニメーション / 運動群 / 変形 / 極分解 / リー理論 / 離散微分幾何学 / 表現論 / 局面
Outline of Final Research Achievements

We study movie from the mathematical point of view. We introduce a structure on the set of a class of movies
and find a common property and a characteristic. We regard a motion and a deformation as a transformation.
with the help of Lie theory in math, and of a technique in computer graphics. We made a book and a video, as well as a paper, for public.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (33 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (5 results) Journal Article (7 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 6 results,  Open Access: 1 results) Presentation (10 results) (of which Int'l Joint Research: 3 results,  Invited: 7 results) Book (3 results) Remarks (7 results) Funded Workshop (1 results)

  • [Int'l Joint Research] アンジェ(フランス)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ビクトリア(ニュージーランド)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ニューサウスウエールズ(オーストラリア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ソウル国立大学(韓国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Victoria University(ニュージーランド)

    • Related Report
      2015 Research-status Report
  • [Journal Article] On the Letac-Massam Conjecture on cones $Q_{A_n}$2017

    • Author(s)
      Piotr Graczyk, Hideyuki Ishi, Salha Mamane, and Hiroyuki Ochiai
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 93(3) Pages: 16-21

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A concise parametrisation of affine transformation2016

    • Author(s)
      Shizuo Kaji and Hiroyuki Ochiai
    • Journal Title

      SIAM J. Imaging Sci

      Volume: 9(3)

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Mathematica module for Conformal Geometric Algebra and Origami Folding2016

    • Author(s)
      Mitsuhiro Kondo, Takuya Matsuo, Yoshihiro Mizoguchi, Hiroyuki Ochiai
    • Journal Title

      The proceedings of SCSS 2016: The 7th International Symposium on Symbolic Computation in Software Science, EPiC Series in Computing

      Volume: 39 Pages: 60-80

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] リーマンの球面2016

    • Author(s)
      落合啓之
    • Journal Title

      現代思想 2016年3月臨時増刊号 総特集=リーマン リーマン予想のすべて, 青土社

      Volume: 2016-3 Pages: 176-185

    • Related Report
      2015 Research-status Report
  • [Journal Article] ラプラシアン固有関数を用いた流体の流れ場のインタラクティブなデザイン手法2014

    • Author(s)
      佐藤 周平, 土橋 宜典, 岩崎 慶, 落合 啓之, 山本 強
    • Journal Title

      電子情報通信学会 論文誌D

      Volume: J97-D No.9 Pages: 1528-1536

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] An Optimization Approach for Designing Fluid Flow Fields2014

    • Author(s)
      Syuhei Sato, Yoshinori Dobashi, Kei Iwasaki, Hiroyuki Ochiai, Tsuyoshi Yamamoto, Tomoyuki Nishita
    • Journal Title

      The 31st Computer Graphics International

      Volume: CGI2014

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mathematical formulation of motion and deformation and its applications2014

    • Author(s)
      Hiroyuki Ochiai and Ken Anjyo
    • Journal Title

      Mathematical Progress in Expressive Image Synthesis I

      Volume: I Pages: 123-129

    • DOI

      10.1007/978-4-431-55007-5_13

    • ISBN
      9784431550068, 9784431550075
    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] From Pok\'emon and 3D Animation to Mathematics2017

    • Author(s)
      Ken Anjyo, Hiroyuki Ochiai
    • Organizer
      Vic Talk
    • Place of Presentation
      Victoria University of Wellington, NZ
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An Elementary Introduction to Matrix Exponential for CG2016

    • Author(s)
      Hiroyuki Ochiai, Ken Anjyo and Ayumi Kimura,
    • Organizer
      SIGGRAPH2016, Course
    • Place of Presentation
      Anaheim Convention Center
    • Year and Date
      2016-07-24
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] An Introduction to Matrix Exponential for CG2016

    • Author(s)
      Ken Anjyo, Hiroyuki Ochiai
    • Organizer
      Vic talk
    • Place of Presentation
      Victoria University of Wellington
    • Year and Date
      2016-02-26
    • Related Report
      2015 Research-status Report
  • [Presentation] An Introduction to Matrix Exponential for CG2016

    • Author(s)
      Hiroyuki Ochiai, Ken Anjyo
    • Organizer
      Weta talk
    • Place of Presentation
      Weta Digital, NZ
    • Year and Date
      2016-02-24
    • Related Report
      2015 Research-status Report
  • [Presentation] リー理論と動画生成2016

    • Author(s)
      落合啓之
    • Organizer
      数学科談話会
    • Place of Presentation
      愛媛大学理学部
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 概説講演“CG 映像制作におけるリー理論”2015

    • Author(s)
      落合啓之
    • Organizer
      表現論シンポジウム
    • Place of Presentation
      静岡県伊豆の国市
    • Year and Date
      2015-11-19
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Computer graphics and mathematics2015

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Computational and Geometric Approaches for Nonlinear Phenomena
    • Place of Presentation
      早稲田大学理工学術院
    • Year and Date
      2015-08-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 行列のできるアニメーション2015

    • Author(s)
      落合啓之
    • Organizer
      ワークショップ "Intersection of Pure Mathematics and Applied Mathematics VIII: Special
    • Place of Presentation
      福岡
    • Year and Date
      2015-02-20
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 伝える技術伝わる心2014

    • Author(s)
      落合啓之
    • Organizer
      九州大学テクノロジーフォーラム2014
    • Place of Presentation
      東京国際フォーラム
    • Year and Date
      2014-12-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] CGにおける運動や変形の記述とその数理2014

    • Author(s)
      落合啓之
    • Organizer
      CEDEC2014
    • Place of Presentation
      パシフィコ横浜
    • Year and Date
      2014-09-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Book] Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition2017

    • Author(s)
      Ken Anjyo and Hiroyuki Ochiai
    • Total Pages
      95
    • Publisher
      Morgan and Claypool
    • Related Report
      2016 Annual Research Report
  • [Book] Mathematical Progress in Expressive Image Synthesis III2016

    • Author(s)
      Yoshinori Dobashi, Hiroyuki Ochiai, (Eds.)
    • Total Pages
      152
    • Publisher
      Springer Verlag
    • Related Report
      2016 Annual Research Report
  • [Book] Mathematical Basics of Motion and Deformation in Computer Graphics2014

    • Author(s)
      Ken Anjyo, Hiroyuki Ochiai
    • Total Pages
      83
    • Publisher
      Morgan & Claypool Publishers
    • Related Report
      2014 Research-status Report
  • [Remarks] 落合啓之のページ

    • URL

      http://user.math.kyushu-u.ac.jp/index.php?ochiai

    • Related Report
      2016 Annual Research Report 2015 Research-status Report
  • [Remarks] 研究者情報(落合啓之)

    • URL

      http://hyoka.ofc.kyushu-u.ac.jp/search/details/K003560/index.html

    • Related Report
      2016 Annual Research Report
  • [Remarks] 落合啓之のページ

    • Related Report
      2015 Research-status Report
  • [Remarks] Ochiai's page

    • URL

      http://user.math.kyushu-u.ac.jp/index.php?ochiai

    • Related Report
      2014 Research-status Report
  • [Remarks] 九州大学大学院数理学府

    • URL

      http://www.math.kyushu-u.ac.jp

    • Related Report
      2014 Research-status Report
  • [Remarks] 九州大学マス・フォア・インダストリ研究所

    • URL

      http://www.imi.kyushu-u.ac.jp

    • Related Report
      2014 Research-status Report
  • [Remarks] math for CG

    • URL

      http://mcg.imi.kyushu-u.ac.jp

    • Related Report
      2014 Research-status Report
  • [Funded Workshop] Symposium MEIS 2016: Mathematical Progress in Expressive Image Synthesis2016

    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2016-11-11
    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2018-03-22  

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