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The optimization and the geometry of the sum of ratios of homogeneous quartic forms

Research Project

Project/Area Number 23656074
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Engineering fundamentals
Research InstitutionFukuoka University (2012-2013)
National Institute of Advanced Industrial Science and Technology (2011)

Principal Investigator

FUJIKI Jun  福岡大学, 理学部, 准教授 (10357907)

Co-Investigator(Kenkyū-buntansha) AKAHO Shotaro  産業技術総合研究所, ヒューマンライフテクノロジー研究部門, グループ長 (40356340)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords四次形式 / 多項式最適化 / グレブナ基底 / 4次形式 / 最適化 / 直線度 / 判別分析 / 較正
Research Abstract

We investigate the optimization of the sum of the ratios of semi-positive definite quartic forms and its geometry. But unfortunately, the optimization and geometry is difficult for us to make it clear, and we can not solved it during the given period. However, we conclude that to understanding the groebner basis is the most important to elucidate the optimization and geometry, especially, to understand the semi-positive definet quartic forms, which should be investigated before considering the ratios of semi-positive definite quartic forms.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (20 results)

All 2013 2012 2011 Other

All Presentation (20 results)

  • [Presentation] クラス部分空間に着目した判別分析2013

    • Author(s)
      坂野鋭, 木村昭悟, 藤木淳
    • Organizer
      第16回画像の認識 ・ 理解シンポジウム (MIRU2013)
    • Related Report
      2013 Final Research Report
  • [Presentation] Pairwise Similarity for Line Extraction From Distorted Images2013

    • Author(s)
      日野英逸, 藤木淳, 赤穗昭太郎, 望月義彦, 村田昇
    • Organizer
      15th International Conference on Computer Analysis of Images and Patterns (CAIP2013)
    • Related Report
      2013 Final Research Report
  • [Presentation] Flexible hypersurface fitting with RBF kernels2013

    • Author(s)
      藤木淳 , 赤穗昭太郎
    • Organizer
      15th International Conference on Computer Analysis of Images and Patterns (CAIP2013)
    • Related Report
      2013 Final Research Report
  • [Presentation] データ対の直線性に基づく画像上の類似度の定義~歪曲画像からの直線検出への応用~2013

    • Author(s)
      日野英逸, 藤木淳, 赤穗昭太郎, 望月義彦, 村田昇
    • Organizer
      電子情報通信学会PRMU 研究会
    • Related Report
      2013 Final Research Report
  • [Presentation] Finding discriminant axes from multiple viewpoints2013

    • Author(s)
      藤木淳
    • Organizer
      The 13th IAPR in International Conference on Machine Vision Applications(MVA2013)
    • Related Report
      2013 Final Research Report
  • [Presentation] Robust hypersurface fitting based on random sampling approximations2012

    • Author(s)
      藤木淳, 赤穗昭太郎, 日野英逸, 村田昇
    • Organizer
      19th International Conference on Neural Information Processing(ICONIP2012)
    • Related Report
      2013 Final Research Report
  • [Presentation] Calibration of radially symmetric distortion based on linearity in the calibrated image2012

    • Author(s)
      藤木淳, 日野英逸, 赤穗昭太郎, 村田昇
    • Organizer
      The workshop on Omnidirectional Vision, Camera Networks and Non-classical Cameras (OMINIVIS2011)
    • Related Report
      2013 Final Research Report
  • [Presentation] 来るべき宇宙世紀へ向けて-亜光速下における画像からの静止系座標-2012

    • Author(s)
      城真範, 藤木淳, 赤穗昭太郎, 田中勝
    • Organizer
      日本物理学会年次大会
    • Related Report
      2013 Final Research Report
  • [Presentation] 準光速で等速直線運動するカメラの幾何学2012

    • Author(s)
      藤木淳, 城真範, 赤穗昭太郎, 田中勝
    • Organizer
      第15回画像の認識・理解シンポジウム(MIRU2012)
    • Related Report
      2013 Final Research Report
  • [Presentation] 較正画像における直線度の最大化に基づく放射対称歪曲の較正2011

    • Author(s)
      藤木淳, 赤穗昭太郎, 日野英逸, 村田昇
    • Organizer
      第14回画像の認識 ・ 理解シンポジウム(MIRU2011)
    • Related Report
      2013 Final Research Report
  • [Presentation] 較正画像における直線度の最大化に基づく放射対称歪曲の較正2011

    • Author(s)
      藤木淳, 赤穂昭太郎, 日野英逸, 村田昇
    • Organizer
      第14回画像の認識・理解シンポジウム
    • Place of Presentation
      石川県, 金沢市文化ホール
    • Related Report
      2011 Research-status Report
  • [Presentation] Calibration of radially symmetric distortion based on linearity in the calibrated image2011

    • Author(s)
      藤木淳, 日野英逸, 赤穂昭太郎, 村田昇
    • Organizer
      The Workshop on Omnidirctional Vision, Camera Networks and Non-classical Cameras
    • Place of Presentation
      スペイン, カタローニャプラザホテル
    • Related Report
      2011 Research-status Report
  • [Presentation] Finding discriminant axes from multiple viewpoints

    • Author(s)
      藤木淳
    • Organizer
      The 13th IAPR in International Conference on Machine Vision Applications
    • Place of Presentation
      立命館大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Flexible hypersurface fitting with RBF kernels

    • Author(s)
      藤木淳,赤穗昭太郎
    • Organizer
      CAIP2013
    • Place of Presentation
      ヨーク大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Pairwise Similarity for Line Extraction From Distorted Images

    • Author(s)
      日野英逸,藤木淳,赤穗昭太郎,望月義彦,村田昇
    • Organizer
      CAIP2013
    • Place of Presentation
      ヨーク大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] データ対の直線性に基づく画像上の類似度の定義 ~ 歪曲画像からの直線検出への応用 ~

    • Author(s)
      日野英逸, 藤木淳, 赤穂昭太郎, 望月義彦, 村田昇
    • Organizer
      電子情報通信学会PRMU研究会
    • Place of Presentation
      NTT武蔵野研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] クラス部分空間に着目した判別分析

    • Author(s)
      坂野鋭, 木村昭悟, 藤木淳
    • Organizer
      第16回画像の認識・理解シンポジウムMIRU2013
    • Place of Presentation
      国立情報学研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] 準光速で等速直線運動するカメラの幾何学

    • Author(s)
      藤木淳, 城真範, 赤穂昭太郎, 田中勝
    • Organizer
      第15解画像の認識・理解シンポジウム(MIRU2012)
    • Place of Presentation
      福岡国際会議場
    • Related Report
      2012 Research-status Report
  • [Presentation] 来るべき宇宙世紀へ向けて -亜光速下における画像からの静止系座標-

    • Author(s)
      城真範, 藤木淳, 赤穂昭太郎, 田中勝
    • Organizer
      日本物理学会年次大会
    • Place of Presentation
      京都産業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Robust hypersurface fitting based on random sampling approximations

    • Author(s)
      藤木淳, 赤穂昭太郎, 日野英逸, 村田昇
    • Organizer
      19th International Conference on Neural Information Processing (ICONIP2012)
    • Place of Presentation
      カタール, ルネッサンスドーハシティーセンターホテル
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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