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幾つかの画像関連問題の計算複雑度の解析と効率的な解決法の提案

Research Project

Project/Area Number 16092209
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionJapan Advanced Institute of Science and Technology

Principal Investigator

浅野 哲夫  Japan Advanced Institute of Science and Technology, 情報科学研究科, 教授 (90113133)

Co-Investigator(Kenkyū-buntansha) 上原 隆平  北陸先端科学技術大学院大学, 情報科学研究科, 准教授 (00256471)
元木 光雄  北陸先端科学技術大学院大学, 情報科学研究科, 助教 (20345656)
小保方 幸次  一関工業高等専門学校, 制御情報工学科, 准教授 (50303326)
河村 泰之  愛媛大学, 教育学部, 講師 (80369967)
BISHUNU Arijit  北陸先端科学技術大学院大学, 情報科学研究科, 助手 (20372493)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥14,300,000 (Direct Cost: ¥14,300,000)
Fiscal Year 2007: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥3,300,000 (Direct Cost: ¥3,300,000)
Keywordsアルゴリズム / 計算幾何学 / 画像処理 / 画像の領域分割 / 指紋認識・同定 / ディスクレパンシ / 計算複雑度 / ハーフトーニング
Research Abstract

最近の画像入力装置の高度化に伴って大規模画像を扱う機会が増えたために,従来からの素朴なアルゴリズムでは計算時間に重大な問題が生じてきた.このような観点から,本研究では,アルゴリズム理論の立場から画像に関連する諸問題に取り組んだ.学術的にはコンピュータビジョンやコンピュータグラフィックスの分野がこれに密接に関連しているが,これらの分野では問題を数学的に定式化して,その計算複雑度を解析することは余り一般的ではない.むしろ,計算機実験を通して人間の目視による半断が優先される傾向にある.本研究では画像に関連する様々な問題について,その本質を数学的に定式化することから始めて,計算複雑度を解析し,最終的には効率の良いアルゴリズムを開発した. 本グループでは「画像関連問題の計算複雑度の解析と効率的な解決法の提案」という点に焦点を合わせながらも,特定研究の他のグループとの共同研究も積極的に行った.その結果として,計算幾何のみならず,グラフアルゴリズムの領域で様々な新発見を得ることができた.それらの成果は異なる国際ジャーナルに発表しているが,SIAM Journal on Computing Avdances in Mathematics, Algorithmica, Thoery of Computing Systemなど国際的にも評価の高いジャーナルに発表している.国際会議の論文も多数あるが,いずれも権威ある国際会議であり,世界的なレベルで評価を得た.

Report

(4 results)
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (31 results)

All 2008 2007 2006 2005 2004 Other

All Journal Article (23 results) (of which Peer Reviewed: 7 results) Presentation (8 results)

  • [Journal Article] A Robust Fingerprint Indexing Scheme Using Minutia Neighborhood Structure and Low-order Delaunay Triangles2007

    • Author(s)
      Xuefeng Liang, Arijit Bishnu and Tetsuo Asano
    • Journal Title

      IEEE Transactions on Information Forensics and Security 2-4

      Pages: 721-733

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Aspect-Ratio Voronoi Diagram and Its Complexity Bounds2007

    • Author(s)
      T. Asano
    • Journal Title

      Information Processing Letters 105

      Pages: 26-31

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial Approach to Fingerprint Binarization and Minutiae Extraction Using Euclidean Distance Transform2007

    • Author(s)
      X. Liang, A. Bishunu and T. Asano
    • Journal Title

      International Journal of Pattern Recognition and Artificial Intelligence 41

      Pages: 1141-1158

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The distance trisector curve2007

    • Author(s)
      T. Asano, J. Matousek, and T. Tokuyama
    • Journal Title

      Advances in Mathematics 212

      Pages: 338-360

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inserting Points Uniformly at Every Instance2006

    • Author(s)
      S.Teramoto T.Asano, N.Katoh, B.Doerr
    • Journal Title

      IEICE Trans. on Info. and Systems E89-D, 8

      Pages: 2348-2356

    • NAID

      110007538521

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A Linear Time Algorithm for Binary Fingerprint Image Denoising Using Distance Transform2006

    • Author(s)
      X.Liang, T.Asano
    • Journal Title

      IEICE Trans. e89-D, 4

      Pages: 1534-1542

    • NAID

      110007504506

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Polyline fitting of planar points under min-sum criterion2006

    • Author(s)
      B.Aronov, T.Asano, N.Katoh, K.Mehlhorn, T.Tokuyama
    • Journal Title

      International Journal on Computational Geometry and Applications 16(2-3)

      Pages: 97-116

    • Related Report
      2006 Annual Research Report
  • [Journal Article] New Dispersed-dot half toning technique by elimination of unstable pixels for electrophotography2005

    • Author(s)
      S.Sasahara, T.Asano
    • Journal Title

      Journal of Electronic Imaging

      Pages: 1-9

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Optimal Spanners for Axis-Aligned Buildings2005

    • Author(s)
      T.Asano, M.de Berg他4名
    • Journal Title

      Computational Geometry : Theory and Applications 30,1

      Pages: 59-77

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The structure and number of global roundings of a graph2004

    • Author(s)
      T.Asano, N.Katoh, H.Tamaki, T.Tokuyama
    • Journal Title

      Theoretical Computer Science 325

      Pages: 425-437

    • NAID

      120000861668

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Optimal Spanners for Axis-Aligned Buildings2004

    • Author(s)
      T.Asano, M.de Berg, O.Cheong, et al.
    • Journal Title

      Computational Geometry : Theory and Applications 30-1

      Pages: 59-77

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Pseudo-approximation algorithm with applications to optimal motion planning2004

    • Author(s)
      T.Asano, D.G.Kirkpatrick, C.K.Yap
    • Journal Title

      Discrete and Computational Geometry 31-1

      Pages: 139-171

    • NAID

      120000861690

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Near-Linear Time Algorithm for Binarization of Fingerprint Images Using Distance Transform2004

    • Author(s)
      Xuefeng Liang, Arijit Bishnu, Tetsuo Asano
    • Journal Title

      Proc. 10th International Workshop, IWCIA 2004

      Pages: 197-208

    • NAID

      120000861688

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Fast Denoising Method for Binary Fingerprint Image2004

    • Author(s)
      Xuefeng Liang, T.Asano
    • Journal Title

      Proc. IASTED Conference on Visualization, Imaging, and Image Processing

      Pages: 309-313

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Disc Covering Problem with Application to Digital Halftoning2004

    • Author(s)
      T.Asano, P.Brass, S.Sasahara
    • Journal Title

      Proc. of the Workshop on Computational Geometry and Applications (CGA 04)

      Pages: 490-497

    • NAID

      120001856641

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Space-Efficient Algorithm for Image Rotation

    • Author(s)
      T. Asano, S. Bitou, M. Motoki and N. Usui
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    • NAID

      10026851442

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Voronoi Diagrams with Respect to Criteria on Vision Information

    • Author(s)
      T. Asano, N. Katoh, H. Tamaki, and T. Tokuyama
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

    • NAID

      10021073115

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zone diagrams: Existence, Uniqueness and Algorithmic Challenge

    • Author(s)
      T. Asano, J. Matousek, and T. Tokuyama
    • Journal Title

      SIAM J. on Computing

    • NAID

      120002337745

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zone diagrams : Existence, Uniqueness and Algorithmic Challenge

    • Author(s)
      T.Asano, J.Matousek, T.Tokuyama
    • Journal Title

      SIAM Journal on Computing (採録決定済)(to appear)

    • NAID

      120002337745

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Combinatorial Approach to Fingerprint Binarization and Minutiae Extraction Using Euclidean Distance Transform

    • Author(s)
      X.Liang, T.Asano
    • Journal Title

      International Journal of Pattern Recognition and Artificial Intelligence. (採録決定済)(to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The distance trisector curve

    • Author(s)
      T.Asano, J.Matousek, T.Tokuyama
    • Journal Title

      Advances in Mathematics. (採録決定済)(to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Linear Time Algorithm for Binary Fingerprint Image Denoising using Distance Transform

    • Author(s)
      X.Liang, T.Asano
    • Journal Title

      電子情報通信学会論文誌D (採録決定)

    • NAID

      110007504506

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A Generalization of Magic Squares with Applications to Digital Halftoning

    • Author(s)
      B.Aronov, T.Asano他4名
    • Journal Title

      Theory of Computing System (採録決定)

    • NAID

      120000861694

    • Related Report
      2005 Annual Research Report
  • [Presentation] Constant-Working-Space Image Scan with a Given Angle2008

    • Author(s)
      T. Asano
    • Organizer
      24th European Workshop on Computational Geometry
    • Place of Presentation
      Nancy, France
    • Related Report
      2007 Annual Research Report
  • [Presentation] Online Uniformity of Integer Points on a Line2008

    • Author(s)
      T. Asano
    • Organizer
      24th European Workshop on Computational Geometry
    • Place of Presentation
      Nancy, France
    • Related Report
      2007 Annual Research Report
  • [Presentation] Optimal Triangulation with Steiner Points2007

    • Author(s)
      Boris Aronov, Tetsuo Asano and Stefan Funke
    • Organizer
      International Symposium on Algorithms and Computation
    • Place of Presentation
      仙台
    • Related Report
      2007 Annual Research Report
  • [Presentation] In-Place Algorithm for Image Rotation2007

    • Author(s)
      Tetsuo Asano, Shinnya Bitou, Mitsuo Motoki and Nobuaki Usui
    • Organizer
      International Symposium on Algorithms and Computation
    • Place of Presentation
      仙台
    • Related Report
      2007 Annual Research Report
  • [Presentation] Dissimilarity Preserving Embedding of Objects on the Plane2007

    • Author(s)
      T. Asano
    • Organizer
      International Xu Guangqi Conference
    • Place of Presentation
      Shanghai, China
    • Related Report
      2007 Annual Research Report
  • [Presentation] On-line uniformity of points2007

    • Author(s)
      T. Asano and S. Teramoto
    • Organizer
      8th Hellenic-European Conference on Computer Mathematics and its Applications
    • Place of Presentation
      Athens, Greece
    • Related Report
      2007 Annual Research Report
  • [Presentation] Linear-Space Algorithms for Distance Preserving Embedding2007

    • Author(s)
      T. Asano, P. Bose, P. Carmi, A. Maheshwari, C. Shu, M. Smid, and S. Wuhrer
    • Organizer
      Canadian Conference on Computational Geometry
    • Place of Presentation
      Ottawa, Canada
    • Related Report
      2007 Annual Research Report
  • [Presentation] Voronoi Diagram with Respect to Criteria on Vision Information2007

    • Author(s)
      T. Asano, N. Katoh, H. Tamaki, and T. Tokuyama
    • Organizer
      4th International Symposium on Voronoi Diagrams in Science and Engineering
    • Place of Presentation
      Pontypridd, Wales, UK
    • Related Report
      2007 Annual Research Report

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Published: 2004-04-01   Modified: 2018-03-28  

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