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Moving Frames & Computer Vision

Moving Frames & Computer Vision
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批准号:
9803154
负责人:
Peter Olver
金额:
$11.5万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1998
资助国家:
美国
项目状态:
已结题
起止时间:
1998-07-01 至 2002-06-30

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中文摘要
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英文摘要
This project is devoted to innovative applications of the geometry ofmoving frames and the mathematical theory of differential invariants toproblems arising in computer vision, with emphasis on medical imaging. Since symmetry forms a basic component of the human visual system, it should benaturally incorporated into mathematical methods for image processing and objectrecognition. The image processing applications to be considered will includedenoising and smoothing, segmentation and edge detection, as well as objectrecognition, including symmetry detection and partial occlusions. Practicalimplementations will be based on the signature curve paradigm, that is based on the construction of suitable differential invariants for the symmetry group under consideration. Metrics that distinguish signature curves of different objects will be compared, with the goal being to recognize and extract objects from both two and three-dimensional images. Practical implementations of the image processing systems will rely on a new method of constructing symmetry-preserving numerical approximations to differential invariants that is to be developed as a part of this project. The applications will be based on a new, practical theory of moving frames, that can be applied to general group actions, both finite and infinite-dimensional. Part of the project will be devoted to the further development of this general theory. Various additional applications, to problems arising in physics, geometry, invariant theory, and the calculus of variations, will also be investigated.
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Geometric Analysis for Classification and Reassembly of Broken Bones
  • 批准号:
    1816917
  • 项目类别:
    Standard Grant
  • 资助金额:
    $41.81万
  • 财政年份:
    2018
  • 负责人:
    Peter Olver
  • 依托单位:
Applications of Moving Frames
  • 批准号:
    1108894
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $34.16万
  • 财政年份:
    2011
  • 负责人:
    Peter Olver
  • 依托单位:
S4 Conference on Symmetry, Separation, Super-integrability and Special Functions
  • 批准号:
    1013877
  • 项目类别:
    Standard Grant
  • 资助金额:
    $2.85万
  • 财政年份:
    2010
  • 负责人:
    Peter Olver
  • 依托单位:
Applications of Moving Frames
  • 批准号:
    0807317
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $29.01万
  • 财政年份:
    2008
  • 负责人:
    Peter Olver
  • 依托单位:
海外基金