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Sampling framework for accurate curvature estimation in discrete surfaces.

Gady Agam1, Xiaojing Tang

  • 1Department of Computer Science, Illinois Institute of Technology, 10 West 31st Street, Chicago, IL 60616, USA. agam@iit.edu

IEEE Transactions on Visualization and Computer Graphics
|September 8, 2005
PubMed
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This study introduces a new framework for accurate curvature estimation on discrete surfaces. The method offers improved accuracy and robustness against noise and irregular sampling, outperforming existing techniques.

Area of Science:

  • Computer Graphics
  • Computational Geometry
  • Geometric Modeling

Background:

  • Accurate curvature estimation is crucial for various applications, including shape analysis, object recognition, and mesh processing.
  • Existing methods for discrete surface curvature estimation often struggle with noise, irregular sampling, and limited geometric representation.

Purpose of the Study:

  • To propose a novel framework for precise curvature estimation in discrete surfaces.
  • To enhance the representation of local surface geometry through a flexible sampling approach.
  • To quantitatively evaluate the proposed framework against established techniques.

Main Methods:

  • A new framework based on local directional curve sampling of discrete surfaces.
  • Controlled sampling frequency to adapt to local geometry.

Related Experiment Videos

  • Quantitative evaluation using randomly generated Bezier surface patches with analytically computed curvature.
  • Main Results:

    • The proposed framework demonstrates smaller estimation errors compared to common techniques.
    • The method shows reduced sensitivity to low sampling density, sampling irregularities, and noise.
    • The local model offers a greater number of degrees of freedom for better geometric representation.

    Conclusions:

    • The novel framework provides a more accurate and robust solution for discrete surface curvature estimation.
    • The controlled sampling approach enhances the representation of local surface geometry.
    • This method has significant implications for applications requiring precise surface analysis.