Agam Gady, Tang Xiaojing
Department of Computer Science, Illinois Institute of Technology, 10 West 31st Street, Chicago, IL 60616, USA.
IEEE Trans Vis Comput Graph. 2005 Sep-Oct;11(5):573-83. doi: 10.1109/TVCG.2005.69.
Accurate curvature estimation in discrete surfaces is an important problem with numerous applications. Curvature is an indicator of ridges and can be used in applications such as shape analysis and recognition, object segmentation, adaptive smoothing, anisotropic fairing of irregular meshes, and anisotropic texture mapping. In this paper, a new framework is proposed for accurate curvature estimation in discrete surfaces. The proposed framework is based on a local directional curve sampling of the surface where the sampling frequency can be controlled. This local model has a large number of degrees of freedoms compared with known techniques and, so, can better represent the local geometry. The proposed framework is quantitatively evaluated and compared with common techniques for surface curvature estimation. In order to perform an unbiased evaluation in which smoothing effects are factored out, we use a set of randomly generated Bezier surface patches for which the curvature values can be analytically computed. It is demonstrated that, through the establishment of sampling conditions, the error in estimations obtained by the proposed framework is smaller and that the proposed framework is less sensitive to low sampling density, sampling irregularities, and sampling noise.
离散曲面上的精确曲率估计是一个具有众多应用的重要问题。曲率是脊线的一个指标，可用于形状分析与识别、目标分割、自适应平滑、不规则网格的各向异性光顺以及各向异性纹理映射等应用中。本文提出了一种用于离散曲面上精确曲率估计的新框架。所提出的框架基于曲面的局部方向曲线采样，其中采样频率可以控制。与已知技术相比，这种局部模型具有大量的自由度，因此能够更好地表示局部几何形状。对所提出的框架进行了定量评估，并与用于曲面曲率估计的常用技术进行了比较。为了进行消除平滑效应的无偏评估，我们使用了一组随机生成的贝塞尔曲面片，其曲率值可以通过解析计算得到。结果表明，通过建立采样条件，所提出的框架获得的估计误差更小，并且该框架对低采样密度、采样不规则性和采样噪声不太敏感。
