The Research And Implementation Of Sampling Framework For Accurate Curvature Estimation In Discrete Surfaces

Curvature estimation in discrete surfaces is an important problem with numerous applications spanning multiple disciplines, such as computer graphics,computer vision, and geometric modeling [1], [2], [3], [4],[5]. Curvature and its associated principal direction vector fields are intrinsic properties that are invariant to rigid body transformations. Curvature isan indicator of ridges and can be used in applications such as shape analysis and recognition, object segmentation, adaptive smooth- ing,anisotropic fairing of irregular meshes, and anisotropic texture mapping. The curvature of a surface depends on second order differential quantities and, so, the estimation of curvature from discrete data is extremely sensitive to noise. Consequently, early work on curvature estimation from discrete data [6] focused on the estimation of the sign of the mean and Gaussian curvatures for segmentation purposes. Technological advances in recent years make it possible to obtain more accurate range data and, so,facilitate curvature estimation in discrete data.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.