Abstract
AbstractWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio‐Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state‐of‐the‐art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12].
Highlights
Processing discrete 3D data to enhance their geometric quality is an important task in many shape modeling and computer graphics applications
Lachaud / Piecewise smooth reconstruction of normal vector field on digital data scale level are related to geometrical properties of the ice/air interface [CLB∗00]
Many works have been proposed for estimating the normal vector field on point clouds or digital shapes [CP05, MOG11, BM12, CLL14], their theoretical guarantees require smoothness on the original shape
Summary
Processing discrete 3D data to enhance their geometric quality is an important task in many shape modeling and computer graphics applications. Lachaud / Piecewise smooth reconstruction of normal vector field on digital data scale level are related to geometrical properties of the ice/air interface [CLB∗00]. Many works have been proposed for estimating the normal vector field on point clouds or digital shapes [CP05, MOG11, BM12, CLL14], their theoretical guarantees require smoothness on the original shape. These methods are often unreliable around sharp features of the surface. When input data is an image, this functional is known as AmbrosioTortorelli (AT) functional [AT90] We adapt it to the piecewise smooth reconstruction of a normal vector field. Experiments show that sharp and vanishing features are correctly delineated even on extremely damaged data
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