Smooth shapes with spherical topology:Beyond traditional modeling,efficient deformation,and interaction

作     者：D.Schmitter P.García-Amorena M.Unser 

作者机构：Biomedical Imaging Groupcole Polytechnique Fédérale de Lausanne(EPFL)1015 LausanneSwitzerland 

出 版 物：《Computational Visual Media》 (计算可视媒体（英文版）)

年 卷 期：2017年第3卷第3期

页      面：199-215页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：funded by the Swiss National Science Foundation under Grant 200020-162343 

主　　题：shape modeling spherical topology parametric surfaces splines differential geometry 

摘      要：Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models and subdivision methods require a large number of parameters to model smooth *** need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation. We present a new method to construct deformable closed surfaces, which includes exact spheres, by combining the best of two worlds: a smooth, interpolating model with a continuously varying tangent plane and well-defined curvature at every point on the surface. Our formulation is considerably simpler than NURBS and requires fewer parameters than polygon meshes. We demonstrate the generality of our method with applications including intuitive user-interactive shape modeling,continuous surface deformation, shape morphing,reconstruction of shapes from parameterized point clouds, and fast iterative shape optimization for image segmentation. Comparisons with discrete methods and non-interpolating approaches highlight the advantages of our framework.