We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets. More specifically, an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortio...This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets. More specifically, an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes. This signal is then sampled on the sphere with the help of an adaptive sampling scheme. Finally, the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing, enhancement, compression, and so on. Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for pro- cessing 3D meshed surfaces by spherical wavelets, which can handle surfaces with complex shapes. A number of experimental ex- amples demonstrate that our algorithm is robust and efficient.展开更多
Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy fo...Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of genus-zero.In addition,we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal maps.Numerical experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal distortions.We subsequently propose an application of our method to surface registrations that still maintain local quadratic convergence.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
基金Supported by the National Natural Science Foundation of China(No.61173102)the NSFC Guangdong Joint Fund(No.U0935004)+2 种基金the Fundamental Research Funds for the Central Universities(No.DUT11SX08)the Opening Foundation of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education of China(No.93K172012K02)the Doctor Research Start-up Fund of North East Dian Li university(No.BSJXM-200912)
文摘This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets. More specifically, an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes. This signal is then sampled on the sphere with the help of an adaptive sampling scheme. Finally, the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing, enhancement, compression, and so on. Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for pro- cessing 3D meshed surfaces by spherical wavelets, which can handle surfaces with complex shapes. A number of experimental ex- amples demonstrate that our algorithm is robust and efficient.
基金supported by National Natural Science Foundation of China(Grant No.12371377)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002)supported by Shanghai Institute for Mathematics and Interdisciplinary Sciences(Grant No.SIMIS-ID-2024-LG)。
文摘Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of genus-zero.In addition,we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal maps.Numerical experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal distortions.We subsequently propose an application of our method to surface registrations that still maintain local quadratic convergence.
