tailieunhanh - Diffusive smoothing of 3D segmented medical data

This paper proposes an accurate, computationally efficient, and spectrum-free formulation of the heat diffusion smoothing on 3D shapes, represented as triangle meshes. The idea behind our approach is to apply a ðr;rÞ-degree Pade´–Chebyshev rational approximation to the solution of the heat diffusion equation. The proposed formulation is equivalent to solve r sparse, symmetric linear systems, is free of user-defined parameters, and is robust to surface discretization. We also discuss a simple criterion to select the time parameter that provides the best compromise between approximation accuracy and smoothness of the solution. Finally, our experiments on anatomical data show that the spectrum-free approach greatly reduces the computational cost and guarantees a higher approximation accuracy than previous work. | Journal of Advanced Research 2015 6 425-431 Cairo University Journal of Advanced Research ORIGINAL ARTICLE Diffusive smoothing of 3D segmented medical data CrossMark Giuseppe Patane CNR-IMATI Genova Italy ARTICLE INFO ABSTRACT Article history Received 5 August 2014 Received in revised form 26 September 2014 Accepted 28 September 2014 Available online 18 October 2014 Keywords Heat kernel smoothing Surface-based representations Pade-Chebyshev method Medical data This paper proposes an accurate computationally efficient and spectrum-free formulation of the heat diffusion smoothing on 3D shapes represented as triangle meshes. The idea behind our approach is to apply a r r -degree Pade-Chebyshev rational approximation to the solution of the heat diffusion equation. The proposed formulation is equivalent to solve r sparse symmetric linear systems is free of user-defined parameters and is robust to surface discretization. We also discuss a simple criterion to select the time parameter that provides the best compromise between approximation accuracy and smoothness of the solution. Finally our experiments on anatomical data show that the spectrum-free approach greatly reduces the computational cost and guarantees a higher approximation accuracy than previous work. 2014 Production and hosting by Elsevier . on behalf of Cairo University. Introduction In medical applications the heat kernel is central in diffusion filtering and smoothing of images 1-6 3D shapes 7 8 and anatomical surfaces 9 10 . However the computational cost for the evaluation of the heat kernel is the main bottleneck for processing both surfaces and volumetric data in fact it takes from O n to O n3 time on a data set sampled with n points according to the sparsity of the Laplacian matrix. This aspect becomes more evident for medical data which are nowadays acquired by PET MRI systems and whose resolution is constantly increasing with the improvement of the underlying imaging protocols and hardware. E-mail