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 (r,r)-degree Padé–Chebyshev rational approximation to the solution of the heat diffusion...
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| Format: | Article |
| Language: | English |
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Elsevier
2015-05-01
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| Series: | Journal of Advanced Research |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090123214001234 |
| _version_ | 1811272914833506304 |
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| author | Giuseppe Patané |
| author_facet | Giuseppe Patané |
| author_sort | Giuseppe Patané |
| collection | DOAJ |
| description | 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 Padé–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. |
| first_indexed | 2024-04-12T22:48:40Z |
| format | Article |
| id | doaj.art-f933a17356d641abb5307cb51c1a536f |
| institution | Directory Open Access Journal |
| issn | 2090-1232 2090-1224 |
| language | English |
| last_indexed | 2024-04-12T22:48:40Z |
| publishDate | 2015-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Advanced Research |
| spelling | doaj.art-f933a17356d641abb5307cb51c1a536f2022-12-22T03:13:26ZengElsevierJournal of Advanced Research2090-12322090-12242015-05-016342543110.1016/j.jare.2014.09.003Diffusive smoothing of 3D segmented medical dataGiuseppe PatanéThis 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 Padé–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.http://www.sciencedirect.com/science/article/pii/S2090123214001234Heat kernel smoothingSurface-based representationsPadé–Chebyshev methodMedical data |
| spellingShingle | Giuseppe Patané Diffusive smoothing of 3D segmented medical data Journal of Advanced Research Heat kernel smoothing Surface-based representations Padé–Chebyshev method Medical data |
| title | Diffusive smoothing of 3D segmented medical data |
| title_full | Diffusive smoothing of 3D segmented medical data |
| title_fullStr | Diffusive smoothing of 3D segmented medical data |
| title_full_unstemmed | Diffusive smoothing of 3D segmented medical data |
| title_short | Diffusive smoothing of 3D segmented medical data |
| title_sort | diffusive smoothing of 3d segmented medical data |
| topic | Heat kernel smoothing Surface-based representations Padé–Chebyshev method Medical data |
| url | http://www.sciencedirect.com/science/article/pii/S2090123214001234 |
| work_keys_str_mv | AT giuseppepatane diffusivesmoothingof3dsegmentedmedicaldata |