Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
153 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Deep Medial Voxels: Learned Medial Axis Approximations for Anatomical Shape Modeling (2403.11790v1)

Published 18 Mar 2024 in cs.CV and cs.AI

Abstract: Shape reconstruction from imaging volumes is a recurring need in medical image analysis. Common workflows start with a segmentation step, followed by careful post-processing and,finally, ad hoc meshing algorithms. As this sequence can be timeconsuming, neural networks are trained to reconstruct shapes through template deformation. These networks deliver state-ofthe-art results without manual intervention, but, so far, they have primarily been evaluated on anatomical shapes with little topological variety between individuals. In contrast, other works favor learning implicit shape models, which have multiple benefits for meshing and visualization. Our work follows this direction by introducing deep medial voxels, a semi-implicit representation that faithfully approximates the topological skeleton from imaging volumes and eventually leads to shape reconstruction via convolution surfaces. Our reconstruction technique shows potential for both visualization and computer simulations.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (63)
  1. G. Mistelbauer, C. Rössl, K. Bäumler, B. Preim, and D. Fleischmann, “Implicit modeling of patient-specific aortic dissections with elliptic fourier descriptors,” in Comput Graph Forum, vol. 40, pp. 423–34, 2021.
  2. S. Oeltze and B. Preim, “Visualization of vasculature with convolution surfaces: method, validation and evaluation,” IEEE Trans Med Imaging, vol. 24, no. 4, pp. 540–48, 2005.
  3. J. Li et al., “Autoimplant 2020-first miccai challenge on automatic cranial implant design,” IEEE Trans Med Imaging, vol. 40, no. 9, pp. 2329–42, 2021.
  4. K. Bäumler et al., “Fluid–structure interaction simulations of patient-specific aortic dissection,” Biomechanics and Modeling in Mechanobiology, vol. 19, no. 5, pp. 1607–28, 2020.
  5. R. Shad et al., “Patient-specific computational fluid dynamics reveal localized flow patterns predictive of post–left ventricular assist device aortic incompetence,” Circulation: Heart Failure, vol. 14, no. 7, p. e008034, 2021.
  6. L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Medical & biological engineering & computing, vol. 46, pp. 1097–1112, 2008.
  7. E. Kerrien, A. Yureidini, J. Dequidt, C. Duriez, R. Anxionnat, and S. Cotin, “Blood vessel modeling for interactive simulation of interventional neuroradiology procedures,” Med Image Anal, vol. 35, pp. 685–98, 2017.
  8. D. Bošnjak, A. Pepe, R. Schussnig, D. Schmalstieg, and T.-P. Fries, “Higher-order block-structured hex meshing of tubular structures,” Engineering with Computers, pp. 1–21, 2023.
  9. N. S. Burris et al., “Vascular deformation mapping for CT surveillance of thoracic aortic aneurysm growth,” Radiology, vol. 302, no. 1, pp. 218–25, 2022.
  10. A. Sarrami-Foroushani et al., “In-silico trial of intracranial flow diverters replicates and expands insights from conventional clinical trials,” Nature Communications, vol. 12, no. 1, pp. 1–12, 2021.
  11. Y. Wang et al., “Deep distance transform for tubular structure segmentation in CT scans,” in Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3833–42, 2020.
  12. S. Li, C. Zhang, and X. He, “Shape-aware semi-supervised 3d semantic segmentation for medical images,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 552–61, Springer, 2020.
  13. J. Hu, B. Wang, L. Qian, Y. Pan, X. Guo, L. Liu, and W. Wang, “Mat-net: Medial axis transform network for 3d object recognition.,” in IJCAI, pp. 774–781, 2019.
  14. C. Lin, C. Li, Y. Liu, N. Chen, Y.-K. Choi, and W. Wang, “Point2skeleton: Learning skeletal representations from point clouds,” in Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4277–86, 2021.
  15. A. J. F. Suárez, E. Hubert, and C. Zanni, “Anisotropic convolution surfaces,” Computers & Graphics, vol. 82, pp. 106–16, 2019.
  16. T. S. Newman and H. Yi, “A survey of the marching cubes algorithm,” Computers & Graphics, vol. 30, no. 5, pp. 854–79, 2006.
  17. Q. Hong, Q. Li, B. Wang, K. Liu, and Q. Qi, “High precision implicit modeling for patient-specific coronary arteries,” IEEE Access, vol. 7, pp. 72020–29, 2019.
  18. M. Piccinelli, A. Veneziani, D. A. Steinman, A. Remuzzi, and L. Antiga, “A framework for geometric analysis of vascular structures: Application to cerebral aneurysms,” IEEE Transactions on Medical Imaging, vol. 28, no. 8, pp. 1141–1155, 2009.
  19. U. Wickramasinghe, E. Remelli, G. Knott, and P. Fua, “Voxel2mesh: 3d mesh model generation from volumetric data,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 299–308, 2020.
  20. D. H. Pak et al., “Distortion energy for deep learning-based volumetric finite element mesh generation for aortic valves,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 485–94, Springer, 2021.
  21. Y. Kanamori, Z. Szego, and T. Nishita, “Gpu-based fast ray casting for a large number of metaballs,” Comput Graph Forum, vol. 27, no. 2, pp. 351–60, 2008.
  22. T. Fries, S. Omerović, D. Schöllhammer, and J. Steidl, “Higher-order meshing of implicit geometries, Part I:Integration and interpolation in cut elements,” Comput Methods Appl Mech Eng, vol. 313, pp. 759–84, 2017.
  23. J. J. Torres and G. Bianconi, “Simplicial complexes: higher-order spectral dimension and dynamics,” J. phys. Complex, vol. 1, no. 1, p. 015002, 2020.
  24. H. Edelsbrunner and J. L. Harer, Computational topology: an introduction. American Mathematical Society, 2022.
  25. J. Giesen, B. Miklos, M. Pauly, and C. Wormser, “The scale axis transform,” in Proc. Annual Symposium on Computational Geometry, pp. 106–15, 2009.
  26. P. Li, B. Wang, F. Sun, X. Guo, C. Zhang, and W. Wang, “Q-mat: Computing medial axis transform by quadratic error minimization,” ACM Trans. Graph., vol. 35, no. 1, pp. 1–16, 2015.
  27. Z. Dou et al., “Coverage axis: Inner point selection for 3d shape skeletonization,” Comput Graph Forum, vol. 41, no. 2, pp. 2329–42, 2022.
  28. Y. Yan, D. Letscher, and T. Ju, “Voxel cores: Efficient, robust, and provably good approximation of 3d medial axes,” ACM Trans. Graph., vol. 37, no. 4, pp. 1–13, 2018.
  29. D. Rebain et al., “LSMAT least squares medial axis transform,” in Comput Graph Forum, vol. 38, pp. 5–18, 2019.
  30. C. Lin et al., “Seg-mat: 3d shape segmentation using medial axis transform,” IEEE Trans Vis Comput Graph, 2020.
  31. J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove, “DeepSDF: Learning continuous signed distance functions for shape representation,” in Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 165–74, 2019.
  32. D. Rebain, K. Li, V. Sitzmann, S. Yazdani, K. M. Yi, and A. Tagliasacchi, “Deep medial fields,” arXiv preprint arXiv:2106.03804, 2021.
  33. K. Genova, F. Cole, A. Sud, A. Sarna, and T. Funkhouser, “Local deep implicit functions for 3d shape,” in Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4857–66, 2020.
  34. B. Yang et al., “P2MAT-Net: Learning medial axis transform from sparse point clouds,” Comput Aided Geom Des, vol. 80, p. 101874, 2020.
  35. P. Erler, P. Guerrero, S. Ohrhallinger, N. J. Mitra, and M. Wimmer, “Points2surf: Learning implicit surfaces from point clouds,” in European Conference on Computer Vision, pp. 108–124, 2020.
  36. S. Peng, M. Niemeyer, L. Mescheder, M. Pollefeys, and A. Geiger, “Convolutional occupancy networks,” in European Conference on Computer Vision, pp. 523–40, 2020.
  37. J. Zhao, J. Zhao, S. Pang, and Q. Feng, “Segmentation of the true lumen of aorta dissection via morphology-constrained stepwise deep mesh regression,” IEEE Trans Med Imaging, 2022.
  38. J. Ma et al., “How distance transform maps boost segmentation CNNs: an empirical study,” in Medical Imaging with Deep Learning, pp. 479–92, PMLR, 2020.
  39. Z. Lin, D. Wei, A. Gupta, X. Liu, D. Sun, and H. Pfister, “Structure-preserving instance segmentation via skeleton-aware distance transform,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 529–539, Springer, 2023.
  40. X. Zhang, K. Sun, D. Wu, X. Xiong, J. Liu, L. Yao, S. Li, Y. Wang, J. Feng, and D. Shen, “An anatomy-and topology-preserving framework for coronary artery segmentation,” IEEE Transactions on Medical Imaging, 2023.
  41. H. Xia and P. G. Tucker, “Fast equal and biased distance fields for medial axis transform with meshing in mind,” Applied Mathematical Modelling, vol. 35, no. 12, pp. 5804–19, 2011.
  42. M. Liao, Z. Wan, C. Yao, K. Chen, and X. Bai, “Real-time scene text detection with differentiable binarization,” in Proc. AAAI conference on artificial intelligence, vol. 34, pp. 11474–81, 2020.
  43. S. Shit et al., “cldice-a novel topology-preserving loss function for tubular structure segmentation,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16560–16569, 2021.
  44. J. McCormack and A. Sherstyuk, “Creating and rendering convolution surfaces,” in Computer Graphics Forum, vol. 17, pp. 113–20, 1998.
  45. M. Kazhdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Proc. EG Symposium on Geometry Processing, vol. 7, 2006.
  46. C. Geuzaine and J. Remacle, “Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities,” Int J Numer Methods Eng, vol. 79, no. 11, pp. 1309–1331, 2009.
  47. F. Milletari, N. Navab, and S.-A. Ahmadi, “V-net: Fully convolutional neural networks for volumetric medical image segmentation,” in International conference on 3D vision (3DV), pp. 565–71, 2016.
  48. Z. Xiong et al., “A global benchmark of algorithms for segmenting the left atrium from late gadolinium-enhanced cardiac magnetic resonance imaging,” Medical Image Analysis, vol. 67, p. 101832, 2021.
  49. A. L. Simpson et al., “A large annotated medical image dataset for the development and evaluation of segmentation algorithms,” arXiv:1902.09063, 2019.
  50. Z. Lambert, C. Petitjean, B. Dubray, and S. Kuan, “Segthor: Segmentation of thoracic organs at risk in ct images,” in Proc. IPTA, pp. 1–6, IEEE, 2020.
  51. Z. Yao et al., “Imagetbad: A 3d computed tomography angiography image dataset for automatic segmentation of type-b aortic dissection,” Front. Physiol., vol. 12, 2021.
  52. C. Zhang, L. Yang, L. Xu, G. Wang, and W. Wang, “Real-time editing of man-made mesh models under geometric constraints,” Computers & Graphics, vol. 82, pp. 174–182, 2019.
  53. G. García-Isla et al., “Sensitivity analysis of geometrical parameters to study haemodynamics and thrombus formation in the left atrial appendage,” Int J Num Method Biomed Eng, vol. 34, no. 8, p. e3100, 2018.
  54. R. Schussnig, D. Pacheco, and T. Fries, “Robust stabilised finite element solvers for generalised newtonian fluid flows,” J Comput Phys, vol. 442, p. 110436, 2021.
  55. R. Schussnig, D. Pacheco, M. Kaltenbacher, and T.-P. Fries, “Semi-implicit fluid–structure interaction in biomedical applications,” Comput Methods Appl Mech Eng, vol. 400, p. 115489, 2022.
  56. R. Schussnig, D. Pacheco, and T. Fries, “Efficient split-step schemes for fluid-structure interaction involving incompressible generalised newtonian flows,” Comput Struct, vol. 260, p. 106718, 2022.
  57. J. Dueñas-Pamplona, J. G. García, J. Sierra-Pallares, C. Ferrera, R. Agujetas, and J. R. López-Mínguez, “A comprehensive comparison of various patient-specific CFD models of the left atrium for atrial fibrillation patients,” Computers Biol Med, vol. 133, p. 104423, 2021.
  58. S. Ranftl, T. Müller, U. Windberger, W. von der Linden, and G. Brenn, “A Bayesian approach to blood rheological uncertainties in aortic hemodynamics,” Int J Numer Method Biomed Eng, 2022.
  59. D. Arndt, N. Fehn, G. Kanschat, K. K. M. Kronbichler, P. Munch, W. Wall, and J. Witte, “ExaDG: High-order discontinuous Galerkin for the exascale,” in Software for Exascale Computing - SPPEXA 2016-2019, (Cham), pp. 189–224, Springer International Publishing, 2020.
  60. D. Arndt, W. Bangerth, M. Bergbauer, M. Feder, M. Fehling, J. Heinz, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, J. Pelteret, B. Turcksin, D. Wells, and S. Zampini, “The deal.II Library, Version 9.5,” J Numer Math, 2023.
  61. N. Fehn, W. A. Wall, and M. Kronbichler, “Robust and efficient discontinuous galerkin methods for under-resolved turbulent incompressible flows,” J Comput Physics, vol. 372, pp. 667–693, 2018.
  62. N. Fehn, P. Munch, W. Wall, and M. Kronbichler, “Hybrid multigrid methods for high-order discontinuous Galerkin discretizations,” J Comput Phys, vol. 415, p. 109538, 2020.
  63. P. Viville, P. Kraemer, and D. Bechmann, “Meso-skeleton guided hexahedral mesh design,” Comput Graph Forum, p. e14932, 2023.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now