Shape from Projections via Differentiable Forward Projector for Computed Tomography

• Published in: arXiv.org
• Main Authors: Koo, Jakeoung, Dahl, Anders B, Bærentzen, J Andreas, Chen, Qiongyang, Bals, Sara, Dahl, Vedrana A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.03.2021
• Subjects: Computer Science - Computer Vision and Pattern Recognition; Computer simulation; Nanoparticles; Optimization; Projectors; Three dimensional models; Tomography
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2006.16120

In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simulate data acquisition, but not for reconstruction, for which a 3D mesh means the inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward model for 3D meshes that bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending recent work in differentiable rendering. We use the proposed forward model to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that the proposed method outperforms traditional voxel-based methods on noisy simulated data. We also apply the proposed method on electron tomography images of nanoparticles to demonstrate the applicability of the method on real data.