Shape from Projections via Differentiable Forward Projector for Computed Tomography

TL;DR

This paper introduces a novel mesh-based 3D shape reconstruction method from projections in computed tomography, using a differentiable forward projector that improves accuracy over voxel-based approaches, especially with noisy data.

Contribution

It presents a differentiable forward model for 3D meshes that enables direct shape reconstruction from projections, bridging the gap between rendering and tomography.

Findings

Outperforms voxel-based methods on noisy simulated data

Effective on real electron tomography images of nanoparticles

Demonstrates applicability to practical tomography problems

Abstract

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.