Shape from projections via differentiable forward projector for computed tomography.

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.

Surface Reconstruction from Structured Light Images Using Differentiable Rendering.

When 3D scanning objects, the objective is usually to obtain a continuous surface. However, most surface scanning methods, such as structured light scanning, yield a point cloud. Obtaining a continuous surface from a point cloud requires a subsequent surface reconstruction step, which is directly affected by any error from the computation of the point cloud. In this work, we propose a one-step approach in which we compute the surface directly from structured light images. Our method minimizes the least-squares error between photographs and renderings of a triangle mesh, where the vertex positions of the mesh are the parameters of the minimization problem. To ensure fast iterations during optimization, we use differentiable rendering, which computes images and gradients in a single pass. We present simulation experiments demonstrating that our method for computing a triangle mesh has several advantages over approaches that rely on an intermediate point cloud. Our method can produce accurate reconstructions when initializing the optimization from a sphere. We also show that our method is good at reconstructing sharp edges and that it is robust with respect to image noise. In addition, our method can improve the output from other reconstruction algorithms if we use these for initialization.

3D distance fields: a survey of techniques and applications.

A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?

Signed distance computation using the angle weighted pseudonormal.

The normals of closed, smooth surfaces have long been used to determine whether a point is inside or outside such a surface. It is tempting to also use this method for polyhedra represented as triangle meshes. Unfortunately, this is not possible since, at the vertices and edges of a triangle mesh, the surface is not C1 continuous, hence, the normal is undefined at these loci. In this paper, we undertake to show that the angle weighted pseudonormal (originally proposed by Thürmer and Wüthrich and independently by Séquin) has the important property that it allows us to discriminate between points that are inside and points that are outside a mesh, regardless of whether a mesh vertex, edge, or face is the closest feature. This inside-outside information is usually represented as the sign in the signed distance to the mesh. In effect, our result shows that this sign can be computed as an integral part of the distance computation. Moreover, it provides an additional argument in favor of the angle weighted pseudonormals being the natural extension of the face normals. Apart from the theoretical results, we also propose a simple and efficient algorithm for computing the signed distance to a closed C0 mesh. Experiments indicate that the sign computation overhead when running this algorithm is almost negligible.