Hybrid-CSR: Coupling Explicit and Implicit Shape Representation for Cortical Surface Reconstruction

We present Hybrid-CSR, a geometric deep-learning model that combines explicit and implicit shape representations for cortical surface reconstruction. Specifically, Hybrid-CSR begins with explicit deformations of template meshes to obtain coarsely reconstructed cortical surfaces, based on which the oriented point clouds are estimated for the subsequent differentiable poisson surface reconstruction. By doing so, our method unifies explicit (oriented point clouds) and implicit (indicator function) cortical surface reconstruction. Compared to explicit representation-based methods, our hybrid approach is more friendly to capture detailed structures, and when compared with implicit representation-based methods, our method can be topology aware because of end-to-end training with a mesh-based deformation module. In order to address topology defects, we propose a new topology correction pipeline that relies on optimization-based diffeomorphic surface registration. Experimental results on three brain datasets show that our approach surpasses existing implicit and explicit cortical surface reconstruction methods in numeric metrics in terms of accuracy, regularity, and consistency

Automated Reconstruction of 3D Open Surfaces from Sparse Point Clouds

Real-world 3D data may contain intricate details defined by salient surface gaps. Automated reconstruction of these open surfaces (e.g., non-watertight meshes) is a challenging problem for environment synthesis in mixed reality applications. Current learning-based implicit techniques can achieve high fidelity on closed-surface reconstruction. However, their dependence on the distinction between the inside and outside of a surface makes them incapable of reconstructing open surfaces. Recently, a new class of implicit functions have shown promise in reconstructing open surfaces by regressing an unsigned distance field. Yet, these methods rely on a discretized representation of the raw data, which loses important surface details and can lead to outliers in the reconstruction. We propose IPVNet, a learning-based implicit model that predicts the unsigned distance between a surface and a query point in 3D space by leveraging both raw point cloud data and its discretized voxel counterpart. Experiments on synthetic and real-world public datasets demonstrates that IPVNet outperforms the state of the art while producing far fewer outliers in the reconstruction.Comment: To be presented at the 2022 IEEE International Symposium on Mixed and Augmented Reality (ISMAR) Workshop on Photorealistic Image and Environment Synthesis for Mixed Reality (PIES-MR

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes

We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping (LTS). The new scheme uses the following basic ingredients: a high order WENO reconstruction in space on unstructured meshes, an element-local high-order accurate space-time Galerkin predictor that performs the time evolution of the reconstructed polynomials within each element, the computation of numerical ALE fluxes at the moving element interfaces through approximate Riemann solvers, and a one-step finite volume scheme for the time update which is directly based on the integral form of the conservation equations in space-time. The inclusion of the LTS algorithm requires a number of crucial extensions, such as a proper scheduling criterion for the time update of each element and for each node; a virtual projection of the elements contained in the reconstruction stencils of the element that has to perform the WENO reconstruction; and the proper computation of the fluxes through the space-time boundary surfaces that will inevitably contain hanging nodes in time due to the LTS algorithm. We have validated our new unstructured Lagrangian LTS approach over a wide sample of test cases solving the Euler equations of compressible gasdynamics in two space dimensions, including shock tube problems, cylindrical explosion problems, as well as specific tests typically adopted in Lagrangian calculations, such as the Kidder and the Saltzman problem. When compared to the traditional global time stepping (GTS) method, the newly proposed LTS algorithm allows to reduce the number of element updates in a given simulation by a factor that may depend on the complexity of the dynamics, but which can be as large as 4.7.Comment: 31 pages, 13 figure