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

An Efficient Framework for Image Matching

AbstractThe goal of this paper is to present an efficient framework for non-rigid medical image matching. Previous non-rigid matching often produces unpredictable deformation field and unwanted stretching in the images. The as-rigid-as-possible nature of the Moving-LS technique thus makes it a new candidate by providing transformation that maintains the rigidity of structures for underlying physical reasons, while producing local deformations. In addition, it is very suitable for parallel computation, and the performance can be accelerated by multi-core processors through employment of multiple threads. The results demonstrate that the proposed matching method has good balance between accuracy and speed, and has potential in many medical applications

Differentiable Subdivision Surface Fitting

In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can handle complex surface topology better than other popular compact representations, such as NURBS. The principal idea is to fit the Loop subdivision surface not directly to the point cloud, but to the IMLS (implicit moving least squares) surface defined over the point cloud. As both Loop subdivision and IMLS have analytical expressions, we are able to formulate the problem as an unconstrained minimization problem of a completely differentiable function that can be solved with standard numerical solvers. Differentiability enables us to integrate the subdivision surface into any deep learning method for point clouds or meshes. We demonstrate the versatility and potential of this approach by using it in conjunction with a differentiable renderer to robustly reconstruct compact surface representations of spatial-temporal sequences of dense meshes

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

Polyhedral Surface: Self-supervised Point Cloud Reconstruction Based on Polyhedral Surface

Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a local geometry to fit the local curve. However, previous methods build either a local plane or polynomial curve. Local plane brings the loss of sharp feature and the boundary artefacts on open surface. Polynomial curve is hard to combine with neural network due to the local coordinate consistent problem. To address this, we propose a novel polyhedral surface to represent local surface. This method provides more flexible to represent sharp feature and surface boundary on open surface. It does not require any local coordinate system, which is important when introducing neural networks. Specifically, we use normals to construct the polyhedral surface, including both dihedral and trihedral surfaces using 2 and 3 normals, respectively. Our method achieves state-of-the-art results on three commonly used datasets (ShapeNetCore, ABC, and ScanNet). Code will be released upon acceptance

KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way

Robust and accurate pose estimation of a robotic platform, so-called sensor-based odometry, is an essential part of many robotic applications. While many sensor odometry systems made progress by adding more complexity to the ego-motion estimation process, we move in the opposite direction. By removing a majority of parts and focusing on the core elements, we obtain a surprisingly effective system that is simple to realize and can operate under various environmental conditions using different LiDAR sensors. Our odometry estimation approach relies on point-to-point ICP combined with adaptive thresholding for correspondence matching, a robust kernel, a simple but widely applicable motion compensation approach, and a point cloud subsampling strategy. This yields a system with only a few parameters that in most cases do not even have to be tuned to a specific LiDAR sensor. Our system using the same parameters performs on par with state-of-the-art methods under various operating conditions using different platforms: automotive platforms, UAV-based operation, vehicles like segways, or handheld LiDARs. We do not require integrating IMU information and solely rely on 3D point cloud data obtained from a wide range of 3D LiDAR sensors, thus, enabling a broad spectrum of different applications and operating conditions. Our open-source system operates faster than the sensor frame rate in all presented datasets and is designed for real-world scenarios.Comment: 8 page