Related papers: Exact computation of the halfspace depth
In this paper, we focus on the task of 3D shape completion from partial point clouds using deep implicit functions. Existing methods seek to use voxelized basis functions or the ones from a certain family of functions (e.g., Gaussians),…
The common occurrence of occlusion-induced incompleteness in point clouds has made point cloud completion (PCC) a highly-concerned task in the field of geometric processing. Existing PCC methods typically produce complete point clouds from…
In this paper, we propose a method to segment regions in three-dimensional point clouds. We assume that (i) the shape and the number of regions in the point cloud are not known and (ii) the point cloud may be noisy. The method consists of…
John W. Tukey (1975) defined statistical data depth as a function that determines centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
Point clouds are often sparse and incomplete, which imposes difficulties for real-world applications. Existing shape completion methods tend to generate rough shapes without fine-grained details. Considering this, we introduce a two-branch…
The task of point cloud completion aims to predict the missing part for an incomplete 3D shape. A widely used strategy is to generate a complete point cloud from the incomplete one. However, the unordered nature of point clouds will degrade…
Point clouds are often sparse and incomplete. Existing shape completion methods are incapable of generating details of objects or learning the complex point distributions. To this end, we propose a cascaded refinement network together with…
The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization,…
We construct a method by which we can calculate the precision with which an algorithm identifies the shape of a cluster. We present our results for several well known clustering algorithms and suggest ways to improve performance for newer…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing…
Single-view point cloud completion aims to recover the full geometry of an object based on only limited observation, which is extremely hard due to the data sparsity and occlusion. The core challenge is to generate plausible geometries to…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
In this paper we study skyline queries in the distributed computational model, where we have $s$ remote sites and a central coordinator (the query node); each site holds a piece of data, and the coordinator wants to compute the skyline of…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
In the practical application of point cloud completion tasks, real data quality is usually much worse than the CAD datasets used for training. A small amount of noisy data will usually significantly impact the overall system's accuracy. In…
Depth estimation is an important step in many computer vision problems such as 3D reconstruction, novel view synthesis, and computational photography. Most existing work focuses on depth estimation from single frames. When applied to…
In view of the difficulty in reconstructing object details in point cloud completion, we propose a shape prior learning method for object completion. The shape priors include geometric information in both complete and the partial point…
We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation…