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High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Controllable generation of 3D assets is important for many practical applications like content creation in movies, games and engineering, as well as in AR/VR. Recently, diffusion models have shown remarkable results in generation quality of…

Feature descriptors of point clouds are used in several applications, such as registration and part segmentation of 3D point clouds. Learning discriminative representations of local geometric features is unquestionably the most important…

Learning new representations of 3D point clouds is an active research area in 3D vision, as the order-invariant point cloud structure still presents challenges to the design of neural network architectures. Recent works explored learning…

3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point…

LiDAR point clouds contain measurements of complicated natural scenes and can be used to update digital elevation models, glacial monitoring, detecting faults and measuring uplift detecting, forest inventory, detect shoreline and beach…

Extracting high-level structural information from 3D point clouds is challenging but essential for tasks like urban planning or autonomous driving requiring an advanced understanding of the scene at hand. Existing approaches are still not…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

Deep neural networks are widely used for understanding 3D point clouds. At each point convolution layer, features are computed from local neighborhoods of 3D points and combined for subsequent processing in order to extract semantic…

Learning local descriptors is an important problem in computer vision. While there are many techniques for learning local patch descriptors for 2D images, recently efforts have been made for learning local descriptors for 3D points. The…

Neural networks transform data through learned representations whose geometry affects separation, contraction, and generalization. Recent work studies this geometry using discrete curvature on neighborhood graphs, suggesting Ricci-flow-like…

We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An…

We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…

In this paper, we propose using curvatures in digital space for 3D object analysis and recognition. Since direct adjacency has only six types of digital surface points in local configurations, it is easy to determine and classify the…

Diffusion probabilistic models are traditionally used to generate colors at fixed pixel positions in 2D images. Building on this, we extend diffusion models to point cloud semantic segmentation, where point positions also remain fixed, and…

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…

Semantic segmentation of aerial point cloud data can be utilised to differentiate which points belong to classes such as ground, buildings, or vegetation. Point clouds generated from aerial sensors mounted to drones or planes can utilise…

Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

How can we tell complex point clouds with different small scale characteristics apart, while disregarding global features? Can we find a suitable transformation of such data in a way that allows to discriminate between differences in this…