Related papers: Towards Stratified Space Learning: 2-complexes

In this paper we propose a new framework for point cloud instance segmentation. Our framework has two steps: an embedding step and a clustering step. In the embedding step, our main contribution is to propose a probabilistic embedding space…

Recovering high-quality surfaces from irregular point cloud is ill-posed unless strong geometric priors are available. We introduce an implicit self-prior approach that distills a shape-specific prior directly from the input point cloud…

We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral…

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…

We present a learning framework for abstracting complex shapes by learning to assemble objects using 3D volumetric primitives. In addition to generating simple and geometrically interpretable explanations of 3D objects, our framework also…

The abstraction of 3D objects with simple geometric primitives like cuboids allows to infer structural information from complex geometry. It is important for 3D shape understanding, structural analysis and geometric modeling. We introduce a…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

Learning meaningful abstract models of Markov Decision Processes (MDPs) is crucial for improving generalization from limited data. In this work, we show how geometric priors can be imposed on the low-dimensional representation manifold of a…

This paper addresses the task of estimating the 6 degrees of freedom pose of a known 3D object from depth information represented by a point cloud. Deep features learned by convolutional neural networks from color information have been the…

A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

Recent years have witnessed the surge of learned representations that directly build upon point clouds. Though becoming increasingly expressive, most existing representations still struggle to generate ordered point sets. Inspired by…

We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

In this paper, we revisit the classical representation of 3D point clouds as linear shape models. Our key insight is to leverage deep learning to represent a collection of shapes as affine transformations of low-dimensional linear shape…