Related papers: EuLearn: A 3D database for learning Euler characte…

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

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…

3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today…

This paper proposes an innovative approach to Hierarchical Edge Aware 3D Point Cloud Learning (HEA-Net) that seeks to address the challenges of noise in point cloud data, and improve object recognition and segmentation by focusing on edge…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…

Point clouds obtained from 3D scans are typically sparse, irregular, and noisy, and required to be consolidated. In this paper, we present the first deep learning based edge-aware technique to facilitate the consolidation of point clouds.…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous graph neural networks (GNN) require a large…

With the advent of deep learning application on edge devices, researchers actively try to optimize their deployments on low-power and restricted memory devices. There are established compression method such as quantization, pruning, and…

Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained…

In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we…

The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point…