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The convolutional neural network (CNN) features can give a good description of image content, which usually represent images with unique global vectors. Although they are compact compared to local descriptors, they still cannot efficiently…

A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…

We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces…

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…

Spatial representation learning is essential for GeoAI applications such as urban analytics, enabling the encoding of shapes, locations, and spatial relationships (topological and distance-based) of geo-entities like points, polylines, and…

This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

Despite their success, modern convolutional neural networks (CNNs) exhibit fundamental limitations, including data inefficiency, poor out-of-distribution generalization, and vulnerability to adversarial perturbations. These shortcomings can…

We discuss how the geometric theory of differential equations can be used for the numerical integration and visualisation of implicit ordinary differential equations, in particular around singularities of the equation. The Vessiot theory…

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…

Generating a coherent 3D scene representation from multi-view images is a fundamental yet challenging task. Existing methods often struggle with multi-view fusion, leading to fragmented 3D representations and sub-optimal performance. To…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

Recent generative models can create visually plausible 3D representations of objects. However, the generation process often allows for implicit control signals, such as contextual descriptions, and rarely supports bold geometric distortions…

Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…

Visualizations of set systems frequently use enclosing geometries for the sets in combination with reduced representations of the elements, such as short text labels, small glyphs, or points. Hence they are generally unable to adequately…