Related papers: Shape DNA: Basic Generating Functions for Geometri…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…
Recent advances in diffusion-based generation techniques enable AI models to produce highly realistic videos, heightening the need for reliable detection mechanisms. However, existing detection methods provide only limited exploration of…
While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations…
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…
We propose Geometric Neural Parametric Models (GNPM), a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics, using a geometric-aware architecture on…
Our goal is to recognize material categories using images and geometry information. In many applications, such as construction management, coarse geometry information is available. We investigate how 3D geometry (surface normals, camera…
We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph…
Image pyramids are commonly used in modern computer vision tasks to obtain multi-scale features for precise understanding of images. However, image pyramids process multiple resolutions of images using the same large-scale model, which…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
With the increasing use of graph-structured data, there is also increasing interest in investigating graph data dependencies and their applications, e.g., in graph data profiling. Graph Generating Dependencies (GGDs) are a class of…
Existing generative models for 3D shapes are typically trained on a large 3D dataset, often of a specific object category. In this paper, we investigate the deep generative model that learns from only a single reference 3D shape.…
Mesh-based learning is one of the popular approaches nowadays to learn shapes. The most established backbone in this field is MeshCNN. In this paper, we propose infusing MeshCNN with geometric reasoning to achieve higher quality learning.…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
Image segmentation is a primary task in many medical applications. Recently, many deep networks derived from U-Net have been extensively used in various medical image segmentation tasks. However, in most of the cases, networks similar to…
The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…
While recent advances in generative latent spaces have driven substantial progress in single-image generation, the optimal latent space for novel view synthesis (NVS) remains largely unexplored. In particular, NVS requires geometrically…