Related papers: Shape DNA: Basic Generating Functions for Geometri…

A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge is to synthesize microstructures, given a finite number of…

Deformable shapes provide important and complex geometric features of objects presented in images. However, such information is oftentimes missing or underutilized as implicit knowledge in many image analysis tasks. This paper presents…

Molecule generation is a very important practical problem, with uses in drug discovery and material design, and AI methods promise to provide useful solutions. However, existing methods for molecule generation focus either on 2D graph…

We proposed a kind of naturally combined shape-color affine moment invariants (SCAMI), which consider both shape and color affine transformations simultaneously in one single system. In the real scene, color and shape deformations always…

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…

Due to its safety-critical property, the image-based diagnosis is desired to achieve robustness on out-of-distribution (OOD) samples. A natural way towards this goal is capturing only clinically disease-related features, which is composed…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these…

Deep learning based 3D shape generation methods generally utilize latent features extracted from color images to encode the semantics of objects and guide the shape generation process. These color image semantics only implicitly encode 3D…

Determining atomistic structures from characterization data is one of the most common yet intricate problems in materials science. Particularly in amorphous materials, proposing structures that balance realism and agreement with experiments…

Accurate prediction of physical properties is critical for discovering and designing novel materials. Machine learning technologies have attracted significant attention in the materials science community for their potential for large-scale…

The advancement of diverse generative deep learning models and their variants has furnished substantial insights for investigating quantum many-body problems. In this work, we design two models based on the foundational architecture of…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

The task of generating natural images from 3D scenes has been a long standing goal in computer graphics. On the other hand, recent developments in deep neural networks allow for trainable models that can produce natural-looking images with…

We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data…

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies.…

Geometrical and appearance quality requirements set the limits of the current industrial performance in injection molding. To guarantee the product's quality, it is necessary to adjust the process settings in a closed loop. Those…