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Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…

Surface roughness and texture are critical to the functional performance of engineering components. The ability to analyze roughness and texture effectively and efficiently is much needed to ensure surface quality in many surface generation…

In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…

In this work, we leverage informative embeddings from foundational models for unsupervised anomaly detection in medical imaging. For small datasets, a memory-bank of normative features can directly be used for anomaly detection which has…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

Oceanic eddy kinetic energy (EKE) is a key quantity for measuring the intensity of mesoscale eddies and for parameterizing eddy effects in ocean climate models. Three decades of satellite altimetry observations allow a global assessment of…

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in object trajectory prediction and simulation. While recent GNN-based approaches have…

We present a statistical model for $3$D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using…

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This…

We present a novel method for single image depth estimation using surface normal constraints. Existing depth estimation methods either suffer from the lack of geometric constraints, or are limited to the difficulty of reliably capturing…

This paper presents a deep normal filtering network, called DNF-Net, for mesh denoising. To better capture local geometry, our network processes the mesh in terms of local patches extracted from the mesh. Overall, DNF-Net is an end-to-end…

This paper proposes a 3D shape descriptor network, which is a deep convolutional energy-based model, for modeling volumetric shape patterns. The maximum likelihood training of the model follows an "analysis by synthesis" scheme and can be…

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

We introduce a differential visual similarity metric to train deep neural networks for 3D reconstruction, aimed at improving reconstruction quality. The metric compares two 3D shapes by measuring distances between multi-view images…

Chirality information (i.e. information that allows distinguishing left from right) is ubiquitous for various data modes in computer vision, including images, videos, point clouds, and meshes. While chirality has been extensively studied in…

Traditional machine learning (ML) algorithms, such as multiple regression, require human analysts to make decisions on how to treat the data. These decisions can make the model building process subjective and difficult to replicate for…

Shape descriptors, i.e., per-vertex features of 3D meshes or point clouds, are fundamental to shape analysis. Historically, various handcrafted geometry-aware descriptors and feature refinement techniques have been proposed. Recently,…

Human shape estimation has become increasingly important both theoretically and practically, for instance, in 3D mesh estimation, distance garment production and computational forensics, to mention just a few examples. As a further…

This article introduces three-filters-to-normal+ (3F2N+), an extension of our previous work three-filters-to-normal (3F2N), with a specific focus on incorporating discontinuity discrimination capability into surface normal estimators…