776 research outputs found
Geometric Approaches for 3D Shape Denoising and Retrieval
A key issue in developing an accurate 3D shape recognition system is to design an efficient shape
descriptor for which an index can be built, and similarity queries can be answered efficiently. While
the overwhelming majority of prior work on 3D shape analysis has concentrated primarily on rigid
shape retrieval, many real objects such as articulated motions of humans are nonrigid and hence
can exhibit a variety of poses and deformations.
Motivated by the recent surge of interest in content-based analysis of 3D objects in computeraided
design and multimedia computing, we develop in this thesis a unified theoretical and computational
framework for 3D shape denoising and retrieval by incorporating insights gained from
algebraic graph theory and spectral geometry. We first present a regularized kernel diffusion for
3D shape denoising by solving partial differential equations in the weighted graph-theoretic framework.
Then, we introduce a computationally fast approach for surface denoising using the vertexcentered
finite volume method coupled with the mesh covariance fractional anisotropy. Additionally,
we propose a spectral-geometric shape skeleton for 3D object recognition based on the second
eigenfunction of the Laplace-Beltrami operator in a bid to capture the global and local geometry
of 3D shapes. To further enhance the 3D shape retrieval accuracy, we introduce a graph matching
approach by assigning geometric features to each endpoint of the shape skeleton. Extensive experiments
are carried out on two 3D shape benchmarks to assess the performance of the proposed
shape retrieval framework in comparison with state-of-the-art methods. The experimental results
show that the proposed shape descriptor delivers best-in-class shape retrieval performance
Time domain analysis of switching transient fields in high voltage substations
Switching operations of circuit breakers and disconnect switches generate transient currents propagating along the substation busbars. At the moment of switching, the busbars temporarily acts as antennae radiating transient electromagnetic fields within the substations. The radiated fields may interfere and disrupt normal operations of electronic equipment used within the substation for measurement, control and communication purposes. Hence there is the need to fully characterise the substation electromagnetic environment as early as the design stage of substation planning and operation to ensure safe operations of the electronic equipment. This paper deals with the computation of transient electromagnetic fields due to switching within a high voltage air-insulated substation (AIS) using the finite difference time domain (FDTD) metho
Feature preserving noise removal for binary voxel volumes using 3D surface skeletons
Skeletons are well-known descriptors that capture the geometry and topology of 2D and 3D shapes. We leverage these properties by using surface skeletons to remove noise from 3D shapes. For this, we extend an existing method that removes noise, but keeps important (salient) corners for 2D shapes. Our method detects and removes large-scale, complex, and dense multiscale noise patterns that contaminate virtually the entire surface of a given 3D shape, while recovering its main (salient) edges and corners. Our method can treat any (voxelized) 3D shapes and surface-noise types, is computationally scalable, and has one easy-to-set parameter. We demonstrate the added-value of our approach by comparing our results with several known 3D shape denoising methods
ShipGen: A Diffusion Model for Parametric Ship Hull Generation with Multiple Objectives and Constraints
Ship design is a years-long process that requires balancing complex design
trade-offs to create a ship that is efficient and effective. Finding new ways
to improve the ship design process can lead to significant cost savings for
ship building and operation. One promising technology is generative artificial
intelligence, which has been shown to reduce design cycle time and create
novel, high-performing designs. In literature review, generative artificial
intelligence has been shown to generate ship hulls; however, ship design is
particularly difficult as the hull of a ship requires the consideration of many
objectives. This paper presents a study on the generation of parametric ship
hull designs using a parametric diffusion model that considers multiple
objectives and constraints for the hulls. This denoising diffusion
probabilistic model (DDPM) generates the tabular parametric design vectors of a
ship hull for evaluation. In addition to a tabular DDPM, this paper details
adding guidance to improve the quality of generated ship hull designs. By
leveraging classifier guidance, the DDPM produced feasible parametric ship
hulls that maintain the coverage of the initial training dataset of ship hulls
with a 99.5% rate, a 149x improvement over random sampling of the design vector
parameters across the design space. Parametric ship hulls produced with
performance guidance saw an average of 91.4% reduction in wave drag
coefficients and an average of a 47.9x relative increase in the total displaced
volume of the hulls compared to the mean performance of the hulls in the
training dataset. The use of a DDPM to generate parametric ship hulls can
reduce design time by generating high-performing hull designs for future
analysis. These generated hulls have low drag and high volume, which can reduce
the cost of operating a ship and increase its potential to generate revenue
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Courbure discrète : théorie et applications
International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
Mathematical Imaging and Surface Processing
Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images.
This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains
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