2,683 research outputs found
GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
We present two new Lagrangian methods for hydrodynamics, in a systematic
comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The
new methods are designed to simultaneously capture advantages of both
smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement
(AMR) schemes. They are based on a kernel discretization of the volume coupled
to a high-order matrix gradient estimator and a Riemann solver acting over the
volume 'overlap.' We implement and test a parallel, second-order version of the
method with self-gravity & cosmological integration, in the code GIZMO: this
maintains exact mass, energy and momentum conservation; exhibits superior
angular momentum conservation compared to all other methods we study; does not
require 'artificial diffusion' terms; and allows the fluid elements to move
with the flow so resolution is automatically adaptive. We consider a large
suite of test problems, and find that on all problems the new methods appear
competitive with moving-mesh schemes, with some advantages (particularly in
angular momentum conservation), at the cost of enhanced noise. The new methods
have many advantages vs. SPH: proper convergence, good capturing of
fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical
viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing.
Advantages vs. non-moving meshes include: automatic adaptivity, dramatically
reduced advection errors & numerical overmixing, velocity-independent errors,
accurate coupling to gravity, good angular momentum conservation and
elimination of 'grid alignment' effects. We can, for example, follow hundreds
of orbits of gaseous disks, while AMR and SPH methods break down in a few
orbits. However, fixed meshes minimize 'grid noise.' These differences are
important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code,
user's guide, test problem setups, and movies are available at
http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm
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
Static/Dynamic Filtering for Mesh Geometry
The joint bilateral filter, which enables feature-preserving signal smoothing
according to the structural information from a guidance, has been applied for
various tasks in geometry processing. Existing methods either rely on a static
guidance that may be inconsistent with the input and lead to unsatisfactory
results, or a dynamic guidance that is automatically updated but sensitive to
noises and outliers. Inspired by recent advances in image filtering, we propose
a new geometry filtering technique called static/dynamic filter, which utilizes
both static and dynamic guidances to achieve state-of-the-art results. The
proposed filter is based on a nonlinear optimization that enforces smoothness
of the signal while preserving variations that correspond to features of
certain scales. We develop an efficient iterative solver for the problem, which
unifies existing filters that are based on static or dynamic guidances. The
filter can be applied to mesh face normals followed by vertex position update,
to achieve scale-aware and feature-preserving filtering of mesh geometry. It
also works well for other types of signals defined on mesh surfaces, such as
texture colors. Extensive experimental results demonstrate the effectiveness of
the proposed filter for various geometry processing applications such as mesh
denoising, geometry feature enhancement, and texture color filtering
Drift-diffusion models for innovative semiconductor devices and their numerical solution
We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization
Geometric Structure Extraction and Reconstruction
Geometric structure extraction and reconstruction is a long-standing problem in research communities including computer graphics, computer vision, and machine learning. Within different communities, it can be interpreted as different subproblems such as skeleton extraction from the point cloud, surface reconstruction from multi-view images, or manifold learning from high dimensional data. All these subproblems are building blocks of many modern applications, such as scene reconstruction for AR/VR, object recognition for robotic vision and structural analysis for big data. Despite its importance, the extraction and reconstruction of a geometric structure from real-world data are ill-posed, where the main challenges lie in the incompleteness, noise, and inconsistency of the raw input data. To address these challenges, three studies are conducted in this thesis: i) a new point set representation for shape completion, ii) a structure-aware data consolidation method, and iii) a data-driven deep learning technique for multi-view consistency. In addition to theoretical contributions, the algorithms we proposed significantly improve the performance of several state-of-the-art geometric structure extraction and reconstruction approaches, validated by extensive experimental results
Radial Basis Functions: Biomedical Applications and Parallelization
Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc.
The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method.
Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work
Surface Denoising based on Normal Filtering in a Robust Statistics Framework
During a surface acquisition process using 3D scanners, noise is inevitable
and an important step in geometry processing is to remove these noise
components from these surfaces (given as points-set or triangulated mesh). The
noise-removal process (denoising) can be performed by filtering the surface
normals first and by adjusting the vertex positions according to filtered
normals afterwards. Therefore, in many available denoising algorithms, the
computation of noise-free normals is a key factor. A variety of filters have
been introduced for noise-removal from normals, with different focus points
like robustness against outliers or large amplitude of noise. Although these
filters are performing well in different aspects, a unified framework is
missing to establish the relation between them and to provide a theoretical
analysis beyond the performance of each method.
In this paper, we introduce such a framework to establish relations between a
number of widely-used nonlinear filters for face normals in mesh denoising and
vertex normals in point set denoising. We cover robust statistical estimation
with M-smoothers and their application to linear and non-linear normal
filtering. Although these methods originate in different mathematical theories
- which include diffusion-, bilateral-, and directional curvature-based
algorithms - we demonstrate that all of them can be cast into a unified
framework of robust statistics using robust error norms and their corresponding
influence functions. This unification contributes to a better understanding of
the individual methods and their relations with each other. Furthermore, the
presented framework provides a platform for new techniques to combine the
advantages of known filters and to compare them with available methods
BRUISE DETECTION IN APPLES USING 3D INFRARED IMAGING AND MACHINE LEARNING TECHNOLOGIES
Bruise detection plays an important role in fruit grading. A bruise detection system capable of finding and removing damaged products on the production lines will distinctly improve the quality of fruits for sale, and consequently improve the fruit economy. This dissertation presents a novel automatic detection system based on surface information obtained from 3D near-infrared imaging technique for bruised apple identification. The proposed 3D bruise detection system is expected to provide better performance in bruise detection than the existing 2D systems.
We first propose a mesh denoising filter to reduce noise effect while preserving the geometric features of the meshes. Compared with several existing mesh denoising filters, the proposed filter achieves better performance in reducing noise effect as well as preserving bruised regions in 3D meshes of bruised apples. Next, we investigate two different machine learning techniques for the identification of bruised apples. The first technique is to extract hand-crafted feature from 3D meshes, and train a predictive classifier based on hand-crafted features. It is shown that the predictive model trained on the proposed hand-crafted features outperforms the same models trained on several other local shape descriptors. The second technique is to apply deep learning to learn the feature representation automatically from the mesh data, and then use the deep learning model or a new predictive model for the classification. The optimized deep learning model achieves very high classification accuracy, and it outperforms the performance of the detection system based on the proposed hand-crafted features. At last, we investigate GPU techniques for accelerating the proposed apple bruise detection system. Specifically, the dissertation proposes a GPU framework, implemented in CUDA, for the acceleration of the algorithm that extracts vertex-based local binary patterns. Experimental results show that the proposed GPU program speeds up the process of extracting local binary patterns by 5 times compared to a single-core CPU program
Piecewise smooth reconstruction of normal vector field on digital data
International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]
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