Summary of Non-rigid 3D Shape Data Retrieval and Description

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered onto each others. Also, different deforming subjects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus, they need to be temporally aligned onto each others. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemmanian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories, or 1D curves, embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the L2 metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a Euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates, (2) the computation of geodesics between 4D surfaces, (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces, and (4) the synthesis of random 4D surfaces. We demonstrate the utility and performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

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4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data

10.36227/techrxiv.13629260.v1 ◽

2021 ◽

Author(s):

HAMID LAGA ◽

Marcel Padilla ◽

Ian H. Jermyn ◽

Sebastian Kurtek ◽

Mohammed Bennamoun ◽

...

Keyword(s):

Statistical Analysis ◽

Building Blocks ◽

Shape Space ◽

Spatiotemporal Variability ◽

3D Shape ◽

Execution Rates ◽

And Performance ◽

Body Shapes ◽

Spatiotemporal Registration ◽

Shape Data

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered onto each others. Also, different deforming subjects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus, they need to be temporally aligned onto each others. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemmanian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories, or 1D curves, embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the L2 metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a Euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates, (2) the computation of geodesics between 4D surfaces, (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces, and (4) the synthesis of random 4D surfaces. We demonstrate the utility and performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

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Shape Similarity Matching With Octree Representations

Volume 3: 26th Computers and Information in Engineering Conference ◽

10.1115/detc2006-99397 ◽

2006 ◽

Author(s):

Jingsheng Zhang ◽

Shana Smith

Keyword(s):

Shape Matching ◽

Shape Representation ◽

Data Retrieval ◽

Data File ◽

The Internet ◽

Shape Information ◽

Shape Representations ◽

3D Shape ◽

Space Efficiency ◽

Octree Representation

Shape matching is one of the fundamental problems in content-based 3D shape retrieval. Since there are typically a large number of possible matches in a shape database, there is a crucial need to perform shape matching efficiently. As a result, shapes must be reduced into a simpler shape representation, and computational complexity is one of the most important criteria for evaluating 3D shape representations. To meet the need, the investigators have implemented a new effective and efficient approach for 3D shape matching, which uses a simplified octree representation of 3D mesh models. The simplified octree representation was developed to improve time and space efficiency over prior representations. In addition, octree representations are rapidly becoming the standard file format for delivering 3D content across the Internet. The proposed approach stores octree information in XML files, rather than using a new data file type, to facilitate comparing models over the Internet. New methods for normalizing models, generating octrees, and comparing models were developed. The proposed approach allows users to efficiently exchange shape information and compare models over the Internet, in standardized data and data file formats, without transferring exact model files. The proposed approach is the first step in a project which will build a complete 3D model database and data retrieval system, which can be incorporated with other data mining techniques.

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Experimental Investigation of Behavior of Impinging Liquid Jet in a Shallow Pool by 3D-LIF

Volume 3: Student Paper Competition; Thermal-Hydraulics; Verification and Validation ◽

10.1115/icone2020-16233 ◽

2020 ◽

Author(s):

Sota Yamamura ◽

Fumihito Kimura ◽

Hiroyuki Yoshida ◽

Akiko Kaneko ◽

Yutaka Abe

Keyword(s):

Liquid Film ◽

3D Visualization ◽

Liquid Jet ◽

Water Pool ◽

Molten Material ◽

3D Shape ◽

The Core ◽

Severe Accidents ◽

Jet Velocity ◽

Shape Data

Abstract In some scenarios of severe accidents, the core materials melt and fall into a water pool in the lower plenum as a jet. The molten material jet is broken up, and heat transfer between molten material and coolant occurs. The aim of this study is to clarify the behavior of liquid jet falling into a shallow pool. In a previous study, it is clarified that, in a shallow pool, the jet spread radially after bottoming, and the atomization occurs with high flow velocity in a shallow pool. the detail of atomization and the spreading of the jet cannot be measured by the limitation of a 2D visualization method. In this study, a 3D-LIF method is used to obtain the detail 3D shape data of the jet. The 3D visualization of the jet is conducted. Using 3D shape data, the liquid film and the atomized droplet are measured. The initial jet velocity is selected as a parameter. As a result, following knowledge is obtained. The thickness of liquid film increases suddenly, and the radius of thin liquid flow increases with the increase of the initial jet velocity. The number of atomized droplets increases with the increase of the initial jet velocity. However, the size of the droplets are not influenced by the initial jet velocity.

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