A novel geometry image to accurately represent a surface by preserving mesh topology

Abstract Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the...

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Autores principales:	Sheng Zeng, Guohua Geng, Hongjuan Gao, Mingquan Zhou
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/8760785a0ebf467fa1981cd34926b26d
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id	oai:doaj.org-article:8760785a0ebf467fa1981cd34926b26d
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spelling	oai:doaj.org-article:8760785a0ebf467fa1981cd34926b26d2021-11-21T12:20:06ZA novel geometry image to accurately represent a surface by preserving mesh topology10.1038/s41598-021-01722-42045-2322https://doaj.org/article/8760785a0ebf467fa1981cd34926b26d2021-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-01722-4https://doaj.org/toc/2045-2322Abstract Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the gridlines the existing geometry images. Thus, errors are unavoidable when a 3D mesh is reconstructed from the chart. In this paper, we propose parameterise surface onto a novel geometry image that preserves the constraint of topological neighbourhood information at integer coordinate points on a 2D grid and ensures that the shape of the reconstructed 3D mesh does not change from supplemented image data. We find a collection of edges that opens the mesh into simply connected surface with a single boundary. The point distribution with approximate blue noise spectral characteristics is computed by capacity-constrained delaunay triangulation without retriangulation. We move the vertices to the constrained mesh intersection, adjust the degenerate triangles on a regular grid, and fill the blank part by performing a local affine transformation between each triangle in the mesh and image. Unlike other geometry images, the proposed method results in no error in the reconstructed surface model when floating-point data are stored in the image. High reconstruction accuracy is achieved when the xyz positions are in a 16-bit data format in each image channel because only rounding errors exist in the topology-preserving geometry images, there are no sampling errors. This method performs one-to-one mapping between the 3D surface mesh and the points in the 2D image, while foldovers do not appear in the 2D triangular mesh, maintaining the topological structure. This also shows the potential of using a 2D image processing algorithm to process 3D models.Sheng ZengGuohua GengHongjuan GaoMingquan ZhouNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Sheng Zeng Guohua Geng Hongjuan Gao Mingquan Zhou A novel geometry image to accurately represent a surface by preserving mesh topology
description	Abstract Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the gridlines the existing geometry images. Thus, errors are unavoidable when a 3D mesh is reconstructed from the chart. In this paper, we propose parameterise surface onto a novel geometry image that preserves the constraint of topological neighbourhood information at integer coordinate points on a 2D grid and ensures that the shape of the reconstructed 3D mesh does not change from supplemented image data. We find a collection of edges that opens the mesh into simply connected surface with a single boundary. The point distribution with approximate blue noise spectral characteristics is computed by capacity-constrained delaunay triangulation without retriangulation. We move the vertices to the constrained mesh intersection, adjust the degenerate triangles on a regular grid, and fill the blank part by performing a local affine transformation between each triangle in the mesh and image. Unlike other geometry images, the proposed method results in no error in the reconstructed surface model when floating-point data are stored in the image. High reconstruction accuracy is achieved when the xyz positions are in a 16-bit data format in each image channel because only rounding errors exist in the topology-preserving geometry images, there are no sampling errors. This method performs one-to-one mapping between the 3D surface mesh and the points in the 2D image, while foldovers do not appear in the 2D triangular mesh, maintaining the topological structure. This also shows the potential of using a 2D image processing algorithm to process 3D models.
format	article
author	Sheng Zeng Guohua Geng Hongjuan Gao Mingquan Zhou
author_facet	Sheng Zeng Guohua Geng Hongjuan Gao Mingquan Zhou
author_sort	Sheng Zeng
title	A novel geometry image to accurately represent a surface by preserving mesh topology
title_short	A novel geometry image to accurately represent a surface by preserving mesh topology
title_full	A novel geometry image to accurately represent a surface by preserving mesh topology
title_fullStr	A novel geometry image to accurately represent a surface by preserving mesh topology
title_full_unstemmed	A novel geometry image to accurately represent a surface by preserving mesh topology
title_sort	novel geometry image to accurately represent a surface by preserving mesh topology
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/8760785a0ebf467fa1981cd34926b26d
work_keys_str_mv	AT shengzeng anovelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT guohuageng anovelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT hongjuangao anovelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT mingquanzhou anovelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT shengzeng novelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT guohuageng novelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT hongjuangao novelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology AT mingquanzhou novelgeometryimagetoaccuratelyrepresentasurfacebypreservingmeshtopology
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A novel geometry image to accurately represent a surface by preserving mesh topology

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