Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds

Lozes, François; Elmoataz, Abderrahim; Lézoray, Olivier

doi:10.1109/tip.2014.2336548

Cited by 60 publications

(49 citation statements)

References 39 publications

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“…In [21], we have proposed a novel definition of patches that can be used for any graph representation associated with meshes or point clouds. In particular, around each vertex, we build a two-dimensional grid (the patch) describing the close neighborhood.…”

Section: Graph Construction From Images On 3d Point Cloudsmentioning

confidence: 99%

“…Figure 5 shows the filtering of a colored point cloud with several operators. The NLA 1 operator defined in Equation (47) corresponds to a filtering operator by alternating the process of non-local dilation and non-local erosion according to the sign of the curvature K w on the graph Equation (21). When w = 1, the filtering is unable to restore the colors on the point clouds.…”

Section: Local Non-local Inpainting and Filtering Of Images On Pointmentioning

confidence: 99%

“…In our previous works [21,22], we have proposed a different approach that can cope with both 3D meshes and point clouds of arbitrary connectivity. To achieve this goal, we proposed the Partial difference Equation (PdE) framework.…”

Section: Introductionmentioning

confidence: 99%

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Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

Elmoataz

Lozes

Talbot

2016

IJGI

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Partial Differential Equations (PDEs)-based morphology offers a wide range of continuous operators to address various image processing problems. Most of these operators are formulated as Hamilton-Jacobi equations or curve evolution level set and morphological flows. In our previous works, we have proposed a simple method to solve PDEs on point clouds using the framework of PdEs (Partial difference Equations) on graphs. In this paper, we propose to apply a large class of morphological-based operators on graphs for processing raw 3D point clouds and extend their applications for the processing of colored point clouds of geo-informatics 3D data. Through illustrations, we show that this simple framework can be used in the resolution of many applications for geo-informatics purposes.

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Section: Graph Construction From Images On 3d Point Cloudsmentioning

confidence: 99%

Section: Local Non-local Inpainting and Filtering Of Images On Pointmentioning

confidence: 99%

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Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

Elmoataz

Lozes

Talbot

2016

IJGI

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“…In [10], we have proposed a new definition of patches that can be used with any graph representation associated to meshes or point clouds. We detail the latter.…”

Section: Graph Weightsmentioning

confidence: 99%

PDE-Based Graph Signal Processing for 3-D Color Point Clouds: Opportunities for cultural heritage

Lozes

Elmoataz

Lézoray

2015

IEEE Signal Process. Mag.

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“…Macdonald et al [33] computed reaction-diffusion processes on point clouds. In [31], Lozes et al proposed a method to solve PDEs on point clouds for image processing using partial difference operators on weighted graphs.…”

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confidence: 99%

Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

Choi¹,

Ho²,

Lui³

2016

SIAM J. Imaging Sci.

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Abstract. Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh structure on point clouds. This task can be simplified with the aid of a parameterization. In particular, conformal parameterizations are advantageous in preserving the geometric information of the point cloud data. In this paper, we extend a state-of-the-art spherical conformal parameterization algorithm for genus-0 closed meshes to the case of point clouds, using an improved approximation of the Laplace-Beltrami operator on data points. Then, we propose an iterative scheme called the North-South reiteration for achieving a spherical conformal parameterization. A balancing scheme is introduced to enhance the distribution of the spherical parameterization. High quality triangulations and quadrangulations can then be built on the point clouds with the aid of the parameterizations. Also, the meshes generated are guaranteed to be genus-0 closed meshes. Moreover, using our proposed spherical conformal parameterization, multilevel representations of point clouds can be easily constructed. Experimental results demonstrate the effectiveness of our proposed framework.Key words. Mesh generation, Triangulation, Quadrangulation, Spherical conformal parameterization, Surface reconstruction, Point cloud, Multilevel representation 1. Introduction. Contemporary scanning technologies enable efficient acquisitions of 3D objects. Using modern 3D scanners, data points are sampled from the surfaces of 3D objects for further analyses and usages. Point clouds are widely applied in computer graphics, vision and many other engineering fields. However, the data points acquired by laser scanners are often complex and unorganized. Moreover, the absence of the connectivity information in point cloud data poses difficulties in understanding the underlying geometry of the 3D objects. This largely hinders the applications of the data. For instance, many applications in 3D printing [38,27] and texture mapping [39,24] are built upon mesh structures. With the rapid development of the computer industry, finding a high quality meshing framework for point cloud data is increasingly important.One possible approach for mesh generation on point clouds is to parameterize a point cloud to a simpler domain with the corresponding genus, such as the unit sphere for genus-0 point clouds. Then, a triangulation or a quadrangulation can be created on the parameter domain instead of the original complicated point cloud. Finally, a mesh structure on the point cloud can be defined with respect to the structure on the parameter domain. The major difficulty of computing parameterizations of point-set surfaces is the extremely limited information they can provide. Most of the existing surface parameterization methods are developed on meshes onl...

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Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds

Cited by 60 publications

References 39 publications

Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

PDE-Based Graph Signal Processing for 3-D Color Point Clouds: Opportunities for cultural heritage

Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

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