Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification

Cœurjolly, David; Dupont, Florent; Jospin, Laurent Valentin; Sivignon, Isabelle

doi:10.1007/11907350_35

Cited by 7 publications

(9 citation statements)

References 13 publications

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“…Regularization example on a digital sphere (r = 10). From left to right the original Marching-Cubes surface, the simplified one using [3] and our regularization. Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In 2d, we may quote early works for digital contour polygonalization, which use digital straightness properties to align digital points onto their estimated tangent line [2]. In 3d, reversible polyhedrization of digital surfaces can be achieved with greedy digital plane segmentation followed by Marching-Cubes sewing [3]. Although they are theoretically reversible, none of these techniques achieve similar visual quality compared to our proposal (see Figure 3) .…”

Section: Introductionmentioning

confidence: 95%

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Digital Surface Regularization by Normal Vector Field Alignment

Cœurjolly¹,

Gueth²,

Lachaud³

2017

Discrete Geometry for Computer Imagery

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Digital objects and digital surfaces are isothetic structures per se. Such surfaces are thus not adapted to direct visualization with isothetic quads, or to many geometry processing methods. We propose a new regularization technique to construct a piecewise smooth quadrangulated surface from a digital surface. More formally we propose a variational formulation which efficiently regularizes digital surface vertices while complying with a prescribed, eventually anisotropic, input normal vector field estimated on the digital structure. Beside visualization purposes, such regularized surface can then be used in any geometry processing tasks which operates on triangular or quadrangular meshes (e.g. compression, texturing, anisotropic smoothing, feature extraction).

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“…Regularization example on a digital sphere (r = 10). From left to right the original Marching-Cubes surface, the simplified one using [3] and our regularization. Fig.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Digital Surface Regularization by Normal Vector Field Alignment

Cœurjolly¹,

Gueth²,

Lachaud³

2017

Discrete Geometry for Computer Imagery

Self Cite

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“…But some work has to be done to propose a good definition for facets and to study the way to group them together to build a Euclidean polyhedron. The strategies used in [6] and in [4] could help us in that way. …”

Section: Resultsmentioning

confidence: 99%

3D noisy discrete objects: Segmentation and application to smoothing

Provot

Debled-Rennesson

2009

Pattern Recognition

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We propose in this paper a segmentation process that can deal with noisy discrete objects. A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the over-segmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object. A method to choose a seed and different segmentation strategies according to the shape of the surface are also proposed, as well as an application to smooth the border of convex noisy discrete objects.

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“…In all these, the coding compression methodology used is paramount. To overcome these types of difficulties, one can transform a discrete data set to a polyhedron P, such that the number of its 2-facets is as small as possible (see [22,23,37,58] for recent contributions to the subject).…”

Section: Polyhedral Reconstruction Of a 3d Digital Setmentioning

confidence: 99%

Some theoretical challenges in digital geometry: A perspective

Asano

Brimkov

Barneva

2009

Discrete Applied Mathematics

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a b s t r a c tIn recent years image analysis has become a research field of exceptional significance, due to its relevance to real life problems in important societal and governmental sectors, such as medicine, defense, and security. The explicit purpose of the present Perspective is to suggest a number of strategic objectives for theoretical research, with an emphasis on the combinatorial approach in image analysis. Most of the proposed objectives relate to the need to make the theoretical foundations of combinatorial image analysis better integrated within a number of well-established subjects of theoretical computer science and discrete applied mathematics, such as the theory of algorithms and problem complexity, combinatorial optimization and polyhedral combinatorics, integer and linear programming, and computational geometry.Published by Elsevier B.V.

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Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification

Cited by 7 publications

References 13 publications

Digital Surface Regularization by Normal Vector Field Alignment

Digital Surface Regularization by Normal Vector Field Alignment

3D noisy discrete objects: Segmentation and application to smoothing

Some theoretical challenges in digital geometry: A perspective

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