Finding ridges and valleys in a discrete surface using a modified MLS approximation

Kim, Soo-Kyun; Kim, Chang-Hun

doi:10.1016/j.cad.2005.10.004

Cited by 24 publications

(12 citation statements)

References 21 publications

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“…Implicit surface fitting is a promising method for ridge-valley lines detection, but the computation time cost is high. Kim et al [23] employ enhanced movingleast-squares approximation to estimate curvatures and corresponding derivatives on each vertex. They reduce the time-complexity compared to Ohtake et al [16] in approximation, which can be seen from their table of curvatures and their derivatives estimation statistics (Table 1).…”

Section: Curves On 3d Meshesmentioning

confidence: 99%

The Extraction of Feature Lines on 3D Models: A Survey

Quan

Meng

Zhang

2014

2014 International Conference on Virtual Reality and Visualization

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Feature lines are perceptually important features on 3D models, and have extensive applications such as mesh simplification, re-gridding, shape analysis, nonphotorealistic rendering and surface smoothing, etc.. This paper gives a comprehensive survey on this field, which has not been summarized before. According to whether feature lines are associated with the line of sight, feature lines can be classified into two categories: viewdependent curves and view-independent curves. Besides, view-independent curves can be further classified according to the type of 3D models, and view-dependent curves can be classified according to the property of feature lines. A complete classified method of feature lines on 3D models is proposed in this paper, and the challenges for feature extraction are also discussed briefly.

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Section: Curves On 3d Meshesmentioning

confidence: 99%

The Extraction of Feature Lines on 3D Models: A Survey

Quan

Meng

Zhang

2014

2014 International Conference on Virtual Reality and Visualization

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“…Curvatures and their derivatives are estimated at mesh vertices by fitting smooth surfaces locally or over the entire mesh such as compactly supported radial basis functions [32], polynomials [25], [28], [33], MLS based implicit functions [34] or using discrete methods [24], [25]. Ridges are traced by detecting zero crossings of the ridge function on the vertices and edges of the meshes.…”

Section: Implicitsmentioning

confidence: 99%

Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines

Musuvathy

Martín

Cohen

2010

2010 Shape Modeling International Conference

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Ridges are extremal curves of principal curvatures on a surface that indicate salient intrinsic features of its shape. This paper presents a novel approach for extracting ridges of improved quality from isosurfaces of volumetric scalar-valued grids by converting them to implicit trivariate B-spline representations. A robust tracing approach demonstrated to extract ridges accurately from parametric Bspline surfaces is extended to extract ridges directly from the implicit representations resulting in accurate and hence smoother, connected ridge curves as compared to approaches that extract ridges directly from discrete representations. This approach can also be used to extract ridges directly from smooth representations such as isosurfaces of volumetric BSpline CAD models and algebraic functions, and extended to extract ridges from polygonal meshes, as demonstrated in the paper. Most of the existing approaches for ridge extraction address only crests, a certain subset of the ridges on a surface. The approach presented in this paper enables extraction of all types of generic ridges on a surface thereby presenting a complete solution.

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“…The main approaches here are local polynomial fitting [2,3,16], the use of discrete differential operators [12], and various combinations of continuous and discrete techniques [23,37]. While estimating surface curvatures and their derivatives with geometrically inspired discrete differential operators [12,27] is much more elegant than using fitting methods, the former usually requires noise elimination and the latter seems more robust.…”

Section: Problem Setting and Solutionmentioning

confidence: 99%

Fast and Faithful Geometric Algorithm for Detecting Crest Lines on Meshes

Yoshizawa

Belyaev

Yokota

et al. 2007

15th Pacific Conference on Computer Graphics and Applications (PG'07)

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A new geometry-based finite difference method for a fast and reliable detection of perceptually salient curvature extrema on surfaces approximated by dense triangle meshes is proposed. The foundations of the method are two simple curvature and curvature derivative formulas overlooked in modern differential geometry textbooks and seemingly new observation about inversion-invariant local surface-based differential forms. Problem setting and solutionThis paper is inspired by two simple but beautiful formulas of classical differential geometry and a seemingly new observation about inversion-invariant local surface-based differential forms. The formulas and observation are the key ingredients of our approach to fast and reliable detection of the so-called crest lines [30], salient subsets of the extrema of the surface principal curvatures along their corresponding curvature lines.Related work. The full set of such extrema, frequently called ridges [25], corresponds to the edges of regression of the envelopes of the surface normals and was first studied by A. Gullstrand in connection with his work in ophthalmology (1911 Nobel Prize in Physiology and Medicine). Since then the ridges and their subsets were frequently used for shape interrogation purposes (see, for example, [14, Sect. 7.4], [11, Chap. 6], [26, Chap. 11], and references therein). The ridges possess many interesting properties. In particular, they can be defined as the loci of surface points where the osculating spheres have high-order contacts with the surface and, therefore, the ridges are invariant under inversion of the surface w.r.t. any sphere [25].The principal difficulty in detecting the crest lines and similar features on discrete surfaces consists of achieving an accurate estimation of surface curvatures and their derivatives. The main approaches here are local polynomial fitting [2,3,16], the use of discrete differential operators [12], and various combinations of continuous and discrete techniques [23,37]. While estimating surface curvatures and their derivatives with geometrically inspired discrete differential operators [12,27] is much more elegant than using fitting methods, the former usually requires noise elimination and the latter seems more robust. On the other hand, as pointed out in [27], fitting methods incorporate a certain amount of smoothing in the curvature and curvature derivative estimation processes and that amount is very difficult to control. Another limitation of fitting schemes consists of their relatively low speed to compare with discrete differential operators. Further, since predefined local primitives are used for fitting, one cannot expect a truly faithful estimation of surface differential properties.Our approach to estimating the surface's principal curvatures and their derivatives is pure geometrical.Two forgotten formulas. The first formula [33, §119] 1 states that for a smooth surface r oriented by its unit normal nwhere ∆ S is the Laplace-Beltrami operator (the surface Laplacian), ∇ S is the surface tangential g...

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Finding ridges and valleys in a discrete surface using a modified MLS approximation

Cited by 24 publications

References 21 publications

The Extraction of Feature Lines on 3D Models: A Survey

The Extraction of Feature Lines on 3D Models: A Survey

Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines

Fast and Faithful Geometric Algorithm for Detecting Crest Lines on Meshes

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