Scale-space feature extraction on digital surfaces

Levallois, Jérémy; Cœurjolly, David; Lachaud, Jacques-Olivier

doi:10.1016/j.cag.2015.05.023

Cited by 5 publications

(12 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[PKG03] and Clarenz et. As shown in [LCL15], this technique does not provide sufficiently robust results on digital surfaces. [CRT04] use Principal Component Analysis on nearby data points.…”

Section: Related Workmentioning

confidence: 97%

“…Even if some existing approaches provide robust feature selection (VCM or [LCL15]), the global minimization of AT functional allows us to have more precise and thin delineation of sharp features. Even if some existing approaches provide robust feature selection (VCM or [LCL15]), the global minimization of AT functional allows us to have more precise and thin delineation of sharp features.…”

Section: Feature Extractionmentioning

confidence: 99%

“…al. [LCL15], which detects features in scale-space, using multigrid convergence properties of curvature estimation with digital integral invariants. It will be compared to our method in section 3.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Piecewise smooth reconstruction of normal vector field on digital data

Cœurjolly

Foare

Gueth

et al. 2016

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

a) (b) (c) (d) Figure 1: Piecewise smooth reconstruction of a normal vector field on a digital shape, normal vectors are represented through the flat shading of faces according to illumination (top-left: perfect digitization / down-right: noisy digitization): (a) input digital shape V , (b) input normal vector field g obtained with digital integral invariant (II) method [CLL14] with r = 3, (c) output normal vector field u and (d) sharpfeatures v superposed in red. Perfect and noisy digitization results are obtained using the same parameters. Our approach smoothes the input normal vector field except across sharp features, which are precisely delineated, thin, and consistent with the smoothing. AbstractWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-ofthe-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12].

show abstract

Section: Related Workmentioning

confidence: 97%

Section: Feature Extractionmentioning

confidence: 99%

See 1 more Smart Citation

Piecewise smooth reconstruction of normal vector field on digital data

Cœurjolly

Foare

Gueth

et al. 2016

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the contrary, at singular point x, we have: In other words, as R tends to zero, these quantities have a dominant 1 R term. We do not go further into details, please refer to [LCL15] for a complete state-of-the-art discussion and mathematical insights but feature detector on digital surfaces can be defined looking to the behavior of G X,x (R) and G X,x (R) for a given range of radii: if the quantities remain constant, we classify x as belonging to a smooth part of the object. If the quantities follow Q (R 1 ) speed, we classify x as belonging to an edge.…”

Section: Feature Detection With Multiscale Approachmentioning

confidence: 99%

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants

Lachaud¹,

Cœurjolly²,

Levallois³

2017

Modern Approaches to Discrete Curvature

Self Cite

View full text Add to dashboard Cite

We present, in details, a generic tool to estimate differential geometric quantities on digital shapes, which are subsets of Z d. This tool, called digital integral invariant, simply places a ball at the point of interest, and then examines the intersection of this ball with input data to infer local geometric information. Just counting the number of input points within the intersection provides curvature estimation in 2D and mean curvature estimation in 3D. The covariance matrix of the same point set allows to recover principal curvatures, principal directions and normal direction estimates in 3D. We show the multigrid convergence of all these estimators, which means that their estimations tend toward the exact geometric quantities onsmooth enough-Euclidean shapes digitized with finer and finer gridsteps. During the course of the chapter, we establish several multigrid convergence results of digital volume and moments estimators in arbitrary dimensions. Afterwards, we show how to set automatically the radius parameter while keeping multigrid convergence properties. Our estimators are then demonstrated to be accurate in practice, with extensive comparisons with state-of-the-art methods. To conclude the exposition, we discuss their robustness to perturbations and noise in input data and we show how such estimators can detect features using scale-space arguments.

show abstract

“…the local shape geometry using maximal digital straight segments of the digital boundary. In [8], these estimators have been analyzed in scale-space (for a range of radii) for a given digital shape. This allows to detect features of the shape thanks to the behavior of estimators on singularities.…”

Section: Curvature Tensor Estimationmentioning

confidence: 99%

Interactive Curvature Tensor Visualization on Digital Surfaces

Perrier

Levallois

Cœurjolly

et al. 2016

Discrete Geometry for Computer Imagery

Self Cite

View full text Add to dashboard Cite

Abstract. Interactive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures, principal directions and normal vector field). More precisely, we combine a fully parallel pipeline on GPU to extract an adaptive triangulated isosurface of the digital object, with a curvature tensor estimation at each surface point based on integral invariants. Integral invariants being parametrized by a given ball radius, our proposal allows to explore interactively different radii and thus select the appropriate scale at which the computation is performed and visualized.

show abstract

Scale-space feature extraction on digital surfaces

Cited by 5 publications

References 18 publications

Piecewise smooth reconstruction of normal vector field on digital data

Piecewise smooth reconstruction of normal vector field on digital data

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants

Interactive Curvature Tensor Visualization on Digital Surfaces

Contact Info

Product

Resources

About