Voronoi-Based Geometry Estimator for 3D Digital Surfaces

Cuel, Louis; Lachaud, Jacques-Olivier; Thibert, Boris

doi:10.1007/978-3-319-09955-2_12

Cited by 15 publications

(18 citation statements)

References 14 publications

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“…When the input data is a complete or partial mesh, the normal is simply estimated as the cross product of face edges. When the input data is a digital object or a height map, we use the digital Voronoi Covariance Measure [9] to estimate the normal vector. Parameters of this estimator are easily set since we know the radius of the tubular object; they also have little influence on the result, since the accumulation image makes the process very robust.…”

Section: Reconstruction Results and Geometric Analysismentioning

confidence: 99%

3D Geometric Analysis of Tubular Objects Based on Surface Normal Accumulation

Kerautret

Krähenbühl

Debled-Rennesson

et al. 2015

Image Analysis and Processing — ICIAP 2015

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Abstract. This paper proposes a simple and efficient method for the reconstruction and extraction of geometric parameters from 3D tubular objects. Our method constructs an image that accumulates surface normal information, then peaks within this image are located by tracking. Finally, the positions of these are optimized to lie precisely on the tubular shape centerline. This method is very versatile, and is able to process various input data types like full or partial mesh acquired from 3D laser scans, 3D height map or discrete volumetric images. The proposed algorithm is simple to implement, contains few parameters and can be computed in linear time with respect to the number of surface faces. Since the extracted tube centerline is accurate, we are able to decompose the tube into rectilinear parts and torus-like parts. This is done with a new linear time 3D torus detection algorithm, which follows the same principle of a previous work on 2D arc circle recognition. Detailed experiments show the versatility, accuracy and robustness of our new method.

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Section: Reconstruction Results and Geometric Analysismentioning

confidence: 99%

3D Geometric Analysis of Tubular Objects Based on Surface Normal Accumulation

Kerautret

Krähenbühl

Debled-Rennesson

et al. 2015

Image Analysis and Processing — ICIAP 2015

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“…However it requires three parameters that are difficult to set for a large class of shapes. Note that the digital version of the VCM has also some multigrid convergence properties for normal directions [18], and this is the implementation we used in our experiments.…”

Section: Mérigot's Voronoi Covariance Measure (Vcm) [8]mentioning

confidence: 99%

Scale-space feature extraction on digital surfaces

Levallois

Cœurjolly

Lachaud

2015

Computers & Graphics

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a b s t r a c tA classical problem in many computer graphics applications consists in extracting significant zones or points on an object surface, like loci of tangent discontinuity (edges), maxima or minima of curvatures, inflection points, etc. These places have specific local geometrical properties and often called generically features. An important problem is related to the scale, or range of scales, for which a feature is relevant. We propose a new robust method to detect features on digital data (surface of objects in Z 3 , which exploits asymptotic properties of recent digital curvature estimators. In Coeurjolly et al.[1] and Levallois et al. [1,2], authors have proposed curvature estimators (mean, principal and Gaussian) on 2D and 3D digitized shapes and have demonstrated their multigrid convergence (for C 3 -smooth surfaces). Since such approaches integrate local information within a ball around points of interest, the radius is a crucial parameter. In this paper, we consider the radius as a scale-space parameter. By analyzing the behavior of such curvature estimators as the ball radius tends to zero, we propose a tool to efficiently characterize and extract several relevant features (edges, smooth and flat parts) on digital surfaces.

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“…It is a measure, first introduced in Mérigot et al (2011) on point clouds which was used to estimate normals. The VCM was also defined on sets of voxels in Cuel et al (2014) and was proven to be a reliable tool to estimate the surface normal. This measure was shown to be resilient to Hausdorff noise and to outliers (Cuel et al, 2015).…”

Section: Voronoi Covariance Measurementioning

confidence: 99%

New methods for the geometrical analysis of tubular organs

Grélard¹,

Baldacci²,

Vialard³

et al. 2017

Medical Image Analysis

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This paper presents new methods to study the shape of tubular organs. Determining precise cross-sections is of major importance to perform geometrical measurements, such as diameter, wall-thickness estimation or area measurement. Our first contribution is a robust method to estimate orthogonal planes based on the Voronoi Covariance Measure. Our method is not relying on a curve-skeleton computation beforehand. This means our orthogonal plane estimator can be used either on the skeleton or on the volume. Another important step towards tubular organ characterization is achieved through curve-skeletonization, as skeletons allow to compare two tubular organs, and to perform virtual endoscopy. Our second contribution is dedicated to correcting common defects of the skeleton by new pruning and recentering methods. Finally, we propose a new method for curve-skeleton extraction. Various results are shown on different types of segmented tubular organs, such as neurons, airway-tree and blood vessels.

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Voronoi-Based Geometry Estimator for 3D Digital Surfaces

Cited by 15 publications

References 14 publications

3D Geometric Analysis of Tubular Objects Based on Surface Normal Accumulation

3D Geometric Analysis of Tubular Objects Based on Surface Normal Accumulation

Scale-space feature extraction on digital surfaces

New methods for the geometrical analysis of tubular organs

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