Extraction of curve-skeletons is a fundamental problem with many applications in computer graphics and visualization. In this paper, we present a simple and robust skeleton extraction method based on mesh contraction. The method works directly on the mesh domain, without pre-sampling the mesh model into a volumetric representation. The method first contracts the mesh geometry into zero-volume skeletal shape by applying implicit Laplacian smoothing with global positional constraints. The contraction does not alter the mesh connectivity and retains the key features of the original mesh. The contracted mesh is then converted into a 1D curve-skeleton through a connectivity surgery process to remove all the collapsed faces while preserving the shape of the contracted mesh and the original topology. The centeredness of the skeleton is refined by exploiting the induced skeleton-mesh mapping. In addition to producing a curve skeleton, the method generates other valuable information about the object's geometry, in particular, the skeleton-vertex correspondence and the local thickness, which are useful for various applications. We demonstrate its effectiveness in mesh segmentation and skinning animation.

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Skeleton extraction by mesh contraction

Curve-skeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curve-skeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.

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Curve-Skeleton Properties, Applications, and Algorithms

Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow

A survey on skeletonization algorithms and their applications

We present an algorithm for curve skeleton extraction via Laplacian-based contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeleton-based manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeleton-driven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easy-to-manipulate structure for effective topology modification, leading to more faithful surface reconstruction.

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Point Cloud Skeletons via Laplacian Based Contraction

A curve-skeleton of a 3D object is a stick-like figure or centerline representation of that object. It is used for diverse applications, including virtual colonoscopy and animation. In this paper, we introduce the concept of hierarchical curve-skeletons and describe a general and robust methodology that computes a family of increasingly detailed curve-skeletons. The algorithm is based upon computing a repulsive force field over a discretization of the 3D object and using topological characteristics of the resulting vector field, such as critical points and critical curves, to extract the curve-skeleton. We demonstrate this method on many different types of 3D objects (volumetric, polygonal and scattered point sets) and discuss various extensions of this approach.

Computing hierarchical curve-skeletons of 3D objects

In this paper a stochastic analysis of the quantization error in a stereo imaging system has been presented. Further the probability density function of the range estimation error and the expected value of the range error magnitude are derived in terms of various design parameters. Further the relative range error is proposed.

Quantization Error in Stereo Imaging systems

The process of reconstruction of a line in 3-D space from a pair of arbitrary perspective views obtains the set of parameters representing the line. This method is widely used in many applications of 3-D object recognition and machine inspection. However in certain applications which require a large degree of accuracy, a study of errors in the process of reconstruction, with the help of a rigorous performance analysis is necessary. In this paper we derive a set of inverse perspective equations for reconstruction of a line in 3-D space based on coplanarity equations. We assume the correspondence between the pair of projections of the line on the image planes. Simulation studies were conducted to observe the effect of noise on errors in the process of reconstruction. We present this performance analysis illustrating the effect of noise and parameters of imaging setup, on errors in reconstruction. Smaller resolution of the image, certain geometric conditions of the line and imaging setup produce poor perform...

Error analysis in reconstruction of a line in 3-D from two arbitrary perspective views

The issues involved in the reconstruction of a quadratic curve in 3-D space from arbitrary perspective projections are described in this paper. Correspondence between the projections of the curve on the image planes is assumed to be established. Equations for reconstruction of the 3-D curve, which give the parameters of the 3-D quadratic curve are determined. Uniqueness of the solution in the process of reconstruction is addressed and solved using additional constraints. As practical examples, reconstruction of circles, parabolas and pair of straight lines in 3-D space are demonstrated.

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Reconstruction of Quadratic Curves in 3-D from Two or More Perspective Views

Objects in nature as well as man made are bound by planar as well as curvilinear surfaces. Hence the reconstruction process of three dimensional objects involves obtaining the geometrical attributes of these planar and curvilinear surfaces, lines, points etc. If a line in 3-D space is viewed from two arbitrary positions, two different images of the same line are obtained. The correspondence between this pair of projections of the line is assumed to be established in this work. The work presented in this paper describes a method of reconstruction of a line in 3-D as an intersection of two planes containing the respective projected line images. The parameters of the line in 3-D space are obtained from the parameters of projected images of the line. Relevant mathematical formulations and analytical solutions for obtaining the parameters of the reconstructed line are given. The effect of noise in the reconstruction and the efficiency of the described reconstruction methodology are studied by simulation studies.

Simulation Studies For The Performance Analysis Of The Reconstruction Of A Line In 3-D From Two Arbitrary Perspective Views Using Two Plane Intersection Method

Raman Balasubramanian

Papers

Computing hierarchical curve-skeletons of 3D objects

Quantization Error in Stereo Imaging systems

Error analysis in reconstruction of a line in 3-D from two arbitrary perspective views

Reconstruction of Quadratic Curves in 3-D from Two or More Perspective Views

Simulation Studies For The Performance Analysis Of The Reconstruction Of A Line In 3-D From Two Arbitrary Perspective Views Using Two Plane Intersection Method