Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

We present a review of the state of the art of segmentation and partitioning techniques of boundary meshes. Recently, these have become a part of many mesh and object manipulation algorithms in computer graphics, geometric modelling and computer aided design. We formulate the segmentation problem as an optimization problem and identify two primarily distinct types of mesh segmentation, namely part segmentation and surface-patch segmentation. We classify previous segmentation solutions according to the different segmentation goals, the optimization criteria and features used, and the various algorithmic techniques employed. We also present some generic algorithms for the major segmentation techniques.

A survey on Mesh Segmentation Techniques

We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours or point sets. This survey is motivated in part by recent developments in space–time registration, where one seeks a correspondence between non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult because it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function and solution approach. We conclude the survey by discussing open problems and future perspectives.

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A Survey on Shape Correspondence

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.

/pdf/skeleton-extraction-by-mesh-contraction-3k4abhe37o.pdf

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.

/pdf/curve-skeleton-properties-applications-and-algorithms-8n6p5tz4yb.pdf

Curve-Skeleton Properties, Applications, and Algorithms

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

We present a 3D matching framework based on a many-to-many matching algorithm that works with skeletal representations of 3D volumetric objects. We demonstrate the performance of this approach on a large database of 3D objects containing more than 1000 exemplars. The method is especially suited to matching objects with distinct part structure and is invariant to part articulation. Skeletal matching has an intuitive quality that helps in defining the search and visualizing the results. In particular, the matching algorithm produces a direct correspondence between two skeletons and their parts, which can be used for registration and juxtaposition.

3D object retrieval using many-to-many matching of curve skeletons

Curve-skeletons are a 1D subset of the medial surface of a 3D object and are useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, mesh repair, 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.

Curve-skeleton applications

In this paper, we introduce the concept of spatial transfer functions as a unified approach to volume modeling and animation. A spatial transfer function is a function that defines the geometrical transformation of a scalar field in space, and is a generalization and abstraction of a variety of deformation methods. It facilitates a field based representation, and can thus be embedded into a volumetric scene graph under the algebraic framework of constructive volume geometry. We show that when spatial transfer functions are treated as spatial objects, constructive operations and conventional transfer functions can be applied to such spatial objects. We demonstrate spatial transfer functions in action with the aid of a collection of examples in volume visualization, sweeping, deformation and animation. In association with these examples, we describe methods for modeling and realizing spatial transfer functions, including simple procedural functions, operational decomposition of complex functions, large scale domain decomposition and temporal spatial transfer functions. We also discuss the implementation of spatial transfer functions in the vlib API and our efforts in deploying the technique in volume animation.

Nicu D. Cornea

Papers

Curve-Skeleton Properties, Applications, and Algorithms

Computing hierarchical curve-skeletons of 3D objects

3D object retrieval using many-to-many matching of curve skeletons

Curve-skeleton applications

Spatial transfer functions: a unified approach to specifying deformation in volume modeling and animation