Nicu D. Cornea

Curve-Skeleton Properties, Applications, and Algorithms

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.

Computing hierarchical curve-skeletons of 3D objects

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.

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

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.

Curve-skeleton applications

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.

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

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.

Real-time volume manipulation

In this paper, we describe a set of algorithms and an implementation (called VolEdit), for interactively manipulating 3D volumetric objects (datasets). The system utilizes skeletons, which allows users/animators to interactively and intuitively specify the location and type of deformation desired. The skeleton is extracted automatically from the volumetric model and indexes the appropriate part of the volume that needs to be transformed by defining piecewise bounds of the volume. The deformed volume is then reconstructed and rendered using commodity graphics cards. The system performs in real-time with near-interactive speeds. The VolEdit system is demonstrated with two volumes, the Visible Human Dataset and a colon MRI dataset.

A generalized family of fixed-radius distribution-based distance measures for content-based fMRI image retrieval

We present a family of distance measures for comparing activation patterns captured in fMRI images. We model an fMRI image as a spatial object with varying density, and measure the distance between two fMRI images using a novel fixed-radius, distribution-based Earth Movers Distance that is computable in polynomial time. We also present two simplified formulations for the distance computation whose complexity is better than linear programming. The algorithms are robust in the presence of noise, and by varying the radius of the distance measures, can tolerate different degrees of within-class deformation. Empirical evaluation of the algorithms on a dataset of 430 fMRI images in a content-based image retrieval application demonstrates the power and robustness of the distance measures.