Variational Curve Skeletons Using Gradient Vector Flow

Abstract

Representing a 3D shape by a set of 1D curves that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, subvoxel accurate curve skeletons from volumetric objects. A reference point inside the object is considered a point source that transmits two wave fronts of different energies. The first front (beta-front) converts the object into a graph, from which the object salient topological nodes are determined. Curve skeletons are tracked from these nodes along the cost field constructed by the second front (alpha-front) until the point source is reached. The accuracy and robustness of the proposed work are validated against competing techniques as well as a database of 3D objects. Unlike other state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying skeletal junction nodes, employs a new energy that does not form medial surfaces, and finally extracts curve skeletons that correspond to the most prominent parts of the shape and hence are less sensitive to noise.

Extracting 3D Parametric Curves from 2D Images of Helical Objects

“…These approaches all operate on the shape boundary, e.g. with a binary representation or surface mesh, and then compute a distance image or use a gradient vector field [19]. The results in the literature show that the binary shape boundary provides enough information to describe the central curve of the shape [20].…”

Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours

“…The main process to find the skeleton is a distance wavefront propagation. In Euclidean spaces (R d , d = 2, 3) this can be modeled either using a continuous distance formulation [5] or via continuous-space morphology [26,36] or via PDEs that simulate these evolution operations [38,3,18,40]. In the discrete 2D or 3D space Z d , the above approaches are replaced by discrete distance transforms and discrete morphology; for surveys and references see [34,36].…”

3D Modeling of Coronary Artery Bifurcations from CTA and Conventional Coronary Angiography

“…1). In order to follow a more realistic trajectory of the vessels, we use a speed function that depends exponentially (as in [5]) on the local vessel structure as follows:…”