Showing papers on "Vector flow published in 2000"
15 Oct 2000
TL;DR: This chapter presents an external force for deformable models, which is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image, and shows that GVF has a large capture range and is able to move deformables models into boundary concavities.
Abstract: – Deformable models are used extensively in image processing, computer vision, and medical imaging applications, particularly to delineate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This chapter presents an external force for deformable models, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional deformable model external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding deformable model is formulated directly from a dynamic force equation rather than a energy minimization formulation. Using several two-dimensional examples and two three-dimensional examples, we show that GVF has a large capture range and is able to move deformable models into boundary concavities.
85 citations
TL;DR: A new external force is designed called hybrid force, which, by combining both forces, joins the main features of each one in the active contour models, and it is proposed that this force should be used for segmentation in deformable active contours.
Abstract: The use of active contour models to track the boundaries of anatomic structures in medical images is a technique that has attracted a great number of efforts during the last decade. Segmentation techniques based in deformable active contours were proposed first by Kass et al. 1 Because of the problems appearing using these models, some solutions have been introduced, such as balloon force 2 or Gradient Vector Flow force (GVF), derived from the Gradient Vector Flow vectorial field. 3 Results obtained with these forces in the tracking endocardiac task in echocardiographic sequences were not adequate. We have designed a new external force called hybrid force, which, by combining both forces, joins the main features of each one.
5 citations
Book•
1 Jan 2000
TL;DR: The first automated method for higher order singularity comparisons is introduced using mathematical theories from geometric (Clifford algebra), and concepts from graph theory and linear programming are utilized to solve these problems.
Abstract: Vector fields are commonly found in almost all branches of the physical sciences. Aerodynamics, dynamical systems, electromagnetism, and global climate modeling are a few examples. These multivariate data fields are often large, and no general, automated method exists for comparing these fields. Existing methods require either subjective visual judgments, or data interface compatibility, or domain specific knowledge. A topology based method intrinsically eliminates all of the above limitations and has the additional advantage of significantly compressing the vector field by representing only key features of the flow. Therefore, large databases are compactly represented and quickly searched.
Topology is a natural framework for the study of many vector fields. It provides rules of an organizing principle, a flow grammar, that can describe and connect together the properties common to flows. Helman and Hesselink first introduced automated methods to extract and visualize this grammar. This work extends their method by introducing automated methods for vector topology comparison. Basic two-dimensional flows are first compared. The theory is extended to compare three-dimensional flow fields and the topology on no-slip surfaces. Concepts from graph theory and linear programming are utilized to solve these problems. Finally, the first automated method for higher order singularity comparisons is introduced using mathematical theories from geometric (Clifford) algebra.
1 citations
TL;DR: In this article, the definition of Lie rotated vector fields in the plane and the conditions of movement of singular points on Lie-Rotated vector fields with variable parameters are given, as well as their conditions of singular point movement.
Abstract: This paper gives the definition of Lie rotated vector fields in the plane and the conditions of movement of singular points on Lie rotated vector fields with variable parameters
1 citations