Generalized gradient vector flow external forces for active contours

Abstract

Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initialization and poor convergence to boundary concavities. GVF is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. In this paper, we generalize the GVF formulation to include two spatially varying weighting functions. This improves active contour convergence to long, thin boundary indentations, while maintaining other desirable properties of GVF, such as an extended capture range. The original GVF is a special case of this new generalized GVF (GGVF) model. An error analysis for active contour results on simulated test images is also presented.1998 Elsevier Science B.V. All rights reserved. ZusammenfassungAktive Umrisse, oder Schlangen, werden vielfach in Computervision-und Bildverarbeitungs-Anwendungen benutzt, um insbesondere Objektgrenzen zu lokalisieren. Ein neuer Typ a¨u{erer Kra¨fte fu¨r aktive Umrisse, Gradient »ector Flow (GVF) genannt, wurde ku¨rzlich eingefu¨hrt, um Probleme anzusprechen, die mit Initialisierung und schlechter Konvergenz zu Grenzkonkavita¨ten zusammenha¨ngen. GVF wird als eine Diffusion des Gradientenvektors einer Graustufen-oder 'Binary Edge'-Karte berechnet, die aus dem Bild gewonnen werden. In diesem Artikel verallgemeinern wir die GVF Formulierung, so da{ zwei ra¨umlich variierende Gewichtsfunktionen eingeschlossen werden. Dies verbessert die Konvergenz aktiver Umrisse zu langen, du¨nnen Grenzmarkierungen, wa¨hrend andere wu¨nschenswerte Eigenschaften des GVF, wie erweiterter Einfangbereich, erhalten bleiben. Das urspru¨ngliche GVF ist ein Spezialfall dieses neuen verallgemeinerten GVF (GGVF) Modells. Eins Fehleranalyse von Ergebnissen aktiver Umrisse mit simulierten Testbildern wird ebenfalls pra¨sentiert.1998 Elsevier Science B.V. All rights reserved. contours actifs, appele`flux de vecteurs gradients (FVG) a e´te´introduit re´cemment pour traiter les proble´mes associe´s a`l'initialisation et la faible convergence vers des concavite´s dans les contours. Le FVG est calcule´comme une diffusion des vecteurs gradients d'une carte des contours d'une image en niveaux de gris ou binaire. Dans cet article, nous ge´ne´ralisons la formulation du FVG pour y inclure deux fonctions de poids a`variation spatiale. Ceci ame´liore la convergence des contours actifs vers les indentations de contours fines et longues, tout en maintenant les autres proprie´te´s inte´ressantes des FVG comme la plage de capture e´tendue. Les FVG originaux sont un cas particulier des mode`les de FVG ge´ne´ralise´s. Une analyse de l'erreur des re´sultats de contours actifs sur des images de test synthe´tiques est aussi pre´sente´e.

Surface Extraction from Volumetric Images Using Deformable Meshes: A Comparative Study

“…To our knowledge, this kind of empirical study does not exist in the context of deformable surface meshes. With 2-D deformable models some quantitative comparisons have been reported, at least in [3,15].…”

Online measurement and evaluation of the Er:YAG laser ablation process using an integrated OCT system

“…In contrast, external energy considers only image dependent properties. The traditional model sets The application of calculus of variations to the snake energy involves finding a minimum of the integral and leads to an Euler-Lagrange differential equation (4) To overcome the poor abilities of outlining concave boundaries and to enlarge the capturing range of edges, we substitute the traditional formulation of gradient-based energies with a gradient vector flow (GVF) field ) , ( y x w  [16] and artificial vertical pressure n  . Implicit Euler timestepping is applied to solve the dynamic system numerically and to compute snake evolution to a local equilibrium…”

Interactive Computer-Aided Diagnosis of Breast Masses: Computerized Selection of Visually Similar Image Sets From a Reference Library

“…Selection of the initial growth boundary contour is important for avoiding the algorithm being trapped by local image noise [25]. In general, the internal force imposes a smoothness constraint on the contour, and the external force is typically determined by the magnitude of the image gradient and moves the vertices to locations with stronger gradients [26]. In mass segmentation, the assumption that the edge of a mass lesion always has the strongest gradients as compared with the surrounding background is frequently violated due to tissue overlap inherent to X-ray projection images.…”

“…As a result, active contours can expand (penetrate) into the surrounding breast tissue. In our scheme, the boundary contour identified by the topographic region growth algorithm is used as the initial contour of the active contour algorithm and a map of generalized gradient vector flow representing the external forces [26] is computed. Unlike to what is the case of a typical active contour algorithm, shrinking is not allowed in our scheme in order to minimize the risk of being trapped inside the mass lesion.…”

“…The scheme then computes two maps. The first one is a map of the generalized gradient vector flow [26] outside the mass as detected by active contour algorithm (step 2) and the second one is a "positive contrast" map. For the first map a pre-trained threshold value (e.g., 80 [17]) is applied to generate a binary representation of the gradient vector flow.…”