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Unformatted text preview: IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 7, NO. 3, MARCH 1998 359 Snakes, Shapes, and Gradient Vector Flow Chenyang Xu, Student Member, IEEE, and Jerry L. Prince, Senior Member, IEEE Abstract— Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initializa- tion and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, 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 snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several two-dimensional (2-D) examples and one three-dimensional (3-D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities. Index Terms— Active contour models, deformable surface mod- els, edge detection, gradient vector flow, image segmentation, shape representation and recovery, snakes. I. INTRODUCTION S NAKES [1], or active contours , are curves defined within an image domain that can move under the influence of internal forces coming from within the curve itself and external forces computed from the image data. The internal and external forces are defined so that the snake will conform to an object boundary or other desired features within an image. Snakes are widely used in many applications, including edge detection [1], shape modeling [2], [3], segmentation [4], [5], and motion tracking [4], [6]. There are two general types of active contour models in the literature today: parametric active contours [1] and geometric active contours [7]–[9]. In this paper, we focus on parametric active contours, although we expect our results to have applications in geometric active contours as well. Parametric active contours synthesize parametric curves within an image domain and allow them to move toward desired features, usually edges. Typically, the curves are drawn toward the edges by potential forces , which are defined to be the negative gradient of a potential function. Additional forces, such as pressure forces [10], together with the potential forces comprise the external forces . There are also internal forces designed to hold the curve together (elasticity forces) and to keep it from bending too much (bending forces)....
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