Comparison Between The Performance of Parametric Active Contour Models

Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. In this research, for the segmentation of anatomical structures in medical images three approaches were implemented and compared like (original snake model, distance potential force model and Gradient Vector Flow (GVF) snake model). We used Computed Tomography image (CT) for our experiments. Our experiments show that original snake model has two problems; first is the limited capture range and the second is the poor convergence. Distance potential force model solved only the first problem of original snake and failed with second problem. Gradient Vector Flow (GVF snake) provides a good capture rang and a good convergence; therefore good results are obtained where GVF snake could successfully segment the anatomical structures from CT images. Introduction Snakes are energy-minimizing curves that are defined within an image and are deformed by the effect of the internal energy of the curve itself and the external forces derived from the image. Snakes are widely used in many applications, including edge detection [1], shape modeling [2], segmentation [3] and motion tracking. There are two key difficulties with parametric active contour algorithms. First, the initial contour which in general must be close to the true boundary or else it will likely converge to the wrong result. The second problem is that active contours have difficulties progressing into boundary concavities [4]. Then, Cohen and Cohen [5] proposed a distance potential force model. The general idea behind this model is to have large external forces far away from the boundaries of the object, thus increasing the capture range of the snake. Even then, snakes based on this model fail to converge to concavities. The technique presented by IBN ALHAITHAM J. FO R PURE & APPL. SC I. VOL.23 (1) 2010 Xu and Prince (GVF snake) addresses these issues and presents a new formulation for active contour modeling [6,7]. In this research, we show the advantages of the GVF snake over the traditional models where we discuss and compare between it and the original model and distance potential force model. Also we discuss some results obtained by implementing and testing the algorithms of these models. Background An original snake is a curve x(s) = [x(s), y (s)] s [0,1] that moves through the spatial domain of an image to minimize the energy functional E = ds s E β s α s )) ( ( x ) ( x" ) ( x' ext 2 2 1 2 1 0        where α and β are weighting parameters that control the snake’s tension and rigidity, respectively, ) ( x' s and ) ( x" s denote the first and second derivatives of x(s) with respect to s. The external energy function E ext is derived from the image so that it takes on its smaller values at the features of interest, such as boundaries. Given a gray-level image I(x, y), viewed as a function of continuous position variables (x, y), typical external energies are designed to lead a snake toward step edges are: E ext (x, y) = 2 y) I(x,  Eext (x, y) =   2 y) I(x, y) (x, G * σ  where y) (x, G σ is a two-dimensional Gaussian function with standard deviation σ and  is the gradient operator. If the image is a line drawing (black on white), then appropriate external energies include [8]: E ext (x, y) = I (x, y) E ext (x, y) = y) I(x, y) (x, G * σ It is easy to see from these definitions that largerσ’s will cause the boundaries to become blurry. Such large σ’s are often necessary, however, in order to increase the capture range of the snake. . (1)