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Improved curvature estimation for accurate localisation of active contours

Energy-minimising active contour models based on dynamic programming have been proposed by Amini et al. (1988) as a discrete multi-stage decision process. The behaviour of the active contour is generally controlled by its internal and external energies. Internal energy is composed of two parts; the first part, acts to shorten the active contour as it iterates towards the interest object, while the second part is the curvature of the active contour and forces smoothness of active contour during its movement towards interest object. In Amini et al., the three points i, i-1 and i-2 were used to estimate the curvature of the active contour at point i. Also the external energy of active contour at this point was calculated as the distance from its previous point to the nearest edge of underlying image. Then due to both of these problems, locking on to interest object does not occur very accurately especially at some points on the boundary of object where curvature changes very quickly. In this paper a reformulated internal energy is proposed to improve the computation of curvature at point i by making use of the three points i-1, i and i+1. Furthermore, external energy of active contour at any point is defined as its distance to nearest edge of underlying image Consequently our proposed active contour model can lock on to interest objects more accurately using the same snake parameters and initial position. Images with single and multiple objects are selected to evaluate the capability of our proposed method. The results show that locking on to interest objects occurs completely like a membrane or thin plate.