Fuzzy Energy-Based Active Contours

This paper presents a novel fast model for active contours to detect objects in an image, based on techniques of curve evolution. The proposed model can detect objects whose boundaries are not necessarily defined by gradient, based on the minimization of a fuzzy energy, which can be seen as a particular case of a minimal partition problem. This fuzzy energy is used as the model motivation power evolving the active contour, which will stop on the desired object boundary. However, the stopping term does not depend on the gradient of the image, as most of the classical active contours, but instead is related to the image color and spatial segments. The fuzziness of the energy provides a balanced technique with a strong ability to reject “weak” local minima. Moreover, this approach converges to the desired object boundary very fast, since it does not solve the Euler–Lagrange equations of the underlying problem, but, instead, calculates the fuzzy energy alterations directly. The theoretical properties and various experiments presented demonstrate that the proposed fuzzy energy-based active contour is better and more robust than classical snake methods based on the gradient or other kind of energies.