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The GVF based ACM defines a new external force field [F.sup.g.sub.xt] = V(x, y), and the new external force field is named gradient vector flow force field.
The gradient vector flow force field can be expressed as V(x, y) = (u(x, y), v(x, y)), and its energy function is
The 1st row results from balloon active contour model, the 2nd row results from distance vector flow active contour model, the 3rd row results from gradient vector flow active contour model, and the 4th row results from our method.
Some techniques are based on a Centroidal Voronoi Diagrams (CVD) approach [13-15], whereas other methods [16-19] compute a vector field by making use of different strategies (i.e., graph cuts minimization , gradient vector flow ).
(i) GVF (gradient vector flow) field computation-based on  algorithm;