Snake growing

Standard edge detectors usually run in two steps: (i) Detection of edge points; (ii) linking of those points to make a coherent edge feature. Optimal edge detectors were designed ([Can 86]) but this was mainly done on the basis of signal processing aspects and such detectors are often criticized for their failure to detect the most salient edges. New algorithms based on Active Contour Models have been introduced in [Kas 88]. They provide a global view of edge detection. An active contour model, called a snake, is an elastic curve C which is moving under the influence of the potential energy created by the image gradient. The minima of the snake functional energy are the edges. Using the regularization theory [Pog 85], they are searched for in the restricted class of controlled continuity splines[Ter 86]. The snake functional energy is the sum of two terms: E = wlEi~t + w2Ec=t. The Internal energy Ei,t describes features of the curve C = v(t) , Ei~t -fc(a[v' l 2 +/~]v'[2). (Parameters a and fl influence the elasticity or stiffness of the curve). The External energy E~t depends on the feature which is searched for in the image (dark lines, white lines, edges, termination of line segments). In edge detection, we use Ec~ = f c ( [ V I ( v ( t ) ) l ) d t where I is the image intensity. The numerical minimization of E is however problematic [Ami 88] because of numerical instability and of numerous parameters in the functional E.