Asymptotic Behavior of Neural Networks and Image Processing

We give in this paper the definition of a formal network and after, some information about the use of its asymptotic properties for segmenting 3D images reconstructed from parallel cross sections (such as those from Computed Tomography or Magnetic Resonance Imaging). The huge size of data makes algorithmic complexity and storage requirements the key points of 3D edge detection. The classical approach consists in computing the gradient by applying an operator which enhances the grey gradient. Most of all these operators are 3D generalization of 2D edge detectors : Roberts[1], Hueckel[2], Prewitt [3], Canny[4],[5],[6], Marr and Hildreth[7],[8] operators. A critical problem of many of these detectors concerns the size of the convolution masks used to implement the operator : small kernel are noise sensitive, but large ones need prohibitive computing times. A solution is to realize an optimal filter with recursive filters [5],[6].