RBF nets for approximating an object’s boundary by image random sampling Original Research Article

Our aim is to discuss the problem of approximating the boundary of an object in a binary image. In contrast to earlier papers on similar topics, we avoid finding contours and then their approximations. Instead, we sample an image in a relatively small number of points (1%–3% of pixels) at random. The collected data is used for imposing constraints on parameters of a radial basis functions (RBF) neural net. It is proved that if the RBF net structure is sufficiently rich to approximate an object boundary, then estimates of RBF net parameters tend to their true values, as the number of samples approaches to infinity. Then, a seemingly linear algorithm of estimating linear weights is proposed and its consistency is also proved. Its implementation, which is based on an iterative use of the linear programming, is briefly discussed and the results of its testing are shortly reported.