Optimization of a discriminant function meant for the recognition of beam sections

The recognition of structural shapes is considered with a statistical approach using silhouette and contour moments or Fourier descriptors. The silhouette moment calculus is reduced on the contour by the Riemann formula. From these characterizations we define different discriminant functions which can be compared to Euclidean distance between the models. These functions are optimized with the help of two performance criteria and a principal component analysis of the model dispersion in the feature space. The optimization, performed with a heuristical method, concerns the weight coefficients associated to the geometrical features. In the case of section shapes which are grouped according to a standard classification, the optimal performance is reached using a spectral decomposition of the contour, in particular, the decomposition error which constitutes an invariant, has made it possible to dissociate shapes with relatively close geometry