A decomposition is described, which parameterizes the geometry and appearance of contours and regions of gray-scale images with the goal of fast categorization. To express the contour geometry, a contour is transformed into a local/global space, from which parameters are derived classifying its global geometry (arc, inflexion or alternating) and describing its local aspects (degree of curvature, edginess, symmetry). Regions are parameterized based on their symmetric axes, which are evolved with a wave-propagation process enabling to generate the distance map for fragmented contour images. The methodology is evaluated on three image sets, the Caltech 101 set and two sets drawn from the Corel collection. The performance nearly reaches the one of other categorization systems for unsupervised learning.