We expose a recently introduced method for computing geometric structures in a digital image, without any a priori information. According to a basic principle of perception due to Helmholtz, an observed geometric structure is perceptually ``meaningful'' if its number of occurences would be very small in a random situation: geometric structures are characterized as large deviations from randomness. This leads us to define and compute alignments, edges, and clusters in an image by a parameter-free method. Maximal meaningful objects are defined, computed, and the results compared with the ones obtained by classical algorithms.