Introduction

Digital images became an object of scientific interest in the seventies of the last century. The emerging science dealing with digital images is called Computer Vision. Computer Vision aims to give wherever possible a mathematical definition of visual perception. It can be therefore viewed in the realm of perception theory. Images are, however, a much more affordable object than percepts. Indeed, digital images are sampled real or vectorial functions defined on a part of the plane, usually a rectangle. They are accessible to all kinds of numerical, geometric, and statistical measurements. In addition, the results of artificial perception algorithms can be confronted to human perception. This confrontation is both advantageous and dangerous. Experimental results may easily be misinterpreted during visual inspection. The results look disappointing when matched with our perception. Obvious objects are often very hard to find in digital images by an algorithm.

In a recent book by Desolneux et al. [54], a general mathematical principle, the so called Helmholtz principle, was extensively explored as a way to define all visual percepts (gestalts) as large deviations from randomness. According to the main thesis of these authors one can compute detection thresholds deciding whether a given geometric structure is present or not in each digital image. Several applications of this principle have been developed by these authors and others for the detection of alignments [50], boundaries [51, 35], clusters [53, 33], smooth curves and good continuations [30, 31], vanishing points [2] and robust point matches through epipolar constraint [128].