The collaboration of grouping laws in vision

Gestalt theory gives a list of geometric grouping laws that could in principle give a complete account of human image perception. Based on an extensive thesaurus of clever graphical images, this theory discusses how grouping laws collaborate, and conflict toward a global image understanding. Unfortunately, as shown in the bibliographical analysis herewith, the attempts to formalize the grouping laws in computer vision and psychophysics have at best succeeded to compute individual partial structures (or partial gestalts), such as alignments or symmetries. Nevertheless, we show here that a never formalized clever Gestalt experimental procedure, the Nachzeichnung suggests a numerical set up to implement and test the collaboration of partial gestalts. The new computational procedure proposed here analyzes a digital image, and performs a numerical simulation that we call Nachtanz or Gestaltic dance. In this dance, the analyzed digital image is gradually deformed in a random way, but maintaining the detected partial gestalts. The resulting dancing images should be perceptually indistinguishable if and only if the grouping process was complete. Like the Nachzeichnung, the Nachtanz permits a visual exploration of the degrees of freedom still available to a figure after all partial groups (or gestalts) have been detected. In the new proposed procedure, instead of drawing themselves, subjects will be shown samples of the automatic Gestalt dances and required to evaluate if the figures are similar. Several numerical preliminary results with this new Gestaltic experimental setup are thoroughly discussed.