Contrast polarity preservation's role in perception: explained and unexplained stimuli

Roncato and Casco (2003, Perception & psychophysics 65 1252-1272) had shown that in situations where the Gestalt principle of good continuity is put into conflict with preservation of contrast polarity (CP) the perception that preserves CP prevails. Parlangeli and Roncato (2010, Perception 39 255-259) have studied this question of preservation of CP more closely and have added an addendum to the rule. They have used stimuli consisting of a checkerboard of perpendicularly arranged rectangular bricks (white, gray, or black) and draughtsmen white, gray, or black disks placed at the corners of the bricks. This study has caused them to add an addendum to the rule of CP-preserved path-conjunction binding: if there are two contour completions that preserve the CP, the one with the higher contrast will prevail. Parlangeli and Roncato find that, for certain shades of the disks and bricks, the perpendicular lines of the checkerboard appear strikingly to be slanted or undulating. Here we consider all possible arrangements of relative magnitudes of checkerboards consisting of bricks of two different shades and disks of two shades as well, as such arrangements with widely varying differences in the magnitude of brightness. We have found a number of cases where the perception is not explained by the rule and addendum of Roncato and Casco, and Parlangeli and Roncato, and a case where preservation of "distant" as well as local CP plays a role in perception. The previously known cases, and the new exceptional unexplained stimuli we have found, warrant further study.