Benary's Cross: belongingness or coarse sampling

Late 19th century Gestalt psychologists rebelled against the tenants of traditional epistemology and newly defined psychophysics. They introduced powerful new ideas. These ideas were supported by a myriad of experiments showing that the whole is not the sum of the parts. These appearance experiments include Simultaneous Contrast, Gelb’s doorway, and Benary’s Cross. The traditional Gestalt explanations of these experiments call for cognitive top-down inferences, that are difficult to describe as detailed computer models. Late 20th century ideas of image processing refined bottom-up sensation mechanisms to include low-level spatial interactions and multi-spatial frequency image analysis. As did Gestalt theory, spatial image processing ideas depart from single pixel models, such as Colorimetry. Spatial models of lightness have been shown to account for Simultaneous Contrast, Gelb’s doorway and Mondrian experiments. Benary’s Cross used two identical gray triangles, surrounded by one black and two white sides, making them have qualitatively equal surrounds. The Gestalt interpretation is that the two gray triangles look different because one appears to belong to the cross and the other does not (“Belongingness”). This paper analyzes Benary’s Cross using spatial-image-processing. This quantitative analysis shows that bottom-up coarse sampling is as good an explanation of apparent lightness as top-down cognition. Sampling is much easier to calculate from image data.