The contrast-dependence of the intermingled numerosity illusion explained

摘要

Last year we reported a new illusion in which there seem to be up to 36% fewer white disks than grey disks when N randomly-located white disks are intermingled with N grey disks on a dark grey field. Similarly, on a light grey field, there seem to be fewer black than dark grey disks. Grey disk numerosity is not affected by intermingling; the illusion is entirely due to the salient set, white or black. When the intermingled disks are segregated by shape, motion, or depth plane, or when the disks are presented side-by-side, the illusion disappears. We now report that blurring the intermingled disks almost eliminates the illusion, as does reducing the size of the grey ones. In our model, perceived numerosity is the 0.87th power of N.sqrt(CE)/C, the square-root of contrast energy normalized by peak-to-trough contrast (C). When disks are segregated, CE is the square of the disk-field luminance difference, contrast normalizes out, and perceived numerosity depends only on N. However, field luminance is averaged with grey disk luminance when computing the CE of intermingled white or black disks, reducing their perceived numerosity.