Vernier acuity as line and dipole detection

Abstract

The vernier judgment is commonly thought of as discriminating the displacement of a portion of a pattern. However, we have found it revealing to consider vernier stimuli in another light; as the composite of a test pattern superimposed on a masking pedestal. The pedestal is the pattern with zero spatial offset, and the test pattern is the luminance distribution which, when added to the pedestal, produces the offset. For example, a vernier offset of an edge can be generated by adding a thin line (the derivative of an edge) to one half of an edge pedestal, and a vernier offset of a line can be generated by adding a thin dipole (the derivative of a line) to one half of a line pedestal. Vernier thresholds for low contrast edge and line pedestals can be directly predicted from detection thresholds of thin lines and dipoles on uniform fields. A surprisingly simple relationship is also derived between vernier thresholds and the size of Ricco's integration zone. We have found this masking paradigm to be fruitful and believe it is relevant to all the hyperacuities, not just vernier.