Going from a Retinotopic to a Spatiotopic Coordinate System for Spatial Attention

The cartoon shown in Figure 1 is grossly misleading, as the complex-valued log-polar mapping of visual field coordinates to cortical visual coordinates in the early visual cortex precludes the type of translation (shift) invariance invoked in simple Cartesian coordinate systems. The failure of translation invariance in mammalian vision has been know for over thirty years, yet researchers continue to ignore this fact when constructing models of spatial vision. See, for example, Schwartz (1980, 1983) for further details.

References

Schwartz, E.L. (1980). Computational anatomy and functional architecture of striate cortex: a spatial mapping approach to perceptual coding. Vision Research, 20(8), 645-669.

Schwartz, E.L. (1983). Cortical mapping and perceptual invariance: a reply to Cavanagh. Vision Research, 23(8), 831-835.