Testing a formal theory of perception is not easy: Comments on Yu, Todd & Petrov (2021) and Yu, Petrov & Todd (2021)

Yu, Todd, and Petrov (2021, Journal of Vision) and their follow-up study (Yu, Petrov, & Todd, 2021, i-Perception) aimed at evaluating the role of three-dimensional (3D) symmetry in binocular shape perception by comparing their experimental data to predictions they derived from our computational models. We point out in this note that their predictions were incorrect, so their studies can neither reject nor support our models of 3D shape perception. We explain (1) the role of the data and the constraints in solving ill-posed inverse problems, (2) the role of binocular depth-order, as opposed to binocular depth-intervals in shape perception, (3) the nature and the effect of 3D compactness as an a priori constraint, and (4) the implications of the separation of binocular disparity and stereoacuity in the two functional streams in the visual cortex.