Local and global shape estimates of binocularly-viewed real objects are consistent

Purpose. To test whether observer's estimates of surface normals in binocular viewing of real objects are consistent with a physically-possible surface, and whether they vary with the bi-directional surface reflectance of the object. Methods. Two observers viewed a smooth, asymmetric, wooden object binocularly from a distance of 70 cm and estimated the normal to the object's surface at 60-74 closely-spaced (4 mm) points along each of two pre-selected, closed contours. The subject adjusted a circle-stick gradient probe (visible only to the left eye) optically superimposed on the object. Each observer repeated these judgments 10 times for each contour and then repeated all measurements for the same object painted matte white. Results. Given the surface normal at each point along a closed contour C(s) on a smooth surface, we can compute the depth difference Δ(s) between the starting point of the contour C(0) and any other point C(s) on the contour, and the net depth difference, Δ(s_ω), accumulated in one complete traverse of the closed contour. If the observer's estimates of surface normals are veridical up to a scaling and translation of the surface along the line of sight, then Δ(s_ω)=0. We numerically estimated the contour integral described above from the observer's estimates. The functions Δ(s) were very similar for the natural wooden and the flat white surfaces for both observers and across observers. We did not reject the hypothesis that all of the values Δ(s_ω) were zero for both observers and both surface conditions (p > 0.01). Conclusions. Observers' performance was consistent with the hypothesis that estimates of local shape are some fixed linear transformation along the line of sight of the true local shape.