Abstract
In Panum's limiting case (PLC), a single vertical line in one eye corresponds to a pair of vertical lines in the other eye, yielding perception of two lines at different depths. Proposed explanations include: 1) The single line is matched with both elements of the pair; 2) Vergence-induced disparity causes matched and unmatched lines to appear in different depths; 3) The unmatched line of the pair is interpreted as occlusion or camouflage. To examine which theory is responsible for depth perception in surfaces composed of multiple ambiguous features, we examined depth perception in random-dot stereograms (RDS) composed of local 2:1 matches (PLC-RDS). With these stimuli observers perceive two transparent surfaces with a depth difference proportional to the separation of the dot-pair. We performed two experiments. In the depth matching experiment, subjects matched the perceived depth in PLC-RDS to a pair of conventional transparent RDS surfaces. The separation of the dot-pair in PLC-RDS was closely matched to the relative disparity of the conventional RDS. Furthermore, the perceived depth between the two RDS variants was indistinguishable when they were adjacent. In a depth discrimination experiment, the upper limit for resolving a fixed relative depth (6, 12, 24, 48 arcmin) was measured for PLC surfaces and transparent surface pairs. The discrimination limit increased with increasing relative depth between the adjacent planes up to about 30 arcmin and then decreased in both PLC and conventional RDSs. The results of the depth discrimination task from PLC surfaces and the two conventional transparent surfaces were very closely matched. Brief presentation (200 ms) was used to limit vergence in both experiments. In conclusion, quantitative depth perception in PLC is closely tied to disparity and as precise as conventional stereopsis. This evidence suggests a common stereoscopic mechanism for both PLC and conventional RDSs and supports the presence of double matching.