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Patrick Garrigan, Phillip J. Kellman; Three-dimensional contour interpolation: Testing the 90-degree constraint. Journal of Vision 2002;2(7):356. doi: 10.1167/2.7.356.
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We have investigated 3-D contour interpolation using a paradigm in which two illusory tabs, slanted in depth about an axis horizontal to the observer, were judged to be in either parallel or converging planes. Speed and accuracy were better when the spatial relations of the tabs supported interpolation of contours and surfaces between them. Control conditions (e.g. tabs with tangent discontinuities removed) indicated that the observed facilitation was the result of contour and/or surface completion. Overall results were consistent with a 3-D elaboration of the 2-D notion of contour relatability. Here we address an important unresolved issue. 2-D relatability includes a 90-degree constraint, such that interpolated contours can not bend through more than 90 deg. Is there a 90-degree constraint that governs 3-D interpolation as well? Initial studies of 3-D interpolation suggested there may not be; a performance advantage was evident even for virtual objects in which the interpolated edges bent in depth through as much as 128 deg. However, stereoscopic slant in our displays was specified entirely through shear. We suspected that slant was greatly underperceived in these displays, due to conflicting perspective cues. To test perception of slant in these displays, we used two methods: 1) an adjustment method (Gillam, 1968) in which the observer matched perceived slant using a Meccano wheel viewed in full-cue conditions, and 2) an adjustment method in which the subjects adjusted the stereoscopic displays to an apparent 90 deg angle. Results from both methods indicated that slant was substantially underperceived (45% on average). This underperception and other factors make a reliable test of the 90 degree principle impractical using the parallel/converging method. We will present results testing the 90 degree constraint using a categorization paradigm whose difficulty is independent of slant, and stereoscopic stimuli whose slant is more accurately perceived.
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