Spatial integration of curved surfaces in structure from motion

Structure-from-motion studies have shown that the perceived slant of a local planar patch is (1) an increasing function of deformation and (2) a decreasing function of the average velocity of the first-order optic flow (Domini Caudek 1999, Todd and Perotti, 1999). Recent findings, however, indicate that local judgments are subject to a process of spatial integration when local patches are embedded in a global optic flow (Di Luca, Domini and Caudek, 2002). To generalize the previous work, in this study we asked human observers to judge the perceived orientation of local patches of a rotating random-dot spherical surface. These patches could either be seen in isolation or as part of the whole surface. In two experimental conditions the axis of rotation was either in front or behind the simulated surface so to allow the same surface patch to project in each condition the same deformation but different average velocities. The results can be summarized as follow: (1) When the patches were judged in isolation perceived orientations were consistent with those in previous studies on local slant perception. (2) When the whole surface was visible, the local judgments were consistent with the perception of a quasi-spherical surface, suggesting a process of spatial integration. (3) These judgments were not consistent, however, with the veridical percept of a spherical surface and they also indicated that different structures were perceived when the position of the axis of rotation was changed. Surprisingly, we also found that when the same random-dot sphere rotates about different axes of rotation it is perceived as having two qualitatively different shapes (see demo on www.cog.brown.edu/~max/pub/sphere_integration/index.htm).