Spatial integration in structure from motion

Recent investigations have shown that the perceived slant of the orthographic projection of a rotating random-dot planar surface is (1) an increasing function of deformation and (2) a decreasing function of tilt of the velocity field (e.g. Domini and Caudek, 1999). Deformation is defined as the sum of the squared horizontal and vertical gradients of the velocity field and tilt as the ratio between the vertical and horizontal gradients. Further findings have also indicated that perceived slant is (3) a decreasing function of the average velocity of the first-order optic flow (e.g. Todd and Perotti, 1999). If the perceptual interpretation of a linear velocity field is affected by the three factors listed above, then some form of spatial integration must also take place. In fact, observers report perceiving a planar rotating surface when viewing a linear velocity field regardless of the fact that, for each local patch of the velocity field, factors 1 and 2 are the same, but factor 3 can largely vary. According to the above hypothesis, we should then expect that perceived orientation of different patches of a rotating random-dot planar surface should be (i) different when they are viewed in isolation, and (ii) equal when they are viewed as part of the same surface. In our investigation, we asked human observers to judge the perceived slant and tilt of local patches of a rotating random-dot planar surface. Surprisingly, we found that the local patches were perceived as having different slants even if the surface was entirely visible. These differences, however, were significantly smaller than those found when the local patches were perceived in isolation, therefore indicating that spatial integration does in fact take place. Perceived tilt was also found to depend on the local mean velocity. Also this effect, however, was significantly reduced when the whole surface was visible