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Massimiliano Di Luca, Carlo Fantoni; Interpolation of occluded surfaces in structure from motion. Journal of Vision 2005;5(8):989. doi: 10.1167/5.8.989.
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Consider two vertically adjacent random dot surfaces twisted 20° around the vertical axis and undergoing a 10° oscillation around the same axis during a period of 1/2 second. The rotation of the surfaces is perceived as rigid when they amodally unified behind a horizontal occlusion. Conversely, when the surfaces are interpreted as separated objects, they are perceived as undergoing a rotation of a different magnitude (see Domini, Caudek and Proffitt 1997). This effect suggests that spatial unification may affect the process of recovering depth in structure from motion stimuli by maximizing rotation coherence between joinable surfaces.
To test our claim we measured the threshold for perceived rigidity of twisted surfaces in 4 conditions resulting by the combination of 2 factors: occlusion (present vs. absent) and surface-similarity (congruent vs. incongruent). Both the simulated slant of the lower surface and the amount of rotation were kept constant at 10°. The simulated slant of the upper plane was varied in a constant stimuli fashion. Observers were required to judge if the twisted pair of surfaces appeared to rotate rigidly or not.
The stimulus is perceived as being a rigid structure for a wider range of slant differences when an occlusion is present. The difference between occlusion-present and occlusion-absent conditions is noticeably reduced when the degree of connectivity between surfaces is lowered by introducing surface dissimilarity. These results support the idea that the surface interpolation process interferes with perceived rigidity of structure from motion stimuli. The amount of perceived rotation is modulated to maximize the coherence between joinable parts in order to achieve a smooth unification of misaligned surfaces (see Fantoni, Gerbino and Kellman 2004). Moreover, perception of surfaces that requires interpolation with torsion is possible with a limited range of twist angle.
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