Carlo Fantoni

Although the role of surface-level processes has been demonstrated, visual interpolation models often emphasize contour relationships. We report two experiments on geometric constraints governing 3D interpolation between surface patches without visible edges. Observers were asked to classify pairs of planar patches specified by random dot disparities and visible through circular apertures (aligned or misaligned) in a frontoparallel occluder. On each trial, surfaces appeared in parallel or converging planes with vertical (in Experiment 1) or horizontal (in Experiment 2) tilt and variable amounts of slant. We expected the classification task to be facilitated when patches were perceived as connected. We found enhanced sensitivity and speed for 3D relatable vs. nonrelatable patches. Here 3D relatability does not involve oriented edges but rather inducing patches' orientations computed from stereoscopic information. Performance was markedly affected by slant anisotropy: both sensitivity and speed were worse for patches with horizontal tilt. We found nearly identical advantages of 3D relatability on performance, suggesting an isotropic unit formation process. Results are interpreted as evidence that inducing slant constrains surface interpolation in the absence of explicit edge information: 3D contour and surface interpolation processes share common geometric constraints as formalized by 3D relatability.

When the eyes move vertically across a jagged diamond, a local shift (LS) of edge discontinuities and a global shape distortion (GD) (ie expansion/contraction opposite to that expected by the aperture effect) are perceived. These phenomena cannot be accounted for by a local motion signals integration rule based either on the intersection of constraint lines or on the velocity vector summation. The threshold for GD perception and the salience of LS and GD (1 to 10 scale) were measured in two experiments by different methods and displays. In experiment 1 we induced GD through mimicking LS with a kinetic pattern constituted of a set of circular illusory apertures revealing drifting gratings. The point of subjective equality for compression/expansion was reached for gratings the linear extrapolations of which form an angle of 94.4°. In experiment 2 observers followed a dot moving along the vertical elongation axis of a static jagged diamond (with 70° or 90° angles), varying in the shape (triangular, wave, square), frequency, and amplitude of edge discontinuities. GD scores were correlated with LS scores that were inversely related to frequency/amplitude ratios of triangular edge discontinuities. Data are partially accounted for by averaging neighbouring local motion-capture vectors. Results prove that there are strong interrelations between phenomena in which visual motion affects visual localisation and phenomena involving apparent deformation of global shape.

We model the visual interpolation of missing contours by extending contour fragments under a smoothness constraint. Interpolated trajectories result from an algorithm that computes the vector sum of two fields corresponding to different unification factors: the good continuation (GC) field and the minimal path (MP) field. As the distance from terminators increases, the GC field decreases and the MP field increases. Viewer-independent and viewer-dependent variables modulate GC-MP contrast (i.e., the relative strength of GC and MP maximum vector magnitudes). Viewer-independent variables include the local geometry as well as more global properties such as contour support ratio and shape regularity. Viewer-dependent variables include the retinal gap between contour endpoints and the retinal orientation of their stems. GC-MP contrast is the only free parameter of our field model. In the case of partially occluded angles, interpolated trajectories become flatter as GC-MP contrast decreases. Once GC-MP contrast is set to a specific value, derived from empirical measures on a given configuration, the model predicts all interpolation trajectories corresponding to different types of occlusion of the same angle. Model predictions fit psychophysical data on the effects of viewer-independent and viewer-dependent variables.