Noise causes slant underestimation in stereo and motion

On the inverse problem of binocular 3D motion perception

It is shown that existing processing schemes of 3D motion perception such as interocular velocity difference, changing disparity over time, as well as joint encoding of motion and disparity, do not offer a general solution to the inverse optics problem of local binocular 3D motion. Instead we suggest that local velocity constraints in combination with binocular disparity and other depth cues provide a more flexible framework for the solution of the inverse problem. In the context of the aperture problem we derive predictions from two plausible default strategies: (1) the vector normal prefers slow motion in 3D whereas (2) the cyclopean average is based on slow motion in 2D. Predicting perceived motion directions for ambiguous line motion provides an opportunity to distinguish between these strategies of 3D motion processing. Our theoretical results suggest that velocity constraints and disparity from feature tracking are needed to solve the inverse problem of 3D motion perception. It seems plausible that motion and disparity input is processed in parallel and integrated late in the visual processing hierarchy.

Humans and many other predators have two eyes that are set a short distance apart so that an extensive region of the world is seen simultaneously by both eyes from slightly different points of view. Although the images of the world are essentially two-dimensional, we vividly see the world as three-dimensional. This is true for static as well as dynamic images. Here we elaborate on how the visual system may establish 3D motion perception from local input in the left and right eye. Using tools from analytic geometry we show that existing 3D motion models offer no general solution to the inverse optics problem of 3D motion perception. We suggest a flexible framework of motion and depth processing and suggest default strategies for local 3D motion estimation. Our results on the aperture and inverse problem of 3D motion are likely to stimulate computational, behavioral, and neuroscientific studies because they address the fundamental issue of how 3D motion is represented in the visual system.

3D surface orientation based on a novel representation of the orientation disparity field

The orientation disparity field from two orthographic views of an inclined planar surface patch (covered by straight lines) is analyzed, and a new tool to extract the patch orientation is provided: the function coupling the average orientation of each pair of corresponding surface contours with their orientation disparity. This function allows identifying the tilt of the surface, and two indeterminacy functions describing the set of surface inclinations (around the vertical and horizontal axes) over convergence angle values compatible with the orientation disparity field. Results of simulations show that the selection of inclination values matching the difference between the areas below the indeterminacy functions are consistent with some surface orientation effects found in psychophysical and computational experiments, like: the unbiased tilt vs. biased slant estimates, the slant underestimation, the surface orientation anisotropy, and the slant/tilt covariation.