What motion distributions yield global transparency and spatial segmentation?

We have examined the ability of observers to parse bimodal local-motion distributions into two global motion surfaces, either overlapping (yielding transparent motion) or spatially segregated (yielding a motion boundary). The stimuli were random dot kinematograms in which the direction of motion of each dot was drawn from one of two rectangular probability distributions. A wide range of direction distribution widths and separations was tested. The ability to discriminate the direction of motion of one of the two motion surfaces from the direction of a comparison stimulus was used as an objective test of the perception of two discrete surfaces. Performance for both transparent and spatially segregated motion was remarkably good, being only slightly inferior to that achieved with a single global motion surface. Performance was consistently better for segregated motion than for transparency. Whereas transparent motion was only perceived with direction distributions which were separated by a significant gap, segregated motion could be seen with abutting or even partially overlapping direction distributions. For transparency, the critical gap increased with the range of directions in the distribution. This result does not support models in which transparency depends on detection of a minimum size of gap defining a bimodal direction distribution. We suggest, instead, that the operations which detect bimodality are scaled (in the direction domain) with the overall range of distributions. This yields a flexible, adaptive system that determines whether a gap in the direction distribution serves as a segmentation cue or is smoothed as part of a unitary computation of global motion.

Continuity - based and discontinuity - based segmentation in transparent and spatially segregated global motion

The mechanisms underlying the parsing of a spatial distribution of velocity vectors into two adjacent (spatially segregated) or overlapping (transparent) motion surfaces were examined using random dot kinematograms. Parsing might occur using either of two principles. Surfaces might be defined on the basis of similarity of motion vectors and then sharp perceptual boundaries drawn between different surfaces (continuity-based segmentation). Alternatively, detection of a high gradient of direction or speed separating the motion surfaces might drive the process (discontinuity-based segmentation). To establish which method is used, we examined the effect of blurring the motion direction gradient. In the case of a sharp direction gradient, each dot had one of two directions differing by 135°. With a shallow gradient, most dots had one of two directions but the directions of the remainder spanned the range between one motion-defined surface and the other. In the spatial segregation case the gradient defined a central boundary separating two regions. In the transparent version the dots were randomly positioned. In both cases all dots moved with the same speed and existed for only two frames before being randomly replaced. The ability of observers to parse the motion distribution was measured in terms of their ability to discriminate the direction of one of the two surfaces. Performance was hardly affected by spreading the gradient over at least 25% of the dots (corresponding to a 1° strip in the segregation case). We conclude that detection of sharp velocity gradients is not necessary for distinguishing different motion surfaces.

Channelled Waves in Anisotropic Mesh Metamaterials

Channelled waves in 2-D periodic anisotropic L-C mesh metamaterials have been investigated. Circuit simulation and the newly developed analytical model of a unit cell have demonstrated full qualitative agreement for both lossless and lossy cases. Isofrequencies for a lattice unit cell and the circuit simulations of finite meshes have shown that propagating waves are channelled from a point source as pencil beams which can travel only along specific trajectories. The beam direction varies with frequency, and at the resonance frequency, the phase and group velocities of the travelling wave are orthogonal. The effect of losses was explored, and it was shown that losses cause qualitative changes of the channelled wave type. It was proven that the channelled waves do not follow the laws of geometrical optics (Snell's law, specular reflection, etc.) at the interfaces of L-C meshes but are governed by the conditions of phase synchronism and impedance matching. Only in the special case of dual L-C and C-L meshes with the interface parallel to the axis of rectangular grid excited at the resonance frequency (X=1) do the channels follow the trajectories of optical rays. A planar mesh test cell has been designed and used for retrieving the unit cell L-C parameters from the S-parameter measurements.