When a surface covered with a regular texture is viewed in perspective, the projected texture provides a number of cues to 3D surface orientation. For oriented textures, one cue is perspective convergence: symmetry lines that are parallel along the surface project to lines that vary systematically in orientation. We investigated the contribution of perspective convergence to perception of 3D sl...

It is known that the perceived slants of large distal surfaces, such as hills, are exaggerated and that the exaggeration increases with distance. In a series of two experiments, we parametrically investigated the effect of viewing distance and slant on perceived slant using a high-fidelity virtual environment. An explicit numerical estimation method and an implicit aspect-ratio approach were se...

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.

In this paper, we study lightlike submanifolds of indefinite Kaehler manifolds. We introduce a class of lightlike submanifold called semi-invariant lightlike submanifold. We consider lightlike submanifold with respect to a quarter-symmetric non metric connection which is determined by the complex structure. We give some equivalent conditions for integrability of distributions with respect to th...

One of the properties of a visual surface along with hardness, distance, and color-with-illumination, is that of slant. This term must be understood to include not-slanted as well as slanted; in other words the variable consists of opposite qualities having zero slant as a norm. There is evidence that optical slant, so-called, is determined by stimulation. When vision is monocular and the head ...

Abstract We construct the exponential map associated to a nonholonomic system that allows us define an exact discrete constraint submanifold. reproduce continuous flow as on this submanifold deriving version of equations. Finally, we derive general family integrators includes particular case trajectory.

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur ...

The slant of a stereoscopically defined surface cannot be determined solely from horizontal disparities or from derived quantities such as horizontal size ratio (HSR). There are four other signals that, in combination with horizontal disparity, could in principle allow an unambiguous estimate of slant: the vergence and version of the eyes, the vertical size ratio (VSR), and the horizontal gradi...

The contribution of slant and tilt to the detection of differences in local surface orientation was examined for structure-from-motion (SFM) displays of a complex sinusoidal surface. Observers judged whether an elliptical SFM gauge figure appeared to be lying on the surface or intersecting it. The gauge figure orientation either matched the local surface orientation or differed from it in slant...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...