A Continuous Perspective on Shape Optimization via Domain Transformations

Shape equivalence under perspective and projective transformations.

When a planar shape is viewed obliquely, it is deformed by a perspective deformation. If the visual system were to pick up geometrical invariants from such projections, these would necessarily be invariant under the wider class of projective transformations. To what extent can the visual system tell the difference between perspective and nonperspective but still projective deformations of shape...

Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape.

We investigated the ability to perceive the metric shape of elliptical cylinders. A large number of previous studies have shown that small perspective variations (< or =10 degrees) afforded by stereovision and by head movements fail to allow accurate perception of metric shape. If space perception is affine (Koenderink & van Doom, 1991), observers are unable to compare or relate lengths in dept...

On Absolutely Continuous Transformations

Dimensionality Reduction on Grassmannian via Riemannian Optimization: A Generalized Perspective

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity between subspaces using various metrics defined on Grassmannian and formulate dimensionality reduction as a non-linear constraint optimization problem conside...

Continuous perspective transformations and the perception of rigid motion.

An exploratory survey of the varieties of optical motion which could serve as stimuli for the perception of motions in the world (6, 7) suggested the hypothesis that one kind of geometrical motion in a plane yields an impression of a rigid motion in space but that any other kind of geometrical motion in a plane does not. The stimulus pattern was always a "texture," that is, a grouping of dark s...