The effect of polar projection on the perception of euclidean structure from motion

A stratified process for the perception of objects: From optical transformations to 3D relief structure to 3D similarity structure to slant or aspect ratio

Previously, we developed a stratified process for slant perception. First, optical transformations in structure-from-motion (SFM) and stereo were used to derive 3D relief structure (where depth scaling remains arbitrary). Second, with sufficient continuous perspective change (≥45°), a bootstrap process derived 3D similarity structure. Third, the perceived slant was derived. As predicted by theoretical work on SFM, small visual angle (<5°) viewing requires non-coplanar points. Slanted surfaces with small 3D cuboids or tetrahedrons yielded accurate judgment while planar surfaces did not. Normally, object perception entails non-coplanar points. Now, we apply the stratified process to object perception where, after deriving similarity structure, alternative metric properties of the object can be derived (e.g. slant of the top surface or width-to-depth aspect ratio). First, we tested slant judgments of the smooth planar tops of three different polyhedral objects. We tested rectangular, hexagonal, and asymmetric pentagonal surfaces, finding that symmetry was required to determine the direction of slant (AP&P, 2019, https://doi.org/10.3758/s13414-019-01859-5). Our current results replicated the previous findings. Second, we tested judgments of aspect ratios, finding accurate performance only for symmetric objects. Results from this study suggest that, first, trackable non-coplanar points can be attained in the form of 3D objects. Second, symmetry is necessary to constrain slant and aspect ratio perception. Finally, deriving 3D similarity structure precedes estimating object properties, such as slant or aspect ratio. Together, evidence presented here supports the stratified bootstrap process for 3D object perception. STATEMENT OF SIGNIFICANCE: Planning interactions with objects in the surrounding environment entails the perception of 3D shape and slant. Studying ways through which 3D metric shape and slant can be perceived accurately by moving observers not only sheds light on how the visual system works, but also provides understanding that can be applied to other fields, like machine vision or remote sensing. The current study is a logical extension of previous studies by the same authors and explores the roles of large continuous perspective changes, relief structure, and symmetry in a stratified process for object perception.

The visual perception of plane tilt from motion in small field and large field: psychophysics and theory

Subjects indicated the tilt of dotted planes rotating in depth, in monocular viewing, under perspective projection. The responses depended on the FOV (field of view) and on the angle W between the tilt and frontal translation (orthogonal to the rotation axis). Response accuracy increased with the FOV, and decreased with W. Our results support the processing of the second-order optic flow in all cases, but indicate that this flow is quantitatively small in small-field, leading to tilt ambiguities. We examine computational models based on the affine components of the optic flow to interpret our results.

A Mathematical Model of Depth Displacement with a Contracting Bar

When a vertical line segment contracts at both ends according to a (decelerating) time law of hyperbolic type, it appears to rotate around its midpoint. The phenomenon is quite surprising from the point of view of projective geometry as the segment should rather appear to recede along the sagittal plane. Apparent displacement in depth is however obtained when the bar simultaneously contracts and is displaced laterally on the frontal plane. But, here again, projective expectations are contradicted, because apparent displacement in depth occurs whether movement of the bar in two dimensions is hyperbolic (decelerating), uniform, harmonic (accelerating), or a mixture of the three. It is suggested here that the visual system operates in such a way as to minimize the differences between the lengths of the velocity vectors of all points of a moving configuration. The mathematical model derived from this hypothesis allows qualitative and quantitative predictions that are in good agreement with experimental results. Copyright 2001 Academic Press.

The role of perspective information in the recovery of 3D structure-from-motion

When investigating the recovery of three-dimensional structure-from-motion (SFM), vision scientists often assume that scaled-orthographic projection, which removes effects due to depth variations across the object, is an adequate approximation to full perspective projection. This is so even though SFM judgements can, in principle, be improved by exploiting perspective projection of scenes on to the retina. In an experiment, pairs of rotating hinged planes (open books) were simulated on a computer monitor, under either perspective or orthographic projection, and human observers were asked to indicate which they perceived had the larger dihedral angle. For small displays (4.6 x 6.0 degrees) discrimination thresholds were found to be similar under the two conditions, but diverged for all larger stimuli. In particular, as stimulus size was increased, performance under orthographic projection declined and by a stimulus size of 32 x 41 degrees performance was at chance for all subjects. In contrast, thresholds decreased under perspective projection as stimulus size was increased. These results show that human observers can use the information gained from perspective projection to recover SFM and that scaled-orthographic projection becomes an unacceptable approximation even at quite modest stimulus sizes. A model of SFM that incorporates measurement errors on the retinal motions accounts for performance under both projection systems, suggesting that this early noise forms the primary limitation on 3D discrimination performance.

Perceiving motion and rigid structure from optic flow: a combined weak-perspective and polar-perspective approach

Structure-from-motion algorithms based on weak-perspective projection have many interesting properties and could serve as a basis for a model of human perception of motion and structure from motion (M&SFM). There is some psychophysical evidence, however, that points to discrepancies between what can be accomplished with these algorithms and the performance of human subjects in certain M&SFM tasks. In light of this evidence, this paper presents a mechanism that both takes advantage of all the possibilities offered by a weak-perspective approach and behaves in a manner that is in close correspondence with human performance in M&SFM tasks. It consists of a novel weak-perspective-based method operating at small visual angles and a complementary, perspective-projection-based method operating at larger visual angles.