Cast shadows in wide perspective.

We investigated the apparent spatial layout of cast shadows up to very wide fields of view. We presented up to 130 degrees wide images in which two 'flat poles' were standing on a green lawn under a cloudless blue sky on a sunny day. The poles threw sharp cast shadows on the green, of which one was fixed. The observer's task was to adjust the azimuth of the shadow of the other pole such that it fitted the scene. The source elevation was kept constant. The two cast shadows are, of course, parallel in physical space, but generically not in the picture plane because of the wide perspective. We found that observers made huge systematic errors, indicating that, generically, they fail to account for these perspective effects. The systematic deviations could be well described by a weighted linear combination of the directions in the picture plane and in the physical space, with weights that depended on the positions of, and distance between, the poles.

What are the uncurved lines in our visual field? A fresh look at Helmholtz's checkerboard.

What are the uncurved lines in our visual field? To answer this question, Helmholtz developed a geometrical model of line-curvature perception, and demonstrated it with his famous checkerboard pattern with pin-cushion distortion. He claimed it looked perfectly regular when viewed monocularly at close range while fixating the centre. Recently, doubts have been expressed whether this demonstration actually works. We tested twenty monocular, stationary observers who could adjust the distortion of a checkerboard pattern over a large range, from barrel-shaped to pin-cushion-shaped. Their task was to adjust the curvature of the edges of the checks such that the checkerboard looked straight and regular. In one condition they had to fixate the centre of the pattern, in another condition they were instructed to let their gaze wander. We found that most observers indeed perceived a pattern with pin-cushion distortion as undeformed, thereby seeing hyperbolic curves in the figure as uncurved lines in the visual field. They set a more strongly curved pattern in the fixation condition than in the free-viewing condition, as also described by Helmholtz. Interestingly, the effect is about half as strong as Helmholtz claimed. Furthermore, we found considerable inter-individual differences.

The perception of doubly curved surfaces from anisotropic textures.

Most existing computational models of the visual perception of three-dimensional shape from texture are based on assumed constraints about how texture is distributed on visible surfaces. The research described in the present article was designed to investigate how violations of these assumptions influence human perception. Observers were presented with images of smoothly curved surfaces depicted with different types of texture, whose distribution of surface markings could be both anisotropic and inhomogeneous. Observers judged the pattern of ordinal depth on each object by marking local maxima and minima along designated scan lines. They also judged the apparent magnitudes of relative depth between designated probe points on the surface. The results revealed a high degree of accuracy and reliability in all conditions, except for a systematic underestimation of the overall magnitude of surface relief. These findings suggest that human perception of three-dimensional shape from texture is much more robust than would be reasonable to expect based on current computational models of this phenomenon.

Object pose: perceiving 3-d shape as sticks and slabs.

Estimating the pose (three-dimensional orientation) of objects is an important aspect of 3-D shape perception. We studied the ability of observers to match the pose of the principal axes of an object with the pose of a cross consisting of three perpendicular axes. For objects, we used a long and a flat spheroid and eight symmetric objects with aspect ratios of dimensions of approximately 4:2:1. Stimulus cues were the contour and stereo for the spheroids, and contour, stereo, and shading for the symmetric objects. In addition, the spheroids were shown with or without surface texture and with or without active motion. Results show that observers can perform the task with standard deviations of a few degrees, though biases could be as large as 30 degrees. The results can be naturally decomposed in viewer-centered coordinates, and it turns out that the estimation of orientation in the frontoparallel plane (tilt) is more precise than estimation of orientation in depth (slant, roll). A comparison of long and flat spheroids shows that sticks lead to better performance than do slabs. This can even be the case within the same object; the pose of the stick-like aspect is seen with more precision than is the pose of the slab-like aspect. The largest biases occurred when the spheroids were displayed with the binocular contour as the only cue. We can explain these biases by assuming that subjects' settings are influenced by the orientation of the rim.

Generic and non-generic conditions for the perception of surface shape from texture.

Li and Zaidi (Vision Research 40 (2000) 217; 41 (2001) 1519) have recently argued that there are two necessary conditions for the perception of 3D shape from texture: (1) the texture pattern must have a disproportionate amount of energy along directions of principal curvature; and (2) the surface must be viewed with a noticeable amount of perspective. In the present article we present evidence that these conclusions are only valid under a limited set of non-generic viewing conditions. Other relevant factors that need to be considered in this context include the distribution of curvature on an object's surface and the set of possible viewing directions from which it can be observed. For generic viewing directions and patterns of curvature, the perception of surface curvature from texture is only minimally affected by the orientation spectrum of the texture pattern or the amount perspective in its optical projection. Li and Zaidi (Vision Research 41 (2001) 1519) have also identified two characteristic patterns of image contours, which they claim to be the only possible source of information within textured images for determining the direction of surface slant or the sign of surface curvature. In the present article we attempt to show that these characteristic patterns can only arise in natural vision for a limited set of non-generic viewing directions. We also review several other factors that can influence the perceived direction of slant or the perceived sign of curvature, which have been identified previously by other investigators.

The beholder's share in the perception of orientation of 2-D shapes.

A considerable amount of research demonstrates that people perceive cardinal orientations (horizontal and vertical) more accurately than other orientations; this is termed the oblique effect. We investigated the interaction of this effect with the degree of elongation of the stimulus. Our stimuli were ellipses with a wide range of aspect ratios, varying from a circle (aspect ratio = 1) to a line (aspect ratio = 123.5). The task was to set a probe line in the same orientation as the long axis of the ellipse. In our first experiment, we determined that performance is degraded as the aspect ratio decreases; furthermore, the bias and response variability are linearly related to a transformation of aspect ratio (roundness). We found significant individual differences; the results show high within-subjects correlations and low between-subjects correlations. In our second experiment, we had observers judge the orientation of circles randomly mixed in with ellipses of low aspect ratio. The observers demonstrated intrinsic preferences and generated reproducible distributions of orientation settings with idiosyncratic profiles. These distributions predict the influence on the response to ellipses with an aspect ratio higher than one and can be considered as the beholder's share in the perception of shape orientation.