Comparison of human performance with algorithms for estimating fractal dimension of fractional Brownian statistics

Five standard methods for estimating fractal dimension were compared by means of one-dimensional fractional Brownian series generated by four different algorithms yielding series with different statistics. The same one-dimensional series were also displayed as jagged lines and as one-dimensional luminance patterns for judgments by human observers. Only the algorithm implementing the maximum-likelihood method, which required that the generation statistic for the fractal series be known, gave better performance than human observers in estimating fractal dimension. However, when the method of generation is not known, one of the four other standard methods for estimating fractal dimension must be used, and these performed significantly worse than human observers.

Temporal aspects of depth contrast

Depth contrast is a contrasting change in the depth of a feature that results from changes in the disparities of other objects in the field of view, even though the disparity of the original feature remains unchanged. Depth contrast effects decrease during continuous viewing of the stimuli and may disappear altogether after several minutes unless the disparities of the inducing features change with time. This fading occurs whenever the inducing features have constant disparity, whether they are stationary or oscillating laterally. Depth contrast effects occur whenever the inducing features are visible within half a second before or after presentation of the test features. When test features are enclosed by a rectangle which is just inside of a circumscribing outer trapezoid, the inner rectangle "shields" the test features from the depth-inducing effects of the outer trapezoid. Surprisingly, this shielding effect persists if the inner rectangle and outer trapezoid have the same slant direction, but fades with time if the slants are opposite in direction.

Depth discrimination of a line is improved by adding other nearby lines

Depth discrimination thresholds are shown to be lowered by up to a factor of 10 when a few reference lines are added to a stimulus containing a single isolated test line. Four reference lines are better than two, which are better than one, and the improvement in performance is greater when the test line lies between the two reference lines in depth. Stereoacuity for the relative depth of a target line, relative to other nearby reference lines, is shown to be insensitive to changes of disparity of the whole pattern of up to about +/- 5 arc min and is only weakly sensitive to larger displacements of up to +/- 10 arc min.

Shape analysis and stereopsis for human depth perception

The perceived relative depth of two isolated short parallel lines in the center of a scene is known to depend on the disparities and positions of other items in the scene, as well as on their own disparities. We demonstrate here that the shapes of these other items also contribute significantly to the perceived depth, and that these non-disparity influences on depth judgements may already be evident when only three dots are presented as stimuli. When two short vertical test lines are surrounded by a trapezoidal "picture frame", the perceived relative depth of the test lines is affected by the shape of the trapezoid as well as by the disparities assigned to its vertical parallel sides. The influence of the trapezoidal frame can be interpreted as an effect of perspective. The induced relative depth of the test lines is measured by recording the amount of "compensating disparity" that must be given to one of the lines in order for observers to judge the two test lines to be equidistant from the observer's viewing position. Surprisingly, for fixed disparities of the vertical edges of the surrounding picture frame, the induced depth of the test lines increases as the difference in the lengths of the vertical sides increases, regardless of whether the perspective interpretation of the difference in the lengths is consistent with or in conflict with the disparity-defined slant. Shape-related apparent depth changes are especially sensitive to the shape of the trapezoid if it is nearly rectangular, and are comparable in magnitude to those resulting from changes in disparity of the surrounding frame. When a pair of short vertical parallel test lines is presented alone, without a surrounding frame or any other items in the scene, excellent relative depth discrimination is displayed by most subjects. However, if the lines are replaced by squares, trapezoids, triangles, single horizontal lines, or other figures of about the same size as the original test lines, the slant discrimination threshold for these plane figures for naïve observers become poorer by a factor of 20-100. By the use of a feedback signal, observers can be trained to use only disparity cues and ignore shape effects. Some observers have difficulty ignoring the shapes of some figures, the "difficult" figures being different for each observer. After training, the relative depth thresholds for most figures approach those of the original unconnected parallel test lines.

Influence of remote objects on local depth perception

The perceived relative depth of two test dots displayed within the fovea is shown to be influenced by other features in the surrounding area. These features can be as far apart as 51 deg and can have relative disparities as large as 20 deg, much larger than the disparities of the test dots. Since this effect is seen for stimuli presented for 100 msec or less, changes in direction of gaze cannot play a role. The effect varies inversely as the spatial separation between the test dots and the remote features, and is insensitive to the relative disparities of these remote features when they are greater than 2 deg. Observers sometimes differ significantly from each other in their responses to various configurations of the outlying features. This appears to rule out response mechanisms which depend only on the stimulus; some characteristics of the observer must be involved in determining the response. For these briefly presented stimuli, observers are unable to report accurately the relative depth of the central foveated test items if they are also required to report the depths of distant peripheral features.