Quantitative functions for size and distance judgments

Abstract

Size-constancy refers to the event that an object of constant physical size is judged to be such, regardless of its location within the three-dimensional physical environment. In the laboratory when size judgments are based upon information received by the visual sense, perfect size-constancy seldom occurs, a result not in keeping with certain functionalist theories of perception (Gibson, 1950; Taylor, 1962). Only a particular combination of instructions, stimulus, and response factors lead to size-constancy (Baird, 1965a;Carlson, 1962;Epstein, 1963), and these results probably can be treated as special cases within a more comprehensive theory (e.g., Akishige, 1961). Before such a theory can be operational, however, several key issues need to be settled. This paper describes some progress toward these prerequisite goals.First, we have extended the range of quantitative data collected for size and distance judgments under Objective instructions and full-cue conditions. The majority of previous results were gathered with a single method on a single value of a dimension such as relative distance or stimulus orientation. We used an extended stimulus series in three conditions. In one situation a relative-size judgment was made between a comparison stimulus at one distance and a standard stimulus at a number of different distances, when both were in a frontal plane. The second situation also involved relative size, but the stimuli were placed flat on a table extending away from the observer and beneath his primary lines of sight. In the third situation ratio estimates of distance along the table were obtained. The same two observers were used in all conditions, and the relative positions of the comparison and standard were varied.Our second concern was theoretical. Since the functionalist theory leading to size-constancy predictions is based upon metric measures of stimuli, and since this approach is inadequate when applied to most data on size and distance, we decided to explore an alternative measure-the subtended visual angle of stimuli at the eye. The task set the observer then is presumed to be the production or estimation of certain visual-angle ratios between the standard and comparison stimuli. The exact ratios depend upon the relative spatial positions of stimuli including their orientation to the eye and ground. Different stimulus and instruction variables require different ratio productions of visual angles. At present we cannot predict exactly which ratio is appropriate for each experimental condition. The important point is that the law of the visual angle is not restricted to a ratio of 1.0 in which the visual angles of the comparison and standard are equal, but is extended to include many other ratios as well.The next step is to defi~e quantitatively the relations among theoretical visual-angle ratios and those actually produced or estimated by observers. When metric measures (arithmetic) are used in graphic plots of theoretical and judged size, the resulting curves are not always linear. It is to our ...

The perception of length on curved and flat surfaces

“…that occurred while judging lengths on the flat planar surface. Such overestimation offrontoparallellengths at far viewing distances has been found in earlier experiments (e.g., Baird & Biersdorf, 1967;1. F. Norman et al, 1996, see Figure 10).…”

“…This effect was also present in Experiments 2 and 3, depending on the particular observer and the experimental condition. It is interesting that this type ofdistortion involving curved lengths in depth is different than the compressive distortion that has typically been found in previous research on the perception ofdepth intervals (e.g., Baird & Biersdorf, 1967;Gilinsky, 1951;Harway, 1963;Loomis et aI., 1992; 1. F. Norman et aI., 1996;Wagner, 1985).…”

“…The ability to perceive length and spatial extent does not necessarily improve when observers view real objects. For example, Baird and Biersdorf (1967) found that judged extents in depth of cardboard strips placed flat on a table top decreased by 21% as the strips were moved farther from the observers, from the front to the rear of the table (see also Thouless, 1931). Frisby,Buckley,and Duke (1996) recently conducted an interesting study oflength discriminations, using real "gnarled" sticks, and found that when the two sticks had different orientations and different distances (Experiment 6), the Weber fraction for binocular viewing averaged 10.6%.…”

“…Previous research on real-world stimuli has used gnarled sticks (Frisby et aI., 1996) or relatively flat ground planes or flat table tops (Baird & Biersdorf, 1967;Gilinsky, 1951;Harway, 1963;Loomis et aI., 1992;Thouless, 1931;Wagner, 1985). It is important to keep in mind, however, that most of the time, human observers are perceiving 3-D objects placed against backgrounds.…”

“…The purpose of our experiments was to investigate this possibility by thoroughly examining the perception of lengths along the surface of a real, physically curved object. Since changes in the orientation of a spatial extent often affect its apparent length and changes in the position and orientation of a surface often influence its perceived depth and curvature (see, e.g., Baird & Biersdorf, 1967;1. F. Norman & Lappin, 1992;Rogers & Graham, 1983), we investigated the effects of these manipulations as well, to see whether they influence the perception of length in a more natural viewing context.…”