John C. Baird

Global precedence in visual pattern recognition

This paper describes the results of three experiments on the global precedence effect, using stimuli derived from the receptive field characteristics of neurons in the visual cortex. Thus, the local cue consists of oriented line segments whose sizes correspond to the average size of the central portion of receptive fields in parafoveal representations of the macaque primary visual cortex. The global cue comprises these line segments distributed within larger rectangular clusters. The first experiment showed that global precedence is obtained when the relative visibility of the local and global cues is specifically evaluated and found to be comparable. In the second experiment, variants of the Garner sorting task produced results indicating that global processing is largely independent of local cues, but that local processing depends heavily on the status of task-irrelevant global cues. These asymmetric interactions are consistent with the notion of a priority for processing global cues. The third experiment demonstrated that the magnitude of global precedence is inversely related to pattern luminance. This latter finding is interpreted, in the context of Sternberg’s additive factors logic (1969), as indicating that this priority for global feature processing is at least partially attributable to aspects of early visual processes.

Relative frequencies of numerical responses in ratio estimation1

This study investigated the frequency of different numerical responses in ratio estimation as a function of the numerical categories actually used by Ss. Analyses were conducted for three series of experiments involving magnitude and free-ratio estimation for the attributes of stimulus length, area, and distance. It was found that Ss use certain numerical categories (e.g., multiples of 1, 10, and 100) much more frequently than others (e.g., 37.5) and that the choice of category depends upon the order of magnitude of the response. The statistical implications for ratio scaling are not dramatic, but are worthy of notice.

Transformation theory of size judgment

Perception of size is assessed by having observers adjust a comparison target at a fixed distance to match the size of a standard located at different distances. Results depend on instructions, target orientation, and available stimulus cues. A mathematical theory assumes that the brain performs an inverse transformation on the proximal information impinging on the retina to recover the original distal size of the target. Results depend on the target visual angle, and the effective target distance and orientation applied in performing the inverse transformation. Effective values are linked to instructions, target location, and stimulus cues. Two models are developed and successfully fit to empirical data. One emphasizes the distance parameter; the second, the orientation parameter.

Test of a cognitive theory of psychophysics: size discrimination.

The cognitive theory of psychophysics proposed in an earlier paper by Baird claims that the ratio of exponents obtained in the method of magnitude estimation for 2 stimulus attributes is equal to the ratio of information transmitted in the method of absolute judgment for those attributes. This theoretical prediction was tested experimentally for visual length and area. Results partially supported the prediction, inasmuch as the ordinal relations among exponents (length higher than area) was the same as the ordinal relation among information measures. However, in one instance, the exact quantitative relationship was significantly different from the predicted value.

Generation of multiple ratio scales with a fixed stitnulus attribute

Psychophysical theories differ in the relative weight given to sensory and cogruuve variables. Two opposing theories are described and tested in an experiment designed to vary a cognitive factor while maintaining a constant sensory factor. The method of magnitude estimation was used with the constant stimulus attribute of line length. The cognitive factor was varied by providing Ss with different feedback concerning the numerical values assigned to the largest and smallest lines in the series. This procedure led to multiple ratio scales for the same stimulus attribute. It is argued that these results support a theory which stresses both cognitive and sensory variables in the explanation of psychophysical functions.

Studies of the Cognitive Representation of Spatial Relations: II. A Familiar Environment.

This experiment tested the ability of people to recall the locations of buildings in a familiar campus setting. Ten graduate students represented the relative locations of buildings by pairwise distance judgments (on a 100-point scale) and by direct mapping of locations on a Tektronix cathode ray terminal. As evaluated by Stevenss power law, both methods led to accurate judgments of relative distance (the average exponent was close to 1). In addition, the pairwise judgments were analyzed by multidimensional scaling (MDS) and the buildings were located in a two-dimensional map. When asked to choose between the MDS representation and the map created directly on the Tektronix, all 10 subjects chose the latter as the more accurate. Moreover, 6 out of 10 subjects thought the direct map was more accurate than the actual map of the building locations. These results suggest that either pairwise judgment or direct mapping yield accurative representations of spatial relations in a familial environment, but that subjects favor the direct map.

An empirical test of two psychophysical models

Abstract Two theoretical relationships between sensitivity measures (Weber fractions, Ekman fractions, and their logarithms) and the exponents of the psychophysical power function were tested empirically with the brightness attribute. One model was based on Weber and Ekman fractions, the other on the logarithms of these measures. The stimulus parameters were time interval between standard and comparison targets and position of the standard in the luminance series. Weber fractions were based on data obtained by the method of constant stimuli, whereas Ekman fractions and exponents were based on data obtained by magnitude estimation. The results were in closer agreement with the theoretical predictions generated by the logarithmic model when group data were analyzed. With individual subjects, a detailed correspondence between fact and theory was not found with either model.

Studies of the Cognitive Representation of Spatial Relations: III. A Hypothetical Environment.

This experiment investigated peoples preferences for the location of facilities in an ideal town. Ten graduate students represented the relative locations of facilities (such as home, school, factory) by two methods: (a) pairwise ideal distances on a 100-point scale and (b) direct planning of locations on a Tektronix cathode ray screen. The pairwise distances were analyzed by multidimensional scaling (MDS) and the facilities were thus situated in a two-dimensional space. Subjects then expressed a preference between the direct plan and the one created by MDS. In addition, the rank order priorities of the facilities were determined for each subject. The entire procedure was repeated after 4 mo. A common central plan was evident in all cases (and rank order priorities were stable), but there was within-subject variability in the plans for different methods and test occasions. Despite such variability, subjects generally preferred their direct plan over the one created by MDS (based on pair estimates). A second group of subjects showed equal preference (on the average) for both types of town representations created by the first group. Both the pair and direct technique seem appropriate for studying cognitive representations of a hypothetical environment.

Overflow, First-Sight, and Vanishing Point Distances in Visual Imagery

The relationship between the size of a familiar object and the distances at which it is imaged is examined in three experiments. The distance at which an imaged object overflows the visual field is linearly related to object size, a result consistent with the size-distance invariance hypothesis (Kosslyn, 1980). The distance at which an object is initially imaged, first-sight distance, is related to the object size by a power function with an exponent less than 1. In addition, time required to scan from the first-sight to the overflow distance increases as a function of the difference between the two distance estimates. The distance at which an imaged object becomes too small to be identified, vanishing point distance, is related to object size by a power function with an exponent less than 1. This result does not support predictions made from the size-distance invariance hypothesis or Kosslyns model of visual imagery. Implications for a theory of visual imagery and memory are discussed.

When Power Functions Fail: A Theoretical Explanation

When the simple power function fails to describe psychophysical results, it is necessary to add or subtract a constant from either the stimuli or responses in order to reinstitute a power function. It is suggested here that this failure results from the nonlinearity of the function between the Weber fraction and stimulus intensity. Computer simulation experiments were conducted which supported this contention.