METODOLOGIA

The vast majority of experiments to be described are either single-interval or two- interval forced-choice tasks, in which the observer must choose one of two responses following the presentation of a single stimulus or a pair o f stimuli respectively. The experim ents were designed to measure thresholds or biases associated with a given perceptual task. This section describes in detail the psychophysical methods employed in the forced-choice experiments. An adaptive method of constant stimuli was used for all but the matching experiments of Chapter 7, the relative disparity effects experiment of

Chapter 3 and the texture experiments of Chapter 6. The m ethods used in these latter experiments will be described in the experimental detail of the appropriate chapter.

Psychophysical procedures and learning

A perceptual threshold is the quantity o f a stimulus cue necessary to detect its presence or absence, or to discriminate it from a standard, on a given proportion of occasions. The concept of the threshold therefore assum es a constant level o f perform ance; the threshold is a stable property o f the visual system. In practice, thresholds will vary with the tiredness, attentiveness and m otivation o f the observer. These artifacts can be rem oved by averaging across many random ly interleaved measurements. Thresholds are also affected by adaptation, which can build up during a series o f stimulus presentations, and by learning. The effect on threshold measurements of adaptation within psychophysical runs is an area of study in its own right (e.g. Legge, 1981) and although adaptation does occur in cyclopean vision it is not thought to be of specific importance to stereoscopic stimuli, when compared with any other types of visual stimuli (see Chapter 1). Where psychophysical studies acknowledge the effects of learning, it is common to assume that threshold performance is asymptotic following a given number of practice trials or informal observations. H ow ever, as mentioned in Chapter 1, RDS stimuli produce particularly strong learning effects. In order to monitor these effects it is therefore necessary to employ a psychophysical procedure which allows frequent threshold measurements to be obtained.

The classical Method of Constant Stimuli requires the observer to make a number o f forced-choice responses to stimuli drawn at random from a predeterm ined set of stim ulus levels. A psychom etric function is then fitted to the responses, often a cumulative normal fitted by Probit analysis (Finney, 1971). Learning can be a problem in at least two ways. Firstly, pilot runs are required in order to set the stimulus levels at a separation which produces a useful psychometric function. A considerable amount of learning may therefore take place which cannot be monitored. Secondly, a large number of observations are required to obtain an accurate threshold measurement. Any learning which occurs during the observations cannot be monitored and will be an artifact in the eventual threshold measurement.

Staircase procedures adapt to the observers forced-choice responses by sequentially increasing or decreasing the stimulus level in order to home in on a predetermined level of performance (e.g. Corn sweet, 1962). These procedures typically obtain a threshold estim ate using few er observations than the classical M ethod of Constant Stimuli. However, staircase procedures do have drawbacks. The stimuli are not presented in a random order, even when two staircases are interleaved, leading to an amount o f serial correlation in the responses. More specifically to learning, the number of trials within a staircase is not predetermined by the experimenter, but by a stopping rule

which depends on the observer's response accuracy. This means that threshold estimates are not obtained after a constant number of presentations. Observer fatigue may occur and accurate setting o f stimulus increments is required, again requiring a prior estimate of performance.

APE: Adaptive Probit Estimation

APE is an adaptive Method of Constant Stimuli designed by W att and Andrews (1981). It com bines the M ethod o f Constant Stimuli with the beneficial aspects of staircase procedures by allowing the chosen set of stimulus levels to be updated on the basis o f the subjects recent response history. In the version used in this thesis a run consists of 64 trials. On any one trial APE selects stimuli random ly from a set of 4 stimulus levels. Following each trial APE computes a Probit analysis on the last 32 trials or, if less than 32 trials have occurred, all the trials which have occurred up to that point. The estimates of the mean and standard deviation arising from the Probit analysis are then used to determine a new set o f 4 stimulus levels, which are placed symmetrically about the estimated 50% point and are narrowed or widened depending on the number of observer errors.

APE has a number of advantages for use in threshold estimation with RDS's. It allows an estimate of the threshold and bias to be taken every 64 trials. There is also a considerable amount o f leeway on the initial estimates o f stimulus levels, removing the need for pilot trials. Both of these properties are advantageous in experiments where learning can be considerable and the initial stages of learning are worthy of examination in their own right, as is the case with RDS's.

Due to increases in computational speed APE has undergone improvements since the publication of the original algorithm. Using M onte-Carlo simulations. W att and Andrews (1981) showed that the first version of APE, which estim ates the ongoing threshold and bias from fewer previous trials than the version employed here, produces smaller standard errors on threshold estimates from a given num ber o f trials, when compared with the classical Method of Constant Stimuli. APE was employed in all the threshold and bias estimation tasks to be presented.

The experimental environment

Experimental sessions were controlled by a "C" computer program written by the author. The program read a set of stored images into Random Access Memory (RAM) prior to each psychophysical run. On the completion o f each run the data were written to a file on the computer's hard-disk and displayed with the psychometric function on the screen. An example of the program output is provided in figure 2.5. The psychometric function was always obtained by fitting a cumulative normal by Probit analysis from 64 trials, as controlled by APE. Threshold is defined throughout this thesis as one standard

d e v i a t i o n o f th e u n d e r l y i n g n o r m a l d i s t r i b u t i o n f i t t e d b y t h i s m e t h o d . O n e s t a n d a r d d e v i a t i o n c o r r e s p o n d s to a p p r o x i m a t e l y th e d i s t a n c e b e t w e e n th e 5 0 % a n d 8 4 % c o r r e c t p o i n t s o f th e p s y c h o m e t r i c f u n c t i o n . T h e l o c a t i o n o f t h e 5 0 % p o i n t , o r m e a n o f th e u n d e r l y i n g n o m i a l d i s t r i b u t i o n , g i v e s an e s t i m a t e o f th e p o in t o f s u b j e c t i v e e q u a l i t y (P S E ) o r b ia s . P r o b i t a n a l y s i s a l s o p r o v i d e s s t a n d a r d e r r o r s f o r t h e e s t i m a t e o f th e s t a n d a r d d e v i a t i o n a n d m e a n , as w e ll a s a v a l u e o f c h i s q u a r e f o r u s e in a s s e s s i n g th e g o o d n e s s - o f - f it o f th e c u m u l a t i v e n o r m a l . O n th e r a r e o c c a s i o n th a t a f u n c t i o n s h o w e d s i g n i f i c a n t d e v i a t i o n f r o m th e p r e d i c t e d c u m u l a t i v e n o r m a l th e e s t i m a t e o f th e t h r e s h o l d a n d b ia s w e r e d i s c a r d e d . T h e r e q u i r e m e n t that i m a g e s be s to r e d in R A M p l a c e d a r e s t r i c t i o n o n th e n u m b e r o f i m a g e s o f a g i v e n siz e a v a i l a b l e f o r u se in e a c h ru n . B y s t r i p p i n g th e s y s t e m s o f t w a r e d o w n to a m i n i m u m , 7 7 0 0 K o f R A M w a s m a d e a v a ila b le . T h i s c o r r e s p o n d s to a set o f 2 0 10 X 10 d e g R D S i m a g e s f r o m w h i c h A P E c o u l d s e l e c t , w h i c h p r o v e d to be a m p l e f o r o b t a i n i n g t h r e s h o l d e s t i m a t e s a c r o s s a w i d e r a n g e o f d i f f e r e n t s e n s i t i v i t i e s . N o i m a g e s l a r g e r th a n 1 0 x 1 0 d e g w e r e u se d in a n y e x p e r i m e n t . s t i m u l u s n 1 7 : 1 6 - 2 4 0 -1. 2 0 - 0 . 9 0 - 0 . 6 0 - 0 . 3 0 0. 0 0. 0 1 . 2 s d P S E c h I r l 1 3 3 5 0 3 3 5 0 66 66 66 5 8 1 1 6 16 1 0 8 0 . 5 8 ( 0 0 1 7 ( 0 . 1 7 7 ( 1 5) 1 0 ) NOT S I G 9 ) NOT S I G IP I] 0 - # - - 2 d -B-B- [ | T 0 —I 2 4 F igure 2.5. An example o f the program output follow ing each run o f 64 trials. This particular example is taken fro m an orientation discrimination experiment to he described in Chapter 5.

T h i s l i m i t a t i o n o n th e n u m b e r o f i m a g e s a v a i l a b l e f o r u s e in a n y s i n g l e ru n i n t r o d u c e d a p o t e n t i a l a rtifa c t. A n R D S c o n s i s t s o f a r e c o g n i z a b l e d o t - p a t t e r n a n d d u r i n g a r u n e a c h R D S c o u l d a p p e a r o n a n u m b e r o f s e p a r a t e o c c a s i o n s . P o t e n t i a l l y , o b s e r v e r s c o u l d t h e r e f o r e l e a r n to a s s o c i a t e a g i v e n d o t - p a t t e r n w ith a p a r t i c u l a r r e s p o n s e , r a t h e r t h a n u s i n g th e a p p r o p r i a t e s t i m u l u s v a r i a b l e ( e .g . d i s p a r i t y ) to m a k e t h e f o r c e d - c h o i c e j u d g e m e n t . T h i s p r o b l e m w a s s o l v e d in a n u m b e r o f d i f f e r e n t w a y s , a c c o r d i n g to th e p a r t i c u l a r task . In s o m e c a s e s it w a s e n s u r e d th a t th e e a c h i n d i v i d u a l d o t - p a t t e r n w a s u se d to g e n e r a t e at le a st o n e s t i m u l u s w h i c h c o r r e s p o n d e d to e a c h o f th e a v a i l a b l e r e s p o n s e s . In o t h e r c a s e s , all th e s tim u li f o r a g i v e n r u n w e r e g e n e r a t e d f r o m j u s t t w o d i f f e r e n t d o t-

patterns. A solution or part-solution is provided in the experimental detail of individual experiments. In all cases, no observer reported a realization that the dot-patterns could potentially be helpful in making judgm ents nor that the reappearance of a given dot- pattern in any way affected responding.

A final check was always employed to ensure that no monocular cue could be used to solve the task. Prior to each experim ent the author perform ed at least one psychophysical run, with feedback, whilst viewing only one o f the displays. The data obtained were invariably at chance for all stimulus levels, confirming the absence o f a monocular cue.