Spatial frequency filtering and target identification

Vision Rcs. Vol. 27, NO. I, pp. 87-96. 1987 Printed in Great Britain. All rights reserved

0042-6989/87 s3.00 + 0.00 Copyright c 1987 Pcrgamon Journals Ltd

SPATIAL FREQUENCY FILTERING AND TARGET IDENTIFICATION

JOEL NORMAN and SHARON EHRLICH

Department of Psychology, University of Haifa, Haifa 31999, Israel

(Received 18 November 1985; in revised form 24 April 1986)

Abstract-Twenty subjects identified filtered pictures of previously learned target stimuli. Five filters were utilized: 3 two-octave wide band-pass and 2 complementary (same cutoff) high- and low-pass. Response times and per cent errors were used to assess performance. The filtered pictures were presented at two sizes: to ten subjects at twice the size presented to the other ten. The results indicated that higher spatial frequencies contribute more to the identification task than do the low spatial frequencies, but also that neither low nor very high frequencies are redundant for identification. It was also seen that both the proximal (c/deg) and the distal (c/picture) scales of spatial frequency measurement are involved in the identification process.

Visual identification Spatial frequency Filtering

INTRODUCTION

The analysis of the visual stimulus into its spatial frequency components has proven a boon to our understanding of the functioning of the visual system, both at the physiological level and at the psychophysical level. However, much of the research utilizing a spatial frequency approach has been limited to relatively simple visual phenomena such as contrast detection thresholds or the apparent contrast of simple suprathreshold stimuli. In comparison, relatively few attempts have been made to relate more complex visual phenomena to spatial frequency concepts. One exception has been Gins- burg (see review in Ginsburg, 1984) who has applied spatial frequency concepts to the understanding of many complex visual phenomena such as geometrical illusions, subjective con- tours, multistable forms, Gestalt grouping principles, and object identification.

(2) Proximal vs Distal Scale: which scale of measurement of spatial frequencies bears the stronger relationship to our measures of ease of identification, the distal scale or the proximal scale? The distal scale refers to the measurement of spatial frequencies in terms of the distal display without taking the observer’s viewing distance into account, and can be expressed in terms of cycles per picture width (c/PW) or per object width. The proximal scale refers to the measurement of the spatial frequencies in terms of the retinal image and is expressed in terms of cycles per degree of visual angle (c/deg). These two issues are examined by presenting subjects with spatially filtered pictures of previously learned targets and assessing performance with the aid of measures of response latency and accuracy.

Spatial frequency content

The present study examines the relations be- What range of spatial frequencies contributes tween spatial frequency content and the com- more to “higher” visual functions, high or low? plex visual task of object or target identification. Ginsburg, for one, tends to emphasize the con- (By “identification” we mean the task of deter- tribution of the lower spatial frequencies to mining which specific member of a class of various complex visual phenomena. Thus, for objects is being presented.) Other than at- example, his analyses of certain geometrical tempting to further demonstrate the relevance illusions, such as the Mueller-Lyer illusion, led of spatial frequency analysis to the identification him to suggest that it is the lower spatial task, we shall focus on two issues: (I) Spatial frequencies that are primarily responsible for Frequency Content: what is the relative con- their occurrence (Ginsburg, 1971, 1978). Carl- tribution of different parts of the spatial fre- son et al. (1984) examined this claim and found quency spectrum to the identification task? that stimuli containing no low frequencies in

87

88 JOEL NORMAN and SHARON EHRLICH

their spectra yield geometrical illusions of a magnitude similar to that obtained with stimuli containing low frequencies. Similarly, Ginsburg (1971, 1978) suggested that some Gestalt grouping phenomena may result from the functioning of low frequency visual filters, but Janez (1984) demonstrated such grouping when viewing highpass filtered images.

What of the process of identification? Gins- burg (1980, p. 222) concluded that low spatial frequencies are sufficient for identification and high spatial frequencies of objects are redundant. Fiorentini et al. (1983) tested the validity of this claim in a study of face perception. They asked subjects to identify filtered photographs of faces (one out of nine faces). Six different spatial frequency filters were used, three complementary pairs of high- and low-pass filters with the same cutoff frequencies, 5, 8 and 12 cycles per face width (c/w). During the training phase the subjects learned to name the unfiltered photographs, until achieving two consecutive errorless runs through the nine photographs. In the test phase the subjects were required to name the filtered photographs. The relative difficulty of a given filter was assessed by the total number of identification errors for that filter. It was found that performance with the 8 c/w high-pass filter was almost as good as with the 8 c/w low-pass filter. This and other findings led these researchers to conclude that “information conveyed by the higher spatial frequencies is not redundant. Rather, it is sufficient by itself to ensure recognition”.

While Fiorentini et al.‘s (1983) results point to a contribution of high spatial frequencies to identification, they do not negate Ginsburg’s (1980) claim that low spatial frequencies are also “sufficient” for identification. Thus, the question still remains as to what are the relative contributions of the high and low spatial frequencies. Assume that one wants to present pictures of a limited bandwidth, which spectral range, high, medium, or low will yield superior identification performance?

In an attempt to answer this question the present study employed both bandpass and low- and high-pass filters, using both response time and response accuracy as measures of performance. If, say, the high spatial frequencies contribute more to identification than low frequencies then we would expect faster response times and fewer errors on the filters with the higher frequency content. The high- and low- pass filters used in the study have common

Table I. The definition of the spatial filters

Proximal scale Distal scale Size I Size 2

Filter (c/de& (c/de@ (ClPW)

Fl 4-16 (8) 2-8 (4) 28.6-l 14.4 (57.2) F2 2-8 (4) I-4 (2) 14.3-57.2 (28.6) F3 14 (2) 0.5-2 (1) 7.2-28.6 (14.3) F4 >4 >2 > 28.6 FS <4 <2 < 28.6

The numbers in parentheses represent the central frequencies of the band-pass filters (Fl-F3).

cutoff frequencies with two of the bandpass filters (see Table 1 above). This makes it possible to assess the independent contribution of both very low and very high frequencies.

Proximal vs distal scale: cycles per degree or cycles per picture width?

Both Ginsburg (1978, 1980) and Fiorentini er al. (1983) define the spatial frequency spectra of their pictures in distal terms, cycles per picture width or cycles per face width, and not in proximal terms, c/deg. Fiorentini et al. (1983) could have utilized the proximal scale of spatial frequency but decided not to do so, explaining that “Since form perception is largely independent of distance, spatial frequency is more ap- propriately expressed in terms of one dimension of the object than in terms of cycles per degree of visual angle” (p. 196). In fact, these researchers chose to try and equate the initial differences between subjects by varying the viewing distances between 1 and 1.9 m, thereby varying the proximal values of spatial frequency by close to a factor of two.

Fiorentini et al. (1983) base their usage of the distal scale on the invariance of form perception with changes in viewing distance, or, in other terms, a combination of size constancy and shape constancy, possibly more akin to size constancy. Is their reliance on only the distal scale justified? On the one hand, the face perception task is much more like a threshold task than a constancy task, in which the highly “blurred” face is, at times, below an identification threshold. This might argue against only using the distal scale, since most threshold phenomena appear to be better related to the proximal scale. But, on the other hand, evidence has been accumulating for the existence of size constancy-like effects with sinusoidally modu- lated displays. Koenderink and van Doom (1982) term these effects “scale invariance” and propose a model to account for them.

Spatial frquency and target identification 89

Perhaps the first attempt to &k out scale of spatial frequencies is relevant, several predic- invariance with a spatial frequency task was tions follow. As far as the three bandpass filters that of Blakemore et al. (1972). They were (Fl-F3) are concerned, one of the Size groups unsuccessful, finding that adaptation should yield performance superior to the other, aftereffects to sine-wave gratings presented at depending on which part of the spectrum con- different distances were determined by the prox- tributes more to the identification task. In the imal (“angular” in their terminology) spatial case of the complementary pair of high- and frequency and not by the distal (“object”) spa- low-pass filters (F4 and F5) an interaction tial frequency. In contrast, a number of studies should emerge between performance and Size have reported what appear to be invariance group. The exact nature of this interaction will effects in a spatial frequency paradigm. It has also depend on whether high or low spatial been reported that, at low frequencies, contrast frequencies prove of greater importance to the thresholds for sine-wave gratings are dependent identification task. Several further predictions on the distal stimulus and not on the proximal follow from the specific filters selected. These stimulus (Hoekstra et al., 1974; Savoy and will be detailed in the Results and Discussion McCann, 1975; McCann et al., 1978; McCann sections. Here we only note that different band- and Hall, 1980). Other studies have indicated pass filters have the same proximal spectra in similar effects for suprathreshold phenomena, the two Size groups, and that the cutoff fre- such as the detection of contrast differences or quencies of the two complementary filters (F4 spatial frequency differences between two sine- and F5) are also the lower cutoff of one band- wave gratings (Jamar and Koenderink, 1983), pass filter (Fl) and the upper cutoff another the duration of the persistence of a grating bandpass filter (F3). (Long and Sakitt, 1981; but also see Lovegrove In sum, the experiment examines two ques- and Meyer, 1984), or the detection of the tions: Which range of spatial frequencies, high sinusoidal modulation of a random-dot display or low, contributes more to the identification (van Meeteren and Barlow, 1981). task? Which scale of spatial frequency measure-

Thus, these studies appear to show scale ment, distal or proximal, is more relevant to the invariance effects for spatial frequency displays. identification of complex objects? But, in view of the large differences between the type of displays employed and the observers’ tasks in the two types of studies, it would seem METHOD somewhat premature to conclude that only the distal scale is relevant for an identification task. Apparatus

We, therefore, decided to examine which scale, A Zilog PDS-8000 microcomputer controlled the distal or the proximal, bears the greater all aspects of the experiment. It controlled the relation to identification performance. We did Kodak Carousel random access slide projector this by dividing our subject population in two (RA-2000) that projected the stimuli and the groups where one group (Size 2 group) was Uniblitz (Vincent Associates, Rochester, N.Y .) presented with the stimuli at twice the size as electronic shutter that determined stimulus du- the second group (Size 1 group). Thus, the two rations. It also controlled the presentation of the groups differed only in the proximal spatial two auditory signals used in the experiment, the frequencies which defined the five spatial filters high-pitched warning tone given before each used in the experiment, being twice as high for stimulus presentation, and the buzzer which the Size 1 group as for the Size 2 group. This can designated error responses in the training be seen in Table 1 where both the proximal and blocks. All the subjects’ responses were fed into distal scale values are given, defining the three the computer, and these were utilized for inter- bandpass filters (Fl-F3) and the two com- trial feedback during the training blocks and for plementary high-pass and low-pass filters (F4 post-block performance information after each and F5, respectively). training and test block.

If only the distal scale of spatial frequencies The response box contained six response is relevant to the identification task there should keys: one “ready” button at the center near the be no differences between the performance of bottom, and five response buttons arranged on the two Size groups, since the distal frequency an imaginary arc, equidistant from the ready spectra of all the filters are the same for both button. A red LED indicator lamp was located groups. On the other hand, if the proximal scale beneath each of the five response buttons and a

90 JOEL NORMAN and SFLARON EHRLICH

yellow one above the ready button. The upper part of the response panel consisted of a row of four seven-segment LEDs. To its right the words “Correct Response” appeared, and to its left the words “Response Given” appeared.

Stimuli

The basic set of target stimuli consisted of a set of 25 photographic transparencies of five model toy tanks on a plain white background. These were equated for overall size. Each tank was photographed from five eye-level vantage points. These were: side view, back view, front view, half front and half side view, and half back and half side view. In the side view, target width was one half the picture frame width. These photographs were digitized to a 256 x 256 pixel resolution, computer filtered with the aid of a FFT, and balanced in their mean grey level (256 levels). Five pseudo- gaussian circularly-symmetric filters were utilized (see details in Table l), three two-octave wide band-pass filters (Fl-F3), and two complementary filters (having the same cutoff frequency), one a high-pass filter and the other a low-pass filter (F4 and F5).

The total of 150 target stimuli, 25 original digitized pictures (S) and live sets of 25 filtered pictures (Fl-F5), were photographed in black- and-white from a Conrac monitor.

The target stimuli were back projected at two different sizes. The Size 1 group targets were all presented at the smaller size of 10 x 7.5 cm (7.2 x 5.4 deg at the 80 cm viewing distance), while the Size 2 targets were presented at the larger size of 20 x 15 cm (14.3 x 10.7 deg). The stimuli were projected at a luminance of 270cd/m2 (as measured in the blank background}.

Subjects

Twenty subjects between the ages of 18 and 27 participated in the experiment. All subjects had normal or corrected-to-normal vision and were paid for participating in the experiment.

Procedure

Each subject participated in three sessions lasting about 2 hr each. The first session was a training session in which the subjects learned the source stimuli. The two other sessions were experimental sessions. Ten subjects were assigned to the Size 1 group and 10 others to the Size 2 group. With the exception of the size of

the stimuli the procedure for the two groups was identical. All sessions were carried out in normal room lighting. Viewing distance was 80cm.

The subjects were told that their task was first to learn the correct number of each tank, and then try and improve their performance by responding as quickly as they could without making errors. At the end of each block the subjects received information concerning how well they did on that block (number of points accumulated in that block, average response time, and the number of errors). This information appeared on the display at the top of the response panel. It was also explained to the subjects that in addition to a base fee paid for participating in the experiment a bonus fee would be added and it would be based on the total number of points accumulated in the experiment. It was further explained that the number of points accumulated in a block would depend on both the accuracy and speed of performance, but that errors lowered the point score much more than slow responses.

The training session was comprised of ten training blocks. Each block consisted of 75 stimulus presentations (3 of each of the source stimuli presented in a random order). The training method was one of “trial and error”. Feed- back after each trial in the training blocks consisted of both the “correct response” and the “response given” being presented on the response panel together with the LED under the correct response button. Three of the subjects who did not attain a criterion of less than IO errors in three of the last five training blocks were required to return for an additional training session identical to the original training session.

The subjects were instructed to press the “ready” button when they were ready for the next stimulus, and that a warning signal would be heard before the target appeared. The entire sequence was as follows: if the computer was ready for the next stimulus before the subject had pressed the “ready” button, the yellow LED indicator lamp came on. A 200 msec warning signal followed 300 msec after the “ready” button had been pressed, and 500 msec later the stimulus was exposed and remained on until the subject pressed one of the response buttons. If no response was given within 3 set (in the training blocks, 2.5 set in the test blocks) the shutter automatically closed. The subjects still had 2 set more during which they could re- spond.

Spatial frequency and target identification 91

The two experimental sessions consisted of eleven blocks each, one training block followed by ten test blocks. The test blocks also consisted of 75 stimulus presentations, but unlike the training blocks no feedback was given after each stimulus presentation. Information concerning performance was given at the end of each block just as it was for the training blocks. The ten test blocks at each experimental session comprised five pairs of blocks, the first block was of the source stimuli (S) followed by a block of each of the five filters (Fl-F5). All the stimuli in a filter block were of the same filter (three repetitions of each of the 25 stimuli). The ordering of the five filters was counterbalanced over subjects, and reversed between the two experimental sessions of a subject.

RESULTS

Identification performance was assessed with the aid of two measures: Response time (RT), the time elapsed from the exposure of the stimulus until the response button was pressed. Only correct responses were included in this measure; Per cent identification errors, the per cent of error responses out of the total number of valid responses. These did not include those rare cases where no response was given or where more than one response was given.

The training session proved quite effective. A plot of the means on the two response measures over the ten blocks of the training session indicated that the bulk of the improvement in performance occurred over the first five blocks with a more moderate rate of improvement from then on. The overall mean response time on the first block was about 2000 msec and this dropped to about 1000 msec by the tenth block. Similarly, per cent errors dropped from about 65 to about 10. There was a continued, but very slight, improvement on the source stimuli blocks during the two experimental sessions.

The overall results for the two Size groups on the five filters are presented in Fig. 1 and in Table 2. Data are also included for the source stimuli (the means of the first blocks without feedback in the two experimental sessions). These are presented to allow a qualitative comparison between the filtered and unfiltered stimuli. Source stimuli results are not included in the following analyses because the subjects were far more practiced on them than on the filtered stimuli.

Table 2. Mean response times and per cent errors

Stimulus We Size 1 Size 2 Total

S RT 989 906 948 PE 3.5 1.7 2.6

Fl ;; 1184 1082 1133 11.1 13.8 12.4

F2 ;; 1205 1205 I205 16.0 17.0 16.5

F3 ;; 1325 1319 1322 30.9 37.7 34.3

F4 E 1151 1012 1082 7.6 6.7 7.1

F5 ;; 1241 1273 1257 20.7 30.5 25.6

RT-response time in msec; PE-per cent errors; S-source stimuli; Fl-F5-filtered stimuli (see Table 1).

Response time and error performance were assessed with the aid of three-way analyses of variance. These are summarized in Tables 3 and 4. Both response time and error performance improved significantly from experiment day 2 to day 3, with mean response time dropping from 1271 to 1129 msec and overall per cent errors from 23.1 to 15.2. None of the interactions involving this variable was significant for both measures of performance in all the analyses performed.

E ._ c

1

!i ; %

q sin 1 1300- main2

VJOO-

“0°- 4 f -- D

son . I I I I I

Fig. I. Mean response times (in msec) and per cent errors as a function of stimulus type for the two size groups. Definitions of the five filters (Fl-F5) are given in Table I. Lines connect the results for the three bandpass filters (FI-F3) and for the two complementary high- and low-pass

filters (F4-F5).


Table 3. Summary of analyses of variance for response times

Source of variance d.f. F P

All five filters: Filters (Fl-FS) Size group (1 and 2) Experiment day (2 and 3)

Significant interactions: Filters x size group

Size group (1 and 2) Experiment day (2 and 3)


High- and low-pass filters: Filters (F4 and FS) Size group (1 and 2) Experiment day (2 and 3)


(4,721 34.51 (1.18) <l U&3) 101.10

(472) 5.03

(2.36) (1.18) (1918)

38.47 CO.0001 <1 NS

95.99 <0.0001

(2.36) 3.41

(L18) 42.13 (1318) <I (139 29.17

(1,W 9.96

<o.ooo1 NS

<o.ooo1

<0.0025

co.05

<0.0001 NS

<O.OOOl

<O.Ol

In the initial analysis, where all five filters were included, filters yielded significant main effects for both response time and per cent errors. The overall differences between the five filters can be seen in the Total column of Table 2. The main effect of Size Group was not significant for response time nor for per cent errors. The interaction between Filters and Size Group was significant for both response time and for per cent errors. This interaction is depicted in Fig. 1, with the exact values appear- ing in the Size 1 and Size 2 columns of Table 2.

In order to gain some more insight into the source of this interaction, separate analyses of variance were carried out on the three band-pass filters (Fl-F3) alone and on the two complementary filters (F4 and FS) alone. In these two analyses Filters also yielded significant main effects. In the case of the two com-

plementary filters, a significant Filter x Size Group interaction was found for both response time and per cent errors. The three band-pass filters yielded a significant interaction between Filters and Size Group only for the response time measure of performance but not for the per cent errors. As can be seen in the figure the source of the interaction for the response times is the difference in performance of the two size groups on Filter 1.

DJ!XUSSION

Spatial frequency content

What is the relative contribution of different spatial frequency ranges to identification? The results presented in Fig. 1 and Table 2 indicate that the relative contribution of the high spatial frequencies to our identification task is greater

Table 4. Summary of analyses of variance for errors in identification

Source of variance

All five filters: Filters (Fl-F5) Size group (1 and 2) Experiment day (2 and 3)


d.f. F P

(4.72) 64.01 <O.OOOl (1918) 1.05 NS (1.18) 25.36 <O.OOOl

(4,72) 2.62 <0.05 Bandpass filters:

Filters (Fl-F3) Size group (1 and 2) Experiment day (2 and 3)

Significant interactions: None

(2936) 68.14 <O.OOOl (1.18) <I NS (1318) 19.53 <O.OOOl

High- and low-pass filters: Filters (F4 and F5) Size xrouo (1 and 2) Expegmeh hay (2 and 3)


(1.18) 70.20 <0.0001 (1.18) 1.35 NS (l,lSj 11.79 -Co.005

(1.18) 5.95 <0.05


Filter Type

Fig. 2. Mean normalized response times (in msec) as a function of filter type for the two size groups. Detinitions of the five filters are given in Table 1. Lines connect the results for the three bandpass filters (Fl-F3) and for the two

complementary high- or low-pass filters (F4-FS).

than that of the low spatial frequencies. Per- formance on the three band-pass filters (Fl-F3) improves quite systematically with higher spatial frequency content. In other words, response times are quicker and error rates lower as the spatial frequency content of these two-octave filters increases. Similarly, in the case of the two complementary filters, high-pass and low-pass (F4 and FS), it is the high-pass which yields the better performance.

Does the superior performance attained with high spatial frequency filters mean that the low spatial frequencies make no contribution to the identification task? The results clearly indicate that this is not the case. It may be recalled that filters F3 and F5 have the same high frequency cutoff and the difference between them is that filter FS contains low frequency components not contained in filter F3 (see Table 1). As can be seen in Table 2, overall performance on filter F5 is superior to that on filter F3 for both the response time and per cent error measures. While the differences appear not to be very large, they are consistent over subjects and statistically significant [t (19) = 3.50, P < 0.01 for response time, and t(19) = 5.15, P < 0.001, for per cent errors].

One may also inquire whether the very high spatial frequencies contribute to identification performance. Comparison of performance on

filters F4 and Fl provides an answer to this question. These two filters have the same low frequency cutoff but filter F4 contains high frequency components not contained in Fl (see Table 1). Here, too, performance on both measures is consistently better for filter F4 than for filter Fl [t(19) = 3.41, P < 0.01 for response time, and t (19) = 5.11, P < 0.001 for per cent errors].

In sum, the results point to a greater contribution of high than low spatial frequencies to the identification task. But they also indicate that both low and very high spatial frequencies play a role in the identification of complex objects, and neither is redundant.

Proximal vs distal scale: cycles per degree or cycles per picture width?

What is the more appropriate spatial frequency measurement scale in an identification task, the distal scale or the proximal scale? Dividing the subjects into two Size groups was expected to yield an answer to this question. Briefly, the idea was that if the distal scale was relevant, no differences between the two Size groups would be found, but if the proximal scale was relevant differences would emerge. The exact nature of these differences would depend on whether high or low spatial frequencies were more important to the identification task.

The high spatial frequencies proved to contribute more to the identification task than the low frequencies. Thus, if the proximal scale is relevant, the following results would be expected: (1) superior performance on the three band-pass filters (Fl-F3) for the Size 1 group compared to the Size 2 group. In each case the c/deg are twice as high for the Size 1 group as for the Size 2 group; (2) an interaction should be found for the two complementary filters (F4 and F5), with superior performance for the Size 2 group on filter F4 and superior performance for the Size 1 group on filter Fl. This is because filter F4 contains more high spatial frequencies for the Size 2 group (above 2 c/deg) than does the same filter for the Size 1 group (above 4 c/deg), while the opposite is true for filter F5 (below 2 c/deg vs below 4 c/deg).

The results presented in Fig. 1 and Table 2 do not totally conform to the predictions of either the distal or the proximal scale. Some of the results appear to support the proximal scale while others the distal scale. The significant interactions between the two complementary filters (F4 and F5) on both performance mea-


sures support the proximal scale. The very slight and nonsignificant trend for fewer errors on the three band-pass filters (Fl-F3) in the Size 1 group also appears, at first, to be consistent with this scale, but the differences are much smaller than would be expected. (Recall the equivalence in proximal spatial frequencies between filters F3 in the Size 1 group and F2 in the Size 2 group, and between filters F2 in the Size 1 group and Fl in the Size 2 group.) On the other hand, the response time data for the three band-pass filters appear much more consistent with the distal scale. The response times for the two Size groups are virtually identical for filters F2 and F3 and those for filter Fl longer, rather than shorter, for the Size 1 group.

A partial solution to this somewhat confusing situation may be found in the data for the source stimuli (S) presented for comparison purposes in Fig. 1 and in Table 2. Response times on the source stimuli were 83 msec faster for the Size 2 group than for the Size 1 group. While this difference is not statistically significant [t (18) = 1.52, P < 0.201, it might hint at some initial difference between the two groups of subjects. On the one hand, this difference might be attributed to the fact that the Size 2 stimuli contain lower proximal frequencies (in c/deg) than the Size 1 stimuli and studies have shown that response time to low frequencies is faster than to high frequencies (e.g. Breitmeyer, 1975). But such a suggestion would be begging the question, being based on the assumption that the proximal scale is the relevant scale, while the data under consid- eration here appear to contradict this assumption. What is more, those studies which have indicated faster response times to low spatial frequencies have used much simpler stimuli, such as sine-wave gratings, and not complex pictures as used here.

An alternative explanation for the difference in the mean response times to the source stimuli is simply that a slightly faster group of subjects were fortuitously assigned to the Size 2 group. Assuming this to be the case we might attempt to partial out this inherent difference by sub- tracting the 83 msec difference from the response times of the Size 1 group. (An analysis of covariance is not possible because of the within-subject design.) The mean normalized response times appear in Fig. 2. As can be seen in Fig. 2 the differences in normalized response times between the two size groups tend, with one exception, to be smaller between pairs of

stimuli containing the same proximal spatial frequencies (in c/deg) than between the same distal stimuli presented at different sizes. In other words, after correction of the raw data of the two subject groups. the results for targets differing in size but with equal spatial frequency spectra become quite similar although not identical. None of these differences, though. attain statistical significance.

These trends together with the significant interaction found for the two complementary filters (F4 and F5) appear to converge on the conclusion that both the proximal scale and the distal scale are relevant to the identification performance examined in this study. Further corroboration of the relevance of the proximal scale can be found in our ability to better interpret some of the detailed results of the experiment while also taking into account the finding that high spatial frequencies contribute more to the identification task than do low spatial frequencies.

Returning to the comparisons between the band-pass and the high- or low-pass filters with the same cutoff frequencies (filters F3 vs F5 and Fl vs F4), we can now make differential predictions for the two Size groups. As was discussed above, filters F3 and F5 differ in that the low frequency components are missing from filter F3. In the Size 2 group the frequencies missing from F3 are below 0.5 c/deg and in the Size 1 group they are below 1 c/deg. Since higher frequencies are missing in the Size 1 group than in the Size 2 group, we would expect bigger differences in performance between these two filters in this group. This is indeed the case, the difference in response times is 84 msec in the Size 1 group and 43 msec in the Size 2 group, the respective figures for per cent errors are 10.2 and 7.2 (all but the 43 msec difference are statistically significant, P -c 0.01). Similarly, in the Fl vs F4 comparison the two filters differ in their high frequency components. In the Size 1 group the frequencies missing from Fl are above 8 c/deg while those missing in the Size 2 group are above 16 c/deg. We would, thus, expect bigger differences between these two filters in the Size 1 group. This, once again, turns out to be the case for both measures of performance, a 70 msec difference compared to a 33 msec difference and a 7.1% difference compared to a 3.4% difference (all but the 33 msec difference are statistically significant, P < 0.01).

In sum, unlike some of the scale invariance


effects mentioned in the Introduction, it would appear that many aspects of performance on an identification task are better described in terms of the proximal scale of spatial frequency measurement. But it should be also emphasized that some aspects of identification performance are better described in terms of the distal scale.

CONCLUSIONS

In his assessment of the contribution of different parts of the spatial frequency spectrum to identification, Ginsburg (1980) suggested that the lower spatial frequencies play the main role and that the higher spatial frequencies are redundant. Fiorentini er al. (1983) showed that this was not the case, high spatial frequencies sufficed in a face identification task. The present study further indicates that not only are the high spatial frequencies sufficient for identification but they yield superior identification performance when compared to low spatial frequencies. On the other hand, it should be noted that no single part of the spectrum (low and very high spatial frequencies) was found to be completely redundant for the task in question. It should, of course, be emphasized that our results were obtained for an identification task where the targets were structurally quite similar, and might have been differentiated with the aid of a limited range of spatial frequencies. Thus, it is possible that lower spatial frequencies might prove to be of greater importance in an identification task where the target ensemble is structurally heterogenous.

The present study also examined the relevance of the proximal (c/deg) and the distal (c/picture) scales of spatial frequency measurement to the identification task. It was found that both scales are involved in the identification process. It is not clear what this bifurcation means, but it should be noted that a similar bifurcation exists for the much more basic and simple contrast detection task, where the proximal scale appears to better describe detection of high frequency gratings and the distal scale the detection of low frequency gratings. Expla- nations of the latter bifurcation in terms of large-scale summation or integration have been put forth (Koenderink and van Doom, 1982), and perhaps these will prove also relevant to the identification task. At a different level of explanation, we might speculate that the involvement of both scales in the identification task stems from the fact that different types of processes

are transpiring simultaneously during the identification process. On the one hand, the identification task depends on sensory-visual resolution limitations, i.e. c/deg (the proximal scale). On the other hand, a cognitive mechanism governs the process of identification itself, that of relating the target to its memory representation. This cognitive mechanism is scale invariant by its very nature, i.e. distal (cf. Larsen and Bundesen, 1978; Koenderink, 1984). These speculations are compatible with the findings of the present study and deserve further research efforts.

Acknowledgemenfs-The authors would like to thank A. Koriat, P. Meer and D. Navon for very helpful comments on an earlier version of this paper, D. Malach and 2. Portnoy of the Signal Processing Laboratory, Faculty of Electrical Engineering, The Technion, for processing the pictures, E. Dichterman for computer programming, A. Papo and Y. Cohen for technical assistance and 0. Courant and T. Fibich for running the experiments.

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Spatial frequency filtering and target identification