Texture Gradient Registration and the Development of Slant Perception

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Running head: SLANT PERCEPTION







Texture Gradient Registration and the Development of Slant Perception
Douglas Degelman and Richard R. Rosinski
University of Pittsburgh






This article was published in the Journal of Experimental Child Psychology, 1976, Volume
21, pages 339-348. Copyright 1976 by Academic Press, Inc. Permission to post this manuscript
has been granted by the publisher.

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Abstract
The processes underlying the development of slant perception were investigated by manipulating
the degree of texture element variability. Subjects at four grade levels were required to make
judgments of physical slant of surfaces with three levels of variability. Absolute error of judg-
ment decreased with age, but texture variability had no effect at any grade level. The results
suggest that there is no improvement in the ability to extract gradient information. Rather,
improvement in the consistency of judgment reflects a developmental change in the relationship
between stimulus information and judgment.

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Texture Gradient Registration and the Development of Slant Perception
Since stimulus information available to an observer remains constant over age,
developmental changes in perceptual ability must reflect age related changes in information
utilization. Few attempts have been made, however, to assess the developmental changes in
information utilization, perhaps because of the difficulty in specifying the information
necessary for a particular task. This difficulty has been overcome in the area of space
perception and specifically the perception of slant (defined as the inclination of a surface
toward or away from an observer).
The informational basis for slant perception has been discussed by Purdy (1960), Flock
(1965), and Rosinski (1974). Purdy, in a mathematical analysis, has demonstrated that for
static, monocular arrays the relative rate of change of certain texture parameters (namely, the
height, width, area, and spacing of elements) defines a texture gradient which potentially
specifies surface slant. It has been shown that there is an invariant relationship between the
information provided by. a texture gradient and physical slant. The gradient available at any
point on the surface is directly related to the cotangent of the angle formed by the surface and
the line of regard. Consequently, the gradients unambiguously specify absolute slant of the
surface relative to any arbitrary reference axis.
As J. J. Gibson (1966) and E. J. Gibson (1969) have argued, there are two possible ways
in which developmental improvements in information utilization may occur, given such an
invariant relationship between texture gradient and physical slant. An individual's ability to
differentiate a gradient may improve; that is, his ability to compare texture elements and
extract the relative rate of change which defines a gradient may improve with age. As the
ability to differentiate a gradient improves, perceptual judgment should improve.

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Gibson (1969) argued that improvements in differentiation (i.e., in extracting information
from stimulation) accompany perceptual development. However, improvement in
differentiation is not sufficient to account for perceptual development. One must also pick up
the relationship between these visual inputs and those of other perceptual systems and detect
the multimodal invariant relationship among these sources of information. This extraction of
invariant relationships is a crucial aspect of development, since potential information may not
be effective if it is not related to physical layout: For example, a particular gradient may
provide no information (may be meaningless) unless the relationship between that optical
gradient and physical slant is established.
Such a conclusion is suggested by Rosinski and Levine (1976, in press). In studying the
effectiveness of various texture gradients, they presented stimulus displays which provided
either linear perspective gradient information or compression (foreshortening) gradient
information. One must, in order to extract a linear perspective gradient, compare the relative
width of texture elements along successive portions of the display. Although the minimal
processing capabilities (estimation and comparison of angular extents) necessary for the dif-
ferentiation of the two gradients are the same, differences in effectiveness were found.
Perspective gradients provided a more effective basis for slant judgment than did compression
gradients. These results suggest that the differential effectiveness of the two gradients may be
due to differences in the degree to which each gradient had been associated with the physical
slant it specified.
Although Purdy's (1960) analysis of texture gradient information assumed that each
texture element had the same physical size, both Purdy and Flock have shown that this analysis
applies to irregularly textured surfaces. If the size of texture elements varies over the surface,

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the gradient is defined as the rate of change in the average size of an element. That is, the
gradient is the relative rate of change of the average size of a texture element across the
display.
This extension of texture gradient theory to irregular surfaces has important implications.
Since size averaging must be used, the differentiation of a gradient should be more difficult
from irregular surfaces than from regular ones. However, since the gradient projected from
regularly or irregularly textured surfaces both define a particular slant, judgments should, in
principle, be equally accurate once the gradient has been differentiated. If perceptual
improvement is the result of improved gradient extraction, children should have considerably
more trouble than adults in judging the slant of irregularly textured surfaces. Children's
performance with regular textures may be nearly as accurate as that of adults. Studies by Flock
and Moscatelli (1964) indicate that adult subjects can differentiate a texture gradient in spite of
variability in texture element size. Regularity of texture element size had no significant effect
on the accuracy of slant judgments. These data suggest that adults are able to use texture
gradients specifying slant in spite of size variability; that is, they are able to overcome the
increased difficulty of differentiating the gradient.
The purpose of the present study was to explore developmental differences in slant
perception; to determine the effect of texture element size variability; and to determine whether
increasing the difficulty of differentiating a gradient would affect children's ability to judge
slant. If perceptual development is related to changes in differentiation ability, texture
variability and age should interact, with increased variability affecting younger subjects more
than older ones. If development is not simply related to changes in differentiation, an age
effect, but no variability effect, should be found. To test these predictions, we used surfaces

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like those found maximally effective by Rosinski and Levine, and manipulated difficulty of
differentiation by varying texture element size.
Method
Subjects
Twenty-four subjects at each of four grade levels (first, mean age 6.4 years; third, mean
age 8.4 years; fifth, mean age 10.3 years; and college student volunteers, mean age 19.3 years)
served as subjects. At each grade level an equal number of males and females were tested.
Subjects who normally wore corrective eyeglasses did so in the experiment.
Apparatus
In order to eliminate sources of information other than monocular texture gradients, the
technique of polar projection shadow casting was used (see Figure 1). A 25 W concentrated arc
lamp (arc size 1.2 mm) projected through a transparent generating surface onto a ground glass
rear projection screen. The generating surface was constructed so as to hold textured surfaces
at one of five slants (30, 40, 50, 60, or 70° from the vertical), with increasing slants indicating
increasing distance of the top of the surface. In order to reduce the possibility of a rectilinear
frame of reference for the subject, the screen was covered with a 13 in. (33 cm) circular
aperture (visual field size equals 20.5°). The axis of rotation of the generating surface bisected
the field of view which was completely filled with the projection of the generating surface at
all slants. A chin stand assured that the subject was at the appropriate station point during the
experiment. Subjects viewed the display monocularly.
Since the subject's head was not rigidly fixed, some amount of projective distortion was
possible if the subject shifted his position. In the present experiment, the maximal possible
displacement of the viewing point would introduce an optical magnification of 1.03, which

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would result in a maximal change in projected slant of less than 0.7°. The effects of such
potential distortions, then, are negligible.
Various stimulus gradients were presented by placing a sheet of textured Plexiglas on the
generating surface. Three textured surfaces were constructed using Tactype solid black squares
No. 2043. Position of the texture elements was identical for the three textured surfaces. Each
Plexiglas surface, 6 in. (15.24 cm) x 23 in. (58.42 cm) was partitioned into 552 1/2 in. (1.2 cm)
cells. Two hundred forty-two square elements were randomly assigned to the cells with the
restrictions that successive rows were staggered (to reduce linear perspective cues) and that no
more than three consecutive elements or three consecutive spaces could appear in a single row.
The mean element size on all three surfaces was 1/4 in. (0.64 cm). Surface 1 consisted only of
1/4 in. (0.64 cm) squares; surface 2 consisted of 1/8 in. (0.32 cm), 1/4 in. (0.64 cm), and 3/8 in.
(0.95) squares; and surface 3 consisted of 1/16 in. (0.16 cm), 1/8 in. (0.32 cm), 1/4 in. (0.64 cm),
3/8 in. (0.95 cm), and 1/2 in. (1.27 cm) squares.
Procedure
Subjects were tested individually and were instructed to set the inclination of a palmboard
to match the slant projected on the screen. Each subject was given four preliminary trials with
full binocular viewing to assure that the instructions and procedure were understood. After these
practice trials each subject made a total of 30 judgments, ten judgments of each surface in
counterbalanced order (two randomized blocks of the five physical slants). Between trials, the
screen was occluded while the physical slant was changed, in. order to eliminate the optical
transformations that accompanied adjustments of the generating surface. Subjects' judgments
were recorded to the nearest degree.
Results

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Several researchers have suggested that changes in error are important aspects of perceptual
development (Gibson, 1969; Lambercier, 1946; Wohlwill, 1963). Gibson, for example, has
shown that reductions in constant and variable error are characteristic of perceptual development.
Since our main concerns were with developmental processes in perception and with accuracy of
judgment, the first analysis involved absolute error, which provides a single index of both
constant and variable error and is thus a measure of developmental change. Absolute error was
analyzed in a 4 (grade) x 2 (sex) x 3 (texture variability) x 5 (slant) x 2 (block) analysis of
variance with repeated measures on the last three factors. Figure 2 presents mean absolute error
for each grade and level of texture variability.
There was a significant effect of grade on absolute error, F(3, 88) = 7.57, p < .001. Error
decreased over grade level. A Newman-Keuls analysis showed significant differences in
performance between Grades 1 and 3, 1 and 5, 1 and adult, 3 and adult, and 5 and adult (all ps
< .01). It is apparent that over the range of ages tested there is a progressive improvement in
slant perception based on texture gradient information.
No effect of texture size variability was found, F(2, 176) = 2.93, p > .05. Within the
range of texture variability used in this study, subjects were apparently able to differentiate
texture gradients regardless of element size variability. Neither constant nor variable error
varied as a function of texture size variability. Likewise, no Grade x Texture variability
interaction was observed, F(6, 176) = .86, p > .10. Younger subjects did not have
correspondingly greater difficulty differentiating the irregular textures.
A significant main effect of physical slant was observed, F(4, 352) = 21.59, p < .001.
Newman-Keuls analysis revealed that the mean absolute error of judgment was significantly

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larger for the slants of 30, 40, and 50° than for the 60 and 70° slants (all ps < .01). All other
main effects and interactions were nonsignificant (ps > .10).
Recently, Poulton (1973) suggested that the use of within-subject designs in
psychophysical experiments may be influenced by unwanted range effects. To ensure that such
range effects did not contaminate our results, a separate between-subject analysis of variance
was conducted using only the data from the first stimulus condition viewed by each subject
(again using absolute errors). As in the previous analysis, the effects of grade, F(3, 72) = 6.48,
p < .001, and physical slant, F(4, 288) = 13.05, p < .001, were significant. No other main
effects or interactions were significant (all ps > .10). The congruence between these two
analyses suggests that range effects did not influence our results.
In addition, a third analysis for position and carryover effects was conducted. This
analysis indicated that there were no position effects, F(2, 2866) = .25, p > .10, and no
carryover effects, F(4, 2866) = .19, p > .10.
The absolute error analysis demonstrated the existence of a developmental effect in this
task. To further examine the locus of this effect, several additional analyses were conducted
(see Table 1). The constant error of judgment varied little across grade, with adults averaging
less than a degree better than the first graders. A randomization test for independent samples
(Siegel, 1956, p. 152) showed no significant differences among grades, t(14,38) = - .02, p >
.10. Therefore, the developmental effect discussed above is not the result of increased
accuracy of judgment.
Variable error over the different grade levels, however, decreased significantly with
age, Cochran's C(4, 719) = .33, p < .01. This pattern of results suggests that the
developmental effect observed in the absolute error analysis is a result of a developmental

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improvement in the consistency of slant judgments rather than their accuracy. These results
are also consistent with Gibson's findings that “variable error decreases steadily with age,
and more consistently than does constant error” (1969, p. 375).
These conclusions were further supported when the slant judgments were evaluated in
an analysis of variance, with the same five factors as in the absolute error analysis. There
was no effect of grade on the judgments of slant, F(3,88) = .15, p > .10. Since an analysis of
slant judgments is responsive only to changes in constant error, this result indicates that there
was no change in constant error over grade. This suggests, in turn, that the observed grade
effect in the absolute error analysis is a result of a change in variable error.
The main effect of sex was significant, F(1, 88) = 7.46, p < .01. Females tended to make
more accurate slant judgments than did males. There was also a significant main effect of
physical slant, F(4, 352) = 321.00, p < .001, indicating that there was a correspondence
between physical and judged slant. All other main effects and interactions were nonsignificant
(all ps > .10).
To provide a means of comparing our data with those of previous studies (see Flock, 1965),
regression equations are presented in Table 2. Individual slopes were analyzed in a 4 (grade) x 3
(texture variability) analysis of variance (see McNemar, 1962, pp. 352-356). Although there is an
apparent trend toward decreasing slopes over grade, this trend is nonsignificant, F(3, 92) = .81, p
> .10. Similarly, there is no significant effect of texture variability on slopes, F(2, 184) = 4.35, p
> .01.
Discussion
The finding that absolute error of judgment decreases with grade replicates and extends the
previous findings of Rosinski and Levine. Our results show that even in the first grade, children

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Document Outline

• Running head: SLANT PERCEPTION
• Texture Gradient Registration and the Development of Slant Perception
  • Abstract
    • The processes underlying the development of slant perception were investigated by manipulating the degree of texture element variability. Subjects at four grade levels were required to make judgments of physical slant of surfaces with three levels of v
    • Texture Gradient Registration and the Development of Slant Perception
    • Since stimulus information available to an observer remains constant over age, developmental changes in perceptual ability must reflect age related changes in information utilization. Few attempts have been made, however, to assess the developmental cha
      • Method
      • Subjects
      • Twenty-four subjects at each of four grade levels (first, mean age 6.4 years; third, mean age 8.4 years; fifth, mean age 10.3 years; and college student volunteers, mean age 19.3 years) served as subjects. At each grade level an equal number of males a
      • Apparatus
      • In order to eliminate sources of information other than monocular texture gradients, the technique of polar projection shadow casting was used (see Figure 1). A 25 W concentrated arc lamp (arc size 1.2 mm) projected through a transparent generating s
        • Procedure
        • Subjects were tested individually and were instructed to set the inclination of a palmboard to match the slant projected on the screen. Each subject was given four preliminary trials with full binocular viewing to assure that the instructions and procedu
        • Means and standard deviations of slant judgments for each grade-slant combination

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