Brightness induction and the Cafe Wall illusion

Perception, 1983, volume 12, pages 131-142

Brightness induction and the Cafe Wall illusion

Mark E McCourtll
Department of Psychology, University of California, Santa Barbara, CA 93106, USA
Received 15 October 1980 , in revised form 27 August 1982

Abstract. The Cafe Wall illusion is a distortion illusion in which the parallel lines of a chessboard­
like figure consisting solely of parallel and perpendicular line elements appear to converge in
alternating rows, creating a wedge distortion similar to that of the well-known Zollner illusion.
Gregory and Heard have formulated an explanation for 'the Cafe Wall illusion which relies upon the
operation of a 'border-locking mechanism' in the visual system. 'The results of the present
experiment suggest an alternative explanation in which the operation of brightness induction within
the mortar regions of the Cafe Wall produces a series of 'twisted cords' or slanted line elements
akin to those of the Fraser or Zollner figures. A series of such 'twisted cords' is shown to be
capable of itself to produce an illusory convergence like that of the Cafe Wall. Manipulations of
the luminance of discrete regions in the mortar lines of the Cafe Wall, designed either to augment
or cancel the effects of brightness induction in the production of these slanted line elements, are
successful in enhancing or reducing, respectively, the wedge distortion of this visual illusion.

1 Introduction
 1.1 Border-locking hypothesis
The Cafe Wall illusion is a distortion illusion in which the parallel lines of a
chessboard-like figure consisting solely of parallel and perpendicular line elements
appear to converge in alternating rows, creating a wedge distortion similar to that
which characterizes the well-known Zollner illusion.
    Gregory and Heard (1979) have reported results from experiments indicating that
the Cafe Wall illusion may be the product of the operation of a 'border-locking
mechanism' in the visual system. They proposed that the normal operation of this
mechanism keeps luminance boundaries in the visual environment in precise spatial
register by compensating, where possible, for the differential latencies associated with
retinal signals generated from regions of dissimilar luminance (Rogers and Anstis
1972). It has been proposed that in the Cafe Wall figure border-locking occurs
between such regions of dissimilar luminance (the light and dark tiles) across narrow
regions of neutral grey or of intermediate luminance (the mortar lines).
    It is postulated that the immediate consequence of the border-locking process in
the Cafe Wall is the pulling together of the light and dark contrasting tiles across the
gap created by the intermediate-luminance mortar region. Gregory and Heard (1979)
report that individual (square) tiles appear to assume trapezoidal shapes, a phenomenon
ascribed to the narrowing of the mortar regions between contrasting tiles as they are
pulled together. A series of tiles with slanted edges is thereby created which is
subsequently integrated, by an independent 'global' process which is not as yet well
characterized, into the overall impression of wedge-like rows of tiles, ie into the Cafe
Wall illusion. Similar global processes, in which repeated small-scale elements evoke
illusory convergences and other large-scale perceptual distortions, are thought to underlie
the well-known Zollner and Fraser figure illusions of direction. In sum, the border­
locking hypothesis of Gregory and Heard (1979) suggests that the small-scale features of
the Cafe Wall are the trapezoidally distorted tile elements whose shapes derive from
~ Address for reprints and correspondence: Department of Physiology, John Curtin School of
Medical Research, The Australian National University, Canberra, ACT 2601, Australia

132                                                                           M E McCourt

contour shifts caused by locking signals which occur across the mortar regions between
tiles of contrasting luminance.
1.2 Brightness indue tion and visual illusions
The phenomena of brightness induction have been implicated in the production of a
wide variety of visual illusions; among these are Mach bands (Fiorentini 1972), the
Hermann grid illusion (Spillmann and Levine 1971; Lavin and Costall 1978), the
Kanizsa figure (Frisby and Clatworthy 1975), and the Ehrenstein illusion (Spillmann
et a11976; lory and Day 1979).
    Brightness induction has recently been shown to operate as a function of several
previously unrecognized variables, eg the spatial frequency (McCourt 1980, 1982)
and orientation (White 1979, 1981; McCourt 1980, 1982) of periodic inducing regions.
This means that if a periodic inducing field, such as a sine-wave or square-wave grating,
is interrupted by a homogeneous test field of equal average luminance, a counterphase
brightness modulation appears within the homogeneous region. What distinguishes these
instances of brightness induction from those expected to accrue from retinal lateral
inhibition (Ratliff 1974) is the observation that such counterphase brightness
modulations are highly directional, preserving both the spatial frequency and the
orientation of the surrounding inducing grating.
    This pattern-dependent brightness-induction effect, along with several of the factors
which govern its strength, is illustrated in figure 1. A number of these factors will be
considered in advance of their forthcoming application to the Cafe Wall illusion.
First, the height of the homogeneous test field affects the perceived contrast of the
induced brightness modulations: the perceived contrast of the modulations decreases
monotonically with increases in the height of the test field (McCourt 1980, 1982).           a
Second, the luminance of the test field must not depart substantially from the average       •
luminance of the inducing field, or the brightness-induction effect is weakened: the
greatest induction effects occur when the test and inducing fields have approximately
the same average luminance. Finally, the spatial frequency and harmonic content of
the periodic inducing field govern the strength of the induction effect: low spatial
frequencies produce stronger induction effects than do high frequencies, and sine-wave
gratings induce brightness modulations of higher perceived contrast than do square-
wave gratings of the same spatial frequency and contrast. For a complete account of
these experiments and results see McCourt (1982).
    The spatial configuration of the Cafe Wall figure, ie the narrow mortar lines
surrounded by light and dark tiles (resembling patches of square-wave grating), bears
a notable resemblance to the configurations shown in figure I, and induced brightness
variations are likely to be generated in its mortar regions. The experiment reported
here had as its objective to investigate the contribution such brightness variations might
make in the production of the Cafe Wall illusion. The results of this experiment, as
well as those of Moulden and Renshaw (1979) which concern the Mi.insterberg illusion,
suggest that brightness induction plays an originating role in the Cafe Wall illusion.

2 Method
2.1 Subjects
The subjects were fifteen undergraduates (eight male, seven female) from the University
of California, Santa Barbara. All subjects were emmetropic or wore corrective lenses.
2.2 Materials
Three cases of the Cafe Wall figure were drafted and photographed. Each photograph
measured 4.7 em in height by 10.5 ern in width. Individual Cafe Wall tiles measured
7.0 mm x 7.0 mm; mortar lines were 0.7 mm in height. The (Michelson) contrast
of the tiles was 86.4%, and the three cases, referred to py
                                                          number, differed solely

Bri ght ness ind ucti on and th e Cafe Wall illusion
                                                                                                       133

with respect to the presence and position of luminance contrast within discrete
regions of their mortar lines. Photographs of the three cases of the Cafe Wall figure
used appear in figure 2.
    Case I is the original Cafe Wall configuration of Gregory and Heard (1979) in
which the mortar luminance is homogeneous and intermediate between those of the
light and dark tiles. Cases 2 and 3 differ from !case I in that luminance contrast has
been added to the mortar lines such that a light patch is situated between the light
tiles and a dark patch between the dark tiles (case 2), or, conversely, the light patch

(a)

(b)                                                     (c)

(d)                                                     (e)
Figure 1. Displays illustrating pattern-dependent brightness-induction effects:
(a) low-spatial-frequency indu cing grating and brightness induction in a homogeneous test field;
(b) higher-spatial-frequency inducin g .grat ing and brightness induction in a narrower test field ;
(c) reduc ed induction effect for square-wave inducing gratings-compare with (b) ;
(d) and (e) reduced perceived induction effect for test fields whose luminance deviates from the
average luminance of the inducing field.                    I
Photographic reproduction may alter the actual luminan ce distributions of the se displays.

M E McCourt

                                                                                                          •
134

                                                                    I

is situated between the dark tiles and the dark patch between the light tiles
(case 3)(1). In the three versions of the Cafe Wall figure uScld in this experiment the
average luminance of the mortar lines (48.0 cd m-2 ) was approximately equal to the

                                                                           Case 1

                                                                           Case 2

                                                                           Case 3
Figure 2. Three experimental cases of the Cafe Wall figure.
Case 1: The original figure in which the mortar luminance is homogeneous and intermediate
between those of the light and dark tiles.
Case 2: Local luminance contrast has been introduced into the mortar lines: dark mortar patches
appear between the dark tiles, and light mortar patches appear between the light tiles. This
manipulation, undert aken to reduce or cancel the effects of brightness induction within the mortar
lines, virtually eliminates the illusory convergence of case I.     :
Case 3: The phase of the local luminance contrast patches has been shifted so that light patches
now appear between dark tiles and dark patches appear between light tiles. Intended to augment or
simulate the effects of brightness induction in the mortar lines of the Cafe Wall figure, this
manipulation enhances the illusory convergence of case I.
(1) The construction and positioning of the luminance patches within the mortar lines of the Cafe
Wall figures used in this experiment were accomplished by first removing the mortar lines from an
intact Cafe Wall figure. The figure from which the mortar regions were removed was placed over a
series of light, dark, and grey patches which could be variably positioned within the cut -out mortar
regions. By moving the top figure relative to the underlying one, cases 1, 2, and 3 of the Cafe Wall
figure were constructed and photographed from the same template. There can be no possibility,
consequently, that subtle differences in either the luminance, contrast, clarity, or periodicity of the
mortar regions of these figures contributed in any way to the differential evaluations which they
received.

Brightness induction and the Cafe Wall illusion                                                 135

average luminance of the light (96.0 cd m- 2 ) and dark (7.0 cd m- 2 ) tiles. Additionally,
the mortar regions situated between tiles of dissimilar luminance remained in each case
at an intermediate, neutral luminance.
   Subjects shown a version of the Zollner illusion were instructed to notice the
apparent convergence of its horizontal parallel line elements. Subjects then viewed
the three cases of the Cafe Wall in a normally lighted room (illuminance of 250 lux)
from a distance of 50 cm. Individual tiles of the Cafe Wall subtended 48 min x 48 min,
while the mortar lines subtended 4.8 min of arc in height. Subjects rank-ordered the
three versions of the Cafe Wall figure based on the degree of perceived convergence of
the parallel line elements. Most subjects reported little difficulty in establishing an
ordinal relation and expressed confidence in their judgments.

3 Results
The rank-orderings of the three photographic versions of the Cafe Wall figure by the
fifteen subjects are shown in table 1. In a test against the null hypothesis of equal
convergence strength, a chi-square analysis of these frequency data shows a highly
significant effect (X2 = 78.8, p < 0.001, d.f. = 4), indicating that the manipulated
variable-the presence and position of luminance contrast within discrete regions of
the mortar lines of the Cafe Wall figure-is capable of altering the degree of perceived
convergence of the parallel lines in this illusion. The effect of these manipulations is
quite robust, as shown in figure 2, where the presence of dark mortar patches
between the dark tiles and light patches between the light tiles (case 2) virtually
eliminates the wedge distortion. Conversely, the presence of dark mortar patches
between the light tiles and light patches between the dark tiles (case 3) greatly
enhances the perceived convergence in the Cafe Wall figure.

Table 1. The rank-ordered strengths of the illusory convergence of the three cases of the Cafe Wall
by fifteen subjects in this experiment.

Case     Rank-orderings

         most     mid      least    total

1         1       14        0       15
2         0        0       15       15
3        14        1        0       15
Total    15       15       15

4 Discussion
According to the border-locking hypothesis the illusory convergence of the parallel
lines in the Cafe Wall accrues from the global integration of local tile contour shifts,
the latter arising because of the border-locking signals generated across the neutral
mortar line between tiles of dissimilar luminance (Gregory and Heard 1979). Note
that these mortar regions, crucial to the generation of border-locking signals, were
present and intact in both of the novel cases of the Cafe Wall figure. The mortar- tile
interfaces of all three cases of the Cafe Wall used appear in detail in figure 3.
   Figure 2 shows that the strength of the illusory convergence of the Cafe Wall can
be changed dramatically without changing the regions across which border-locking
signals are supposed to operate (Gregory and Heard 1979). A problem thus arises for
the border-locking hypothesis which, unfortunately, is not presently framed in
sufficient detail to allow the application of a critical test. It is possible, for example,
that the luminance contrast with neighboring regions of the mortar lines could affect,
in an unspecified manner, the production of border-locking signals.

136                                                                                     M E McCourt

   The results of the present experiment nevertheless suggest an alternative explanation
for the Cafe Wall illusion which is based on the brightness-induction phenomenon
described earlier (McCourt 1980, 1982) After a critical review of the proposed
explanation, in which the brightness-induction hypothesis is examined vis-a-vis data
from previous studies, the various theoretical accounts of the Cafe Wall illusion are
considered.

                                      Case 1

                                      Case 2

                                      Case 3

Figure 3. Magnified views of the regions of tile -mortar interface in the three cases of the Cafe Wall
figure shown in figure 2. Case 1 is the original version. The mortar regions, like those from A to A
between tiles of contrasting luminance, are reported by Gregory and Heard (1979) to be the site of
generation of border-locking signals. Case 2, intended to cancel the effects of brightness induction,
preserves these mortar regions (from A to A) unaltered. Case 3, intended to augment the effects of
                                                                                                         e
brightness induction within mortar regions from B to Band C to C, likewise leaves the mortar
regions from A to A unaltered.
4.1 Mortar luminance
The degree of apparent convergence in the Cafe Wall depends upon the luminance of
its mortar regions (Gregory and Heard 1979). Deviations of the mortar luminance
from the average luminance of the light and dark tiles reduce the strength of the
illusory convergence. The strength of brightness induction in homogeneous test fields
(eg a mortar line of the Cafe Wall) is likewise dependent upon the luminance relation
between the test and inducing fields (McCourt 1982; Foley and McCourt
forthcoming). As shown in figures ld and Ie, deviations in the luminance of the
test field from the average luminance of the inducing grating decrease the magnitude
of the perceived brightness modulations.
4.2 Mortar-line height
The wedge distortion of the Cafe Wall occurs only if its mortar lines are sufficiently
narrow. Gregory and Heard (1979) report that they must not exceed 10 min of
visual angle. The brightness-induction phenomenon of figure I is monotonically
related to the height of the homogeneous test field (McCourt 1980, 1982). Induction
effects of the greatest perceived contrast were found to occur in the narrowest test
fields (the smallest employed measured 6 min of arc).
4.3 Tile contrast
Gregory and Heard (1979) report that the Cafe Wall illusion is most robust when tile
contrast is near unity; lower tile contrasts necessitate narrower mortar lines to sustain
the same degree of apparent convergence in the illusion. The perceived contrast of the
induced brightness variations in displays like those of figure 1 is similarly related to the
contrast of the inducing pattern (McCourt 1982; Foley and McCourt forthcoming).

Brightness induction and the Cafe Wall illusion                                                         137

Over several octaves of stimulus contrast the magnitude of the induced brightness
modulations in narrow test fields, as measured by a cancellation technique, is
proportional to the luminance contrast of the surrounding inducing grating.
4.4 Phase of tile displacement
The direction of the wedge distortion of the Cafe Wall reverses with half-cycle shifts
in the phase of alternate rows of tiles (Gregory and Heard 1979). Reversals in the
direction of the vanishing points of alternate wedges are accompanied by a passage
through zero distortion when the Cafe Wall assumes a chessboard configuration
(Gregory 1977).
   The degree of apparent convergence in the related Munsterberg figure (cf figure 4)
likewise varies as a function of the tile displacement (Moulden and Renshaw 1979).
Wedge distortion was found to be maximal with half-cycle phase shifts, and minimal
or no distortion occurred when the figure was in a chessboard phase. Intermediate
phases produced intermediate-strength wedge distortions. The dependence of the
illusory convergence upon the phase of the tile displacement is compatible with the
proposed brightness-induction mechanism. Since the induction effect has strong
directional properties (White 1979, 1981; McCourt 1980, 1982), induced brightness
variations will occur principally in the mortar regions of the Cafe Wall which are
bounded by tiles of similar luminance'

138                                                                                   M E McCourt

This is true also of the Mtmsterberg figure (Moulden and Renshaw 1979). Both
peripheral viewing and defocusing effectively low-pass filter the distribution of
spatial free:'lencies which comprise the Cafe Wall figure. The augmented illusory
convergence which accompanies low-pass spatial-frequency filtering may arise
indirectly because of the greater strength of brightness induction which occurs, for
example, when high spatial frequencies are removed from compound inducing gratings
(McCourt and Foley 1982). This is illustrated in figure 1c, where the square-wave
inducing grating produces a weaker brightness-induction effect than does the sine-wave
grating of equal spatial frequency and contrast. The probable effect of increasing the
contrast of the brightness variations within the mortar regions of the Cafe Wall is
shown in figure 2, where case 3, possessing high-Ienhanced-) contrast luminance
variations, appears to have greater convergence than case 1 in which visually induced
brightness variations of lower contrast are suggested to support the illusion. Low­
pass-filtering square-wave inducing gratings increases the perceived contrast of their
induced effects; and if brightness-induction effects are involved in the production of
the wedge distortion of the Cafe Wall figure, then peripheral viewing and defocusing
are operations which are predicted to produce greater perceived convergence.
4.6 Isoluminant conditions
Gregory (1977) and Gregory and Heard (1979) report that the Cafe Wall illusion persists
if colored tiles are used in place of achromatic tiles, but not under conditions of iso­
luminance. The fact that illusory convergence does not occur under conditions of
isoluminance reveals that luminance contrast is required for the production of the
distortion. Note that in the absence of luminance contrast, brightness induction
within the mortar regions of the Cafe Wall is also eliminated.
4.7 Relation to the Miinsterberg illusion
Both the Munsterberg and Cafe Wall figures consist of rows of light and dark square
tiles alternately phase-shifted by one-half cycle. The difference between them is that
each row of tiles in the Munsterberg figure (see figure 4) is separated from the other
rows by mortar lines whose luminance is equal to that of the dark tiles. Thus the
Munsterberg figure is essentially a limiting case of the more general Cafe Wall figure,
in which the luminance of the mortar lines is variable (Gregory and Heard 1979).
    The spatial and intensive parameters which govern the strength of the illusory
convergence of the Munsterberg figure (Moulden and Renshaw 1979) are generally in
accord with those reported for the Cafe Wall figure (Gregory 1977; Gregory and
Heard 1979). In addition to the phase-adjustment variable already mentioned,
Moulden and Renshaw (1979) demonstrated the primary importance of the presence
of the mortar lines themselves in the production of the illusory convergence of the
Munsterberg figure. A Munsterberg figure from which the mortar lines have been

Figure 5. A Mtinsterberg figure from which the mortar lines have been removed. The illusory
convergence has largely been eliminated. The presence of mortar lines is shown to be essential for
the production of the Cafe Wall and Mtinsterberg illusions. See text for details.

Brightness induction and the Cafe Wall illusion                                                    139

removed is shown in figure 5. The illusory convergence of this figure is very much
attenuated in comparison with the intact version shown in figure 4. Without its
mortar lines, moreover, the Munsterberg figure of figure 5 bears a strong resemblance
to the cancelled version (case 2) of the Cafe Wall figure (figure 2).
   In sum, the illusory convergence of the Cafe Wall is most severe when the mortar
lines have a luminance intermediate between those of the light and dark tiles. When
the mortar is darkened, as in the Miinsterberg figure, the illusory convergence is
reduced. It is abolished altogether, or very nearly so, when the mortar lines of these
figures are simply removed. Removing the mortar lines from these figures also removes
the regions within which brightness induction can occur. Thus the progression in the
strength of the row-convergence illusion which accompanies changes in the presence
and/or luminance of the mortar lines of these figures has a parsimonious interpretation
within the framework of the brightness-induction hypothesis.
4.8 Brightness-induction hypothesis
Experimental manipulations of the luminance of discrete regions within the mortar
lines of the Cafe Wall figure have been shown to \change, in a predictable manner, the
degree of perceived wedge distortion in this illusibn. Parameters of the stimulus
which were previously found to influence the strength and occurrence of the illusory
convergence have been individually examined and their close correspondence with the
parameters which govern the strength of brightness induction has been underscored.
   The brightness-induction hypothesis proposes that the row convergence seen in the
Cafe Wall figure arises in two stages. First, brightness variations are induced within
the mortar lines of the Cafe Wall by lateral inhibitory mechanisms similar to those
described by McCourt (1982). The positions of these induced brightness variations
are such that they effectively join together the corner regions of the phase-displaced
like-luminance tile squares (as in case 3 of figures 2 and 3), thereby creating within
each mortar line the appearance of a series of 'twisted cords' or slanted line elements.
The direction in which these lines slant across the mortar reverses with each mortar
line, and this results in a Zollner-type configuration'P'.

(3)Moulden and Renshaw (1979) tested the hypothesis of Robinson (1972) that a Zollner-type
arrangement of 'inducing' and 'victim' lines might underlie the Munsterberg illusion. This idea was
rejected, however, in the light of the experimental result that the optimal tile phase-displacement
(ie that producing the greatest illusory convergence) corresponded to a figure geometry where
inducing lines intersected their victim lines at 60° angles. i Convergence in the Zollner illusion is
maximal when the intersection angle between these lines 1     s 15- 30°, whereas little or no effect is
reported for angles as large as 60° (Wallace and Crampin [969; Oyama 1975).
    Significantly the angle of intersection yielding maxima convergence in the Zollner illusion is
nearly identical to that which produces the maximal angl -expansion effect (Blakemore et al 1970;
Carpenter and Blakemore 1973). This has been taken to imply that the inhibitory interaction
between the inducing and victim lines of the Zollner figure results in the tilting of the (continuous)
victim line away from the orientation of the inducing line in the vicinity of each intersection. Thus
the inducing lines ultimately produce a series of reciprocally-slanted (ie induction-repelled) victim­
line segments, and it is the series of these latter line segments which constitutes the proximal
stimulus for the Zollner convergence. It is likewise such a series of slanted line segments which
constitutes the input for the second 'global-integrative' stage of the Cafe Wall illusion mechanism
described above. This theory also provides an explanation for the 'negative' Zollner illusions which
occur with shallow « 10°) inducing-line intersection angles (Oyama 1975). Shallow inducing angles,
rather than provoking an inhibitory (angle-expansion) interaction with the victim line, may instead
lie within the excitatory pass-band of the orientation-selective units responding to the victim line.
The two orientations will thus be integrated; the mean orientation of the two lines may represent
their integration product (Carpenter and Blakemore 1973). The series of slanted line segm.ents thus
produced may constitute the input to the hypothesized 'global-integration' process (cf figure 6 for
an example of how this might occur).

140                                                                                       ME McCourt

   Second, the series of slanted mortar-line elements thus produced by brightness
induction is integrated by a global process similar to that which underlies the Zollner
or Fraser figure illusions. It is this second process which is postulated to underlie
their large-scale convergence. This explanation for illusions of direction was originally
proposed by Fraser (1908). More recently Moulden and Renshaw (1979) and Taylor
and Woodhouse (1980) have shown repeated slanted line elements produce convergence­
type effects.
   Figure 6 illustrates how a series of repeated slanted line elements within the Cafe
Wall is capable of generating a powerful impression of illusory convergence.

Figure 6. A Cafe Wall figure in which slanted light and dark 'twisted cords' pass through the
mortar lines connecting the corner regions of phase-displaced light and dark tiles. Masking of the
tile areas above and below the mortar lines makes the twisted-cord appearance of the mortar lines
apparent. This figure illustrates that a powerful illusory convergence can be created in the Cafe
Wall figure by the simple introduction of local slanted elements to its mortar lines.

4.9 Border-locking, irradiation, and brightness induction
The major hypotheses put forward to account for the row-convergence illusions of
the Miinsterberg and Cafe Wall figures share a common feature : each proposes an
explanation for how repeated small-scale slanted elements arise within these figures. For
example, border-locking signals are thought to generate a series of trapezoidally tilted
tiles (Gregory and Heard 1979) ; 'irradiation' is held to engender a series of tilted
mortar-line segments which join the corners of the displaced dark tile squares
(Moulden and Renshaw 1979); and brightness-induction effects of the type reported
by McCourt (1982) are here argued to cause the appearance of light and dark patches

Figure 7: An illustration of the generic similarity of the Fraser and Cafe Wall illusions of direction.
Here a series of twisted-cord mortar lines is shown to produce the same illusory convergence as that
which characterizes the intact Cafe Wall illusion. It is postulated the the 'braiding' of the mortar
lines of the Cafe Wall figure occurs through the operation of brightness induction.

Brightness induction and the Cafe Wall illusion                                                      141

within the mortar lines of the Cafe Wall figure which join the corner regions of the
phase-displaced light and dark tile squares.
   It has generally been conceded once the mechanism producing local slanted line
elements such as these has been described the sufficient condition for the occurrence
of the illusory convergence in these figures is met. In figure 7, it is shown that, like
the Fraser 'twisted-cord' or 'LIFE' figure (Fraser 1908) and the 'reduced' Munsterberg­
like figure of Taylor and Woodhouse (1980), a series of Cafe Wall mortar lines
consisting solely of alternately-reversing diagonally-striped line elements can produce
the characteristic illusory convergence of the figure as a whole.
   The issue of the compatibility of the three hypotheses which have been put
forward to account for these illusions cannot at present be completely resolved.
Irradiation (Moulden and Renshaw 1979) and brightness induction appear to share
the central proposition that a type of lateral inhibition ultimately underlies the
convergence effect, since it produces the precursory slanted line elements. The
concept of border locking (Gregory and Heard 1979) is principally a functional
explanation of the Cafe Wall illusion whose mechanistic basis may very well be a form
of lateral interaction but whose theoretical basis, because of the present incompatible
results, seems to require further elaboration.
Acknowledgements. I thank John Foley for his assistance with various phases of this and related
projects. Thanks go also to Ken Pulliam for his interest and enthusiasm, and to Jack Loomis for
his helpful criticisms. I additionally thank Richard Gregory for providing the motivation for this
study and for his comments on the manuscript.

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142                                                                                      M E McCourt

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p                                                   © 1982 a Pion publication printed in Great Britain