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Perception, 2008, volume 37, pages 245 ^ 270doi:10.1068/p5429The awakening of Attneave’s sleeping cat: Identification
of everyday objects on the basis of straight-line versions of
outlinesJoeri De Winter, Johan Wagemans(cid:244)
Laboratory of Experimental Psychology, University of Leuven, Tiensestraat 102, B 3000 Leuven,
Belgium; e-mail: johan.wagemans@psy.kuleuven.be
Received 21 February 2005, in revised form 31 May 2007; published online 22 February 2008Abstract. Attneave (1954 Psychological Review 61 183 ^ 193) demonstrated that a line drawing of
a sleeping cat can still be identified when the smoothly curved contours are replaced by
straight-line segments connecting the positive maxima and negative minima of contour curvature.
Using the set of line drawings by Snodgrass and Vanderwart (1980 Journal of Experimental
Psychology: Human Learning and Memory 6 174 ^ 215) we made outline versions (with known
curvature values along the contour) that can still be identified and that can be used to test
Attneave’s demonstration more systematically and more thoroughly. In five experiments (with
444 subjects in total), we tested identifiability of straight-line versions of 184 stimuli with different
selections of points to be connected (using 24 to 28 subjects per stimulus per condition).
Straight-line versions connecting curvature extrema were easier to identify than those based on
inflections (where curvature changes sign), and those connecting salient points (determined by
161 independent subjects) were easier than those connecting midpoints. However, identification
varied considerably between objects: some were almost always identifiable and others almost
never, regardless of the selection criterion, whereas identifiability depended on the specific shape
attributes preserved in the straight-line version of the outline in other objects. Results are dis-
cussed in relation to Attneave’s original hypotheses as well as in the light of more recent theories
on shape perception and object identification.1 Introduction
A skilled draughtsman needs only a few well-selected line segments to depict an everyday
object. Our ancestors interpreted some cracks in the rocks as representations of (parts
of ) a familiar object (eg a mammoth) and added a few markings to strengthen the
impression (Halverson 1992). Humans are so good at identifying objects in line drawings
that it must tell something about the way the visual system extracts and processes the
essential information for object identification from the more natural visual stimulation.
Computer vision systems, on the other hand, have the greatest difficulties in processing
new images of objects, even when they have stored several related images in their data-
base. This glaring contrast has inspired research into the information available in line
drawings (eg Koenderink and van Doorn 1982).More than half a century ago, Attneave (1954) argued that the information about
object shape is not distributed homogeneously in an image but is concentrated at
contours (where the continuous distribution of spectral or grey-level values is usually
the sharpest) and furthermore, that information along the contour is concentrated
at points where the curvature reaches extreme values (curvature extrema). He used
two demonstrations to support his intuition about the role of curvature extrema. In
one demonstration, he asked participants to mark salient points along the contour of a
random shape, and showed that the frequency plots were centred on the curvature
extrema (see figure 1a). In a second demonstration, which has become known as
Attneave’s sleeping cat (see figure 1b), he created a version of a line drawing of his
sleeping cat by connecting the curvature extrema by straight lines. The fact that this(cid:244) Author to whom all correspondence should be addressed.246J De Winter, J Wagemans(a)(b)(c)Figure 1. (a) First demonstration by Attneave (1954) of the importance of curvature extrema: people
mark them as more salient points along the contour of a random shape (higher frequency is
represented by a longer line). (b) Second demonstration by Attneave (1954) of the importance
of curvature extrema (known as Attneave’s sleeping cat). A sleeping cat can still be identified in
a straight-line version connecting the curvature extrema, removing all the continuous curvature
along the contour. (c) Lowe’s (1985) variation in which midpoints between curvature extrema
are connected by straight-line segments.straight-line version was still easy to recognise, showed that the continuous curvature
changes along the contour are not important and that the critical information about
shape is located at curvature extrema.Attneave’s intuition has sparked a lot of interest in several areas of research.
Resnikoff (1985) formalised the notion of information using classic measures from
information theory and has provided mathematical proof of information concentration
at curvature extrema. More recently, Feldman and Singh (2005) proposed an alterna-
tive quantification scheme and extended Attneave’s original idea by showing that the
same logic implies that negative curvature extrema (minima) must be more informative
than positive curvature extrema (maxima). The reason is that all natural objects are
more convex than concave and closed contours must, therefore, always turn inwards
again after they have turned away from the object centre.Attneave’s demonstration about the salience of curvature extrema in random shapes
(based on an unpublished study on 16 similar random shapes with 80 participants)
has received further empirical support from a study on 12 silhouettes of sweet potatoes
with 12 participants (Norman et al 2001). Using contour versions derived from the
set of 260 line drawings of everyday objects by Snodgrass and Vanderwart (1980), we
have obtained salience data from 161 participants, which appear in a separate paper
(De Winter and Wagemans 2008). Attneave’s anecdotal demonstration with the sleep-
ing cat still awaits experimental confirmation when applied to other everyday objects.There are several good reasons, both theoretical and empirical ones, for performing
a more thorough study inspired by Attneave’s sleeping cat. First, it is not clear how
Attneave selected the salient curvature extrema to be connected by straight lines. It is
highly unlikely that he did so using mathematical techniques. He probably relied on
his own intuitions as a keen observer. In fact,
it is quite likely that Attneave did
not even start from a line drawing with continuously curved lines but immediately
drew the straight-line version while he was watching his sleeping cat (see footnote 2
in Feldman and Singh 2005). Selecting curvature extrema is not a trivial matter.
Mathematically, there is a local curvature extremum whenever a curvature value is
surrounded by two segments of larger or smaller curvature values. When the contour
is traced and its corresponding curvature values are plotted in a so-called curvature
graph, all curvature singularities can be located with mathematical precision (see fig-
ure 2). It is useful to distinguish between three types of curvature singularities: positive
maxima (M(cid:135)), negative minima (m(cid:255)), and inflections (I), points where the curvaturem(cid:255)IM(cid:135)e
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C(cid:135)(cid:255)Figure 2. An example of a smoothly curved contour derived from a line drawing of an anchor by Snodgrass and Vanderwart (1980).
Superimposed on the contour are the curvature singularities: local maxima of curvature or positive maxima (M(cid:135)) are marked by squares,
local negative minima of curvature or negative minima (m(cid:255)) are marked by triangles, and zero crossings or inflections (I) are marked
by circles. Below the outline, the curvature of the outline is plotted with the starting point indicated on the outline (the contour is traced
in counterclockwise direction). The same curvature singularities are also marked on the curvature graph (with the same symbols).iS
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w/248J De Winter, J Wagemanschanges sign and goes through zero. The example in figure 2 shows clearly that many
of the local curvature extrema are not salient (they are sometimes even located on
what looks like a straight-line segment). This observation necessitates the use of a
justifiable selection criterion, which Attneave did not specify. In contrast, we tested
and compared several ones. The more general issue of how to define curvature (and
curvature extrema) at different spatial scales and how to select the most relevant per-
ceptual ones falls outside the scope of the present study (see Lowe 1988; Witkin 1986;
and appendix 4 in De Winter and Wagemans 2006).Second, Attneave did not use a control condition in which other points were con-
nected by straight lines. Lowe (1985) showed that a straight-line version formed by
connecting midpoints (points halfway between extrema) is also easy to identify (see
figure 1c). Moreover, Biederman (1988) tested several variants of line drawings of cats
(including figures 1b and 1c) and showed that error rates and correct naming times
varied considerably, even between those that appeared easy to recognise (eg from 17%
and 1078 ms for figure 1b and 39% and 939 ms for figure 1c, to about 700 ms and no
errors for normal line drawings).Third,in line with Lowe’s sleeping cat, Kennedy and Domander (1985) showed
that points halfway between corner points (midpoints) are more informative than
corner points, and that points halfway between midpoints and corner points are even
more informative still. They used short line segments rather than single points (for
which they have been criticised by Deregowski 1986) and fragmented versions may be
quite different than straight-line versions because additional processes like filling-in
come into play (see also Panis et al 2008). Nevertheless, there are good mathematical
reasons to believe that inflections (often close to midpoints between extrema) are per-
ceptually important too: a change in curvature sign is easier to compute, more robust,
and more stable under transformations than maxima or minima of curvature (Van Gool
et al 1994) and inflections on the contour correspond to parabolic lines on the 3-D object
surface, separating convex and concave surface regions (Koenderink and van Doorn
1982). In other words, comparing straight-line versions connecting curvature extrema
with straight-line versions connecting other points is not just interesting for the sake of
comparison; it is also theoretically meaningful.For all these reasons, we have embarked upon a large-scale study, consisting of
several experiments, in which we have tested Attneave’s idea about the role of curva-
ture extrema for object identification(cid:246)as demonstrated with his sleeping cat (cid:246)using
much larger sets of stimuli and groups of participants. We have created silhouette and
contour versions of the famous Snodgrass and Vanderwart (1980) set of line drawings
of everyday objects and we have determined identification norms for them (Wagemans
et al 2008; see also appendix in Wagemans et al 1998). Because we have continuous
curvature values along these contours, we can also examine whether segmentations
of these stimuli confirm segmentation rules like the minima rule by Hoffman and
Richards (1984; see De Winter and Wagemans 2006), whether fragmented versions
are indeed easier to recognise with fragments around inflections than around extrema,
as suggested in the study by Kennedy and Domander (1985; see Panis et al 2008), and
whether curvature extrema are more salient than other points, as suggested by Attneave’s
first demonstration (figure 1a) and confirmed by a more thorough study with random
shapes (Norman et al 2001; see De Winter and Wagemans 2008). The study with
straight-line versions which we present here is, therefore, part of a larger research
program on the role of curvature singularities in shape and object perception (for
an overview, see De Winter and Wagemans 2004), which provides interesting bench-
mark data to test several theoretical proposals, both from perceptual psychology and
computer vision.Straight-line versions of object outlines2492 General methods
Because all five experiments reported here belong to the same large-scale study, they
share several aspects of the methods for data acquisition (eg subjects, stimuli, proce-
dure) and data analysis (eg scoring, dependent variables, a posteriori analyses). To avoid
repetition in the description of the individual experiments, we include these general
aspects of the methods here, and focus on the specific details in which the methods
differ between experiments below. We will also use tables to make it easier to maintain
an overview of the differences and similarities between the experiments.2.1 Subjects
First-year psychology students at the University of Leuven participated in all experi-
ments in this study as a mandatory component of their curriculum. They were always
naive regarding the purpose of the experiment and unfamiliar with the stimuli (we
used different samples with new freshmen in each of four consecutive academic years).
Depending on the number of conditions in each experiment, we used a different num-
ber of subjects to have data from 20 to 30 subjects per stimulus per condition within
a reasonable time per subject (about 20 min).2.2 Stimuli
The stimulus set consisted of 184 straight-line versions derived from the 260 line
drawings of everyday objects by Snodgrass and Vanderwart (1980). In a previous large-
scale study (Wagemans et al 2008; see also De Winter and Wagemans 2004), we made
silhouette and contour versions of the complete Snodgrass and Vanderwart set. First,
silhouettes were made by filling-in the interior surfaces in black. Their outlines were
then extracted automatically and spline-fitted to obtain smooth curvature values at all
points along the contour. We then determined the degree of identifiability in a group
of 356 subjects. Not all of these outlines were equally easy to identify (range between
0% and 100%), and because we expected that the identifiability would be poorer for
the straight-line versions to be tested here, we selected only those that were still
reasonably identifiable as a silhouette. The lower limit was set to 20%, meaning that
the silhouette was still named correctly by 20% of the subjects in the previous study.
Based on this criterion, 66 outlines were excluded.Some additional outlines were excluded from the remaining 194 ones for the follow-
ing reasons: (i) Outlines that are completely convex have no inflections and therefore
cannot be used in one of the two conditions (see below). Based on this criterion, 6 out-
lines were excluded (eg ball, barrel). (ii) Because of the spline-fitting procedure, some
outlines had some small anomalies in the outline shape (eg small local distortions at
the vertices) and they were excluded because these anomalies could have affected the
straight-line versions differentially and hence our major results of interest. Based on
this criterion, 3 outlines were excluded (bee, broom, needle). (iii) To be able to divide
the number of stimuli into equal subgroups, we excluded one additional outline with
low identifiability (telephone). These selection criteria led to a set of 184 stimuli (out of
260), with an average identification rate of 87.3% (SD (cid:136) 19:4%). The consequence
of using this subset from the Snodgrass and Vanderwart (1980) set of stimuli is that
our results concern identification based on 2-D outlines of everyday 3-D objects. We
assume that the original Snodgrass and Vanderwart line drawings capture the 3-D
structure of their objects as well as possible but we cannot say anything about the
identifiability of straight-line versions that would be derived from non-canonical views.
From the smooth contours obtained from the spline-fitted outlines, we extracted
particular curvature singularities (using different selection criteria in the different
experiments) and we connected them by straight lines, as Attneave (1954) may have
done to create his sleeping cat. In experiments 1, 2, and 3, we compared straight-line
versions connecting extrema (as Attneave did in figure 1b) with straight-line versions250J De Winter, J Wagemansconnecting inflections (often close to halfway between extrema, as Lowe did in figure 1c).
In experiments 4 and 5, we started from salient points as determined empirically from
another large-scale study with an independent group of 161 subjects (De Winter and
Wagemans 2008). In experiment 4, we then selected the most salient points and con-
nected either these points by straight lines or points halfway between them (midpoints).
In experiment 5, we created another variant based on the midpoints. In all of the
stimuli used in the present study, we filled the interior surface of these straight-line
versions with light-grey (75% of maximum luminance) to create silhouettes (see figures
4, 7, 8, and 9 for examples). We make these stimuli available on our website, along
with their identifiability in their silhouette version as well as in the versions tested here
(see http://ppw.kuleuven.be/labexppsy/johanw/wag 2D.htm).Half of the straight-line stimuli presented to a subject were constructed with points
of one type (extrema or salient points), and the other half of the stimuli with points of the
complementary type (inflections or midpoints). The assignment of stimuli to conditions
was always counterbalanced between subjects. The two groups of stimuli were always
matched to have approximately the same average identifiability, the same number of living
versus non-living objects, and the same average number of inflections.2.3 Procedure
The experiments were performed in a computer classroom with 33 PCs separated by
about 1 m. There were usually multiple sessions with a maximum number of 30 subjects
per session. We presented all the stimuli centred on a 17 inch CRT display at a view-
ing distance of approximately 0.7 m. The display resolution was set to 1024 by 768
pixels and a refresh rate of 60 Hz. Stimuli were all contained within a box of 6406
480 pixels (not drawn as such), for a maximum viewing angle of 16.3 deg by 12.2 deg.Each straight-line version was presented for a maximum of 5 s and then replaced
by a fixation cross. Subjects were asked to identify each stimulus and subsequently
input the name via the computer keyboard and click on an OK button when finished.
Subjects could begin typing the name of the object as soon as they had identified the
stimulus and they could type and correct as long as they wanted. If the subject clicked
on OK in a time period shorter than 5 s, the stimulus was removed from the screen
and the next stimulus appeared. The presentation order was randomised for each
subject separately and the experimenter secured silence throughout the session until he
finished with the last subject.2.4 Scoring
In the previous study with silhouettes and outlines (Wagemans et al 2008; see also
De Winter and Wagemans 2004), we used two criteria to score the responses as cor-
rect or incorrect. With the more stringent criterion, a response was counted as correct
only when the name given was the same as that listed by Snodgrass and Vanderwart
(1980). With the more liberal criterion, synonyms and colloquial names that clearly
indicated the same concept were also considered correct. However, remotely related
names that were referring to different basic-level categories (eg ‘‘dog’’ for ‘‘fox’’ or ‘‘fly’’
for ‘‘bee’’) were not allowed. Because we used Flemish subjects in all of our experiments
and Flemish has many more synonyms and colloquial names than English or Dutch
(eg Severens et al 2005), we decided to use the more liberal criterion in the present
study (as well as in the related ones by De Winter and Wagemans 2008 and Panis et al
2008). It is the best measure of basic-level identification. Scoring was done automatically
for all names that were already in our database from the previous study. New names were
scored manually by applying the same criteria (in the case of doubt, the two authors
decided jointly). The database was updated with the new names (and their scoring) each
time a new experiment was performed. All experiments in this study used the same
scoring criteria and the results are therefore comparable across the different experiments.Straight-line versions of object outlines2512.5 Data analysis
We determined the average percentages of correct identification in each condition
and compared them with a t-test when there were only two conditions, or an analysis
of variance (ANOVA) when there were more than two conditions. Because we believe that
our data set may also be used as a benchmark to test specific models of object recognition
(particularly computer vision or pattern recognition models), we also made available on
our website the identification rates of all of the individual stimuli in all of the different
versions of this study (see http://ppw.kuleuven.be/labexppsy/johanw/wag 2D.htm).As a first step in an exploratory analysis of the factors determining identification
of straight-line versions, we determined the stimulus difference between the straight-
line version and the original outline version for all stimuli, and correlated performance
with it. The stimulus different was quantified as follows (see figure 3 for an example).
First, the original silhouette was drawn in black, the straight-line version was drawn
in white, and the two versions were overlaid, so that the difference in overlap in one
direction was then visible in black. The area of the difference was then calculated as
the number of black pixels. Next, the same procedure was repeated, but now the
straight-line version was drawn in black and the original version in white and the area
in this direction of the difference was also calculated. Finally, the total stimulus differ-
ence computed in this way was the sum of the two black areas remaining after applyingTypeContour/OverlapOriginalSP100Original (cid:255) SP100SP100 (cid:255) Original{Original (cid:255) SP100}
(cid:135)
{SP100 (cid:255) Original}Figure 3. Stimulus difference between the straight-
line versions and the original outlines was
quantified as the total area of the nonoverlapping
parts. The three-step procedure is illustrated
here for the straight-line version of the airplane
in experiment 4 (connecting salient points).
First, we calculated the area of the original
outline (Original) minus the overlapping area
of
the straight-line version (SP100), resulting
in the black parts shown in ‘Outline (cid:255) SP100’.
Second, we calculated the area of the straight-
line version (SP100) minus the overlapping area
of the original outline (Original), resulting in
the black parts
shown in ‘SP100 (cid:255) Outline’.
Third, the two black areas were added.252J De Winter, J Wagemansthe overlay-and-subtract procedure in both directions. To avoid area differences in the
original outlines affecting the results, this deviation measure was then divided by
the original outline area. We could then correlate the relative stimulus difference for
each condition with the decrease in identification rate in that condition.We also computed other stimulus measures (contour length, number of corner
points, contour length divided by the number of corner points, average length of all
the straight-line segments, variability of it, etc) and correlated performance with them.
However, we generally obtained weak correlations. Therefore we are not reporting
them here because they did not help us in explaining the differences in identification
rate. In section 8 we include some of our observations from these exploratory analyses,
as an illustration of the potential of this approach. All our stimuli have also been made
available on our website (both as bitmaps and as pixel files) so that anyone with partic-
ular ideas about relevant stimulus variables determining identification can test them on
our benchmark data sets (see http://ppw.kuleuven.be/labexppsy/johanw/wag 2D.htm).3 Experiment 1: Curvature singularities (cid:246) one extremum per lob
3.1 Introduction
In the first three experiments, curvature singularities were corner points connected by
straight-line segments. They differed only in the way the curvature singularities were
selected. In experiment 1, we selected only one curvature extremum for each segment
of the contour with a particular sign of curvature: one maximum (M(cid:135)) per segment of
positive curvature and one minimum (m(cid:255)) per segment of negative curvature.3.2 Methods
The aspects of the methods common to all of the experiments have been reported
in section 2, above. Here, we describe only the specific aspects of the methods that are
unique to this experiment (see table 1 for an overview).Table 1. Methodological details of the five experiments.Number of subjects
Number of stimuliStimulus conditionsNumber of stimuli per subject
Number of subjectsper stimulus per conditionExperiment156
184184
28250
184184
25E vs IE vs IE vs I3206
18446
264108
184
SP100 vs MP100
SP75 vs MP75
184
27524
142MPT142
243.2.1 Subjects. 56 participants (13 male, 43 female, mean age 19.3 years) were tested in
two sessions with a maximum number of 30 participants in each session.3.2.2 Stimuli. The two conditions in this experiment consisted of straight-line versions
connecting either curvature extrema (E) or inflections (I). Each outline contour in our
set of stimuli had more extrema than inflections. To make sure that the number of
points to be connected was equal in both conditions, we used the following criterion
to select extrema. Within a fragment of positive or negative curvature (called here a
lob), we selected the extremum with the highest absolute curvature. This automatically
results in an equal number of extrema and inflections per outline, because each lob with
positive curvature is followed by a lob of negative curvature (and vice versa), with an
inflection point inbetween. The mean number of selected points across stimuli was 29.7
(median (cid:136) 24:5). Stimulus examples are shown in figures 4, 7, and 8.Group
GroupExperiment 1
Experiment 1Experiment 2
Experiment 2Experiment 3
Experiment 3Experiment 4
Experiment 4Experiments 4 and 5
Experiments 4 and 5E
EI
IE
EI
IE
EI
ISP100
SP100MP100
MP100SP100
SP100MPT
MPT96%
96%0%
0%100%
100%0%
0%96%
96%4%
4%96%
96%4%
4%56%
56%38%
38%78%
78%78%
78%100%
100%100%
100%100%
100%100%
100%100%
100%100%
100%100%
100%100%
100%4
4(cid:136)
(cid:136)5
586%
86%96%
96%28%
28%88%
88%41%
41%60%
60%0%
0%22%
22%15%
15%92%
92%Figure 4. Examples of straight-line versions of the Snodgrass and Vanderwart (1980) pictures, constructed by connecting a number of curvature
extrema (E) or salient points (SP), inflections (I) or midpoints (MP). On the basis of the identification rates in the different conditions, we
distinguish between three groups: in the group in the first row (4), the E or SP version is identified better than the I or MP version. In the
group in the second row ((cid:136)) both versions are identified equally well. In the group in the third row (5), the I/MP version is identified better
than the E/SP version. Below each example is the identification rate (in %) for that particular stimulus.iS
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3254J De Winter, J Wagemans3.2.3 Procedure. Each subject received all 184 stimuli, half of them in E version and
half in I version (stimulus assignment was counterbalanced across subjects). Each stim-
ulus was thus presented to 28 subjects per condition.important3.3 Results and discussion
The most
identification results are tabulated: separately per condition
in table 2 (see over), and comparatively between conditions in table 3. Some stimulus
measures that might correlate with identifiability are included in table 4. The distribu-
tion of identification rate in the two conditions is plotted in figure 5a.Identification was still reasonable or good for the straight-line versions connecting
the extrema (E versions), but it was rather poor for the straight-line versions con-
necting the inflections (I versions). Mean and median identifications were 46.4% and
41.1% for E versions and 20.4% and 3.6% for I versions (see table 2). A t-test on the
means revealed a large statistical difference between the two conditions: t366 (cid:136) 7:28,
p 5 0:001. The fact that E versions can still be identified in many cases (eg 50 are
within 10% of the identification rate of the original outlines) supports Attneave’s (1954)
idea that continuous curvature changes are often not needed. Moreover, the fact that
E versions are easier to identify than I versions confirms that Attneave’s version of
the sleeping cat (figure 1b) was more representative of everyday objects than Lowe’s
version (figure 1c). However, there was a considerable range of identification per-
formance across the stimuli (see figure 5a): there are relatively more E versions with
high identification rates (eg 470%) than I versions, and more I versions with lower
identification rates (eg 530%) than E versions, but in both versions identifiability is
distributed across the whole range from 0% to 100%. This stimulus variability may be
informative about stimulus variables affecting identifiability.As a point of departure for an exploratory analysis of stimulus differences leading
to these identification differences, we distinguished three groups of stimuli (see table 3):
(i) those in which the identification rates were in line with the average difference
(E 4 I), (ii) those with no difference (E (cid:136) I ), and (iii) those in which the differ-
ence was in the opposite direction (E 5 I ). Examples of each group are given in
figure 4. The first group was clearly the largest (127 stimuli or 69.0% of the stimuli),
and the mean and median difference in identification here was 38.6% and 35.7%,
respectively. The second group consisted of 45 stimuli (24.5% of the stimuli), 41 of
which were not identified at all (0% identification in both conditions). Many of theTable 3. Overview of the comparative results of the five experiments.Experiment1234 (100%)4 (75%)Number of stimuli in first group127154166163152(E 4 I or SP 4 MP)Mean difference in first group
Q1 of difference in first group
Median difference in first group
Q3 of difference in first group
Number of stimuli in second group(E (cid:136) 1 or SP (cid:136) MP)38.6
17.9
35.7
57.1
45Number of stimuli in third group1212.5
20.0
46.0
76.0
191145.6
20.0
39.9
73.1
11739.6
15.0
33.0
59.0
147(E 5 1 or SP 5 MP)Mean difference in third group
Q1 of difference in third group
Median difference in third group
Q3 of difference in third group(cid:255)6.5 (cid:255)15.3 (cid:255)11.5 (cid:255)14.8
(cid:255)12.5 (cid:255)16.0 (cid:255)14.9 (cid:255)17.0
(cid:255)3.6 (cid:255)12.0 (cid:255)10.2 (cid:255)15.0
(cid:255)4.1 (cid:255)13.0
(cid:255)3.6(cid:255)6.044.9
18.5
44.4
66.7
248(cid:255)10.2
(cid:255)12.0
(cid:255)9.3
(cid:255)6.557322.3
8.3
20.8
29.6
2148(cid:255)16.2
(cid:255)23.4
(cid:255)10.6
(cid:255)4.6Table 2. Overview of the identification results (in %) of the five experiments.Identification rateExperimental conditionExperiment 1Experiment 2Experiment 3Experiment 4Experiment 5FullEIEIEISP100 MP100 SP75 MP75MPTMean
SD
Q1 a
Median a
Q3 a# 0% b
# 100% b
# within 10% c46.4
39.3
3.6
41.1
86.645
20
5020.4
28.1
0.0
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53a Q1 (cid:136) first quartile (25% point of the distribution), Q3 (cid:136) third quartile (75% point), and median (cid:136) second quartile (50% point).
b # 0% (cid:136) the number of stimuli with 0% identification and # 100% (cid:136) the number of stimuli with 100% identification.
c # within 10% (cid:136) the number of stimuli that are identified more or less as the same as the original version ((cid:6)10%).Table 4. Overview of the correlational measures of the five experiments.Full18487.3
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48
–FullFullFullExperiment 1Experiment 2Experiment 3Experiment 4Experiment 5M(cid:135)m(cid:255)IEIEIEISP100MP100SP75MP75MPT19.1
9.0
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N(e)J De Winter, J WagemansExp 1—E
Exp 1—IExp 2—E
Exp 2—IExp 3—E
Exp 3—IExp 4—SP100
Exp 4—MP100Exp 4—SP75
Exp 4—MP75Exp 4—SP100-142
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0N(f)41020–3040–5060–7080–9041020–3040–5060–7080–9010–2030–40
Identification rate=%50–6070–8049010–2030–40
Identification rate=%50–6070–80490Figure 5. Distribution of the identification rates in all of the experimental conditions. In each
panel, the number of observations in each of the 10% bins is indicated, separately for the E/SP
versions (in black) and the I/MP versions (in white). The location of the average identification
rate along the x-axis is indicated by an arrow (solid for the E/SP versions and dashed for the I/MP
versions). (a) Experiment 1. (b) Experiment 2. (c) Experiment 3. (d) Experiment 4; 100% versions.
(e) Experiment 5, 75% versions. (f ) Comparison between the SP100-142 of experiment 4 (see text
for more details) and MPT versions of experiment 5. In all of the experiments, the distribution for
E/SP versions is skewed more to the right (higher identifiability), whereas the distribution for I/MP
versions is skewed more to the left (lower identifiability).objects in this category have large round sections in the outline (eg ‘apple’ in figure 6a).
Owing to our selection procedure in this experiment (only one extremum per lob),
the straight-line versions have only a small number of straight-line segments with
large parts of the shapes chopped off and sharp corners in both the E and the I
versions. In the last group, with only 12 stimuli (6.5%), the I versions were easier to
identify than the E versions, but the difference was usually small (mean (cid:136) (cid:255)6:5%,
median (cid:136) (cid:255)3:6%). Sometimes the identification difference seems to be based on someStraight-line versions of object outlines257E—0%(a)I—0%E—64%I—82%(b)Figure 6. Examples of straight-line versions derived from outlines. (a) Outline of an apple with
curvature singularities marked as in figure 2. Below the outline are the straight-line versions
connecting extrema (E) or inflections (I), shown left and right, respectively. None of these ver-
sions can be identified because large round parts are chopped off and replaced by a single
straight-line segment in both cases. (b) Outline of a nail with curvature singularities marked
as in figure 2. Below the outline are the straight-line versions. The I version appeared somewhat
easier to identify than the E version (probably based on a local detail such as the tip of the
nail). The identification rate is mentioned below each stimulus.stimulus feature that may be diagnostic and that happens to be preserved better in
the I version than in the E version (eg ‘nail’ in figure 6b). We will return to the possible
shape differences underlying the variability in identification rate in the straight-line
versions in section 8.We explored to what extent these identification differences can be explained by
a simple factor (see table 4): stimulus difference between the straight-line version and
the original outline (see section 2 for computational details). Correlation between the
magnitude of the stimulus difference (sum of the overlap differences relative to the orig-
inal silhouette area) and the identification difference (identification rate of the original
silhouette minus identification rate of the straight-line version) was reasonably high:
r (cid:136) 0:53 for the E condition ( p 5 0:001) and r (cid:136) 0:35 for the I condition ( p 5 0:001).
We will return to this in section 8.4 Experiment 2: Curvature singularities (cid:246) strongest extrema
4.1 Introduction
In this experiment, we have dropped the restriction that each contour segment must
deliver one extremum to be connected by straight-line segments. Here, we have just
taken the strongest extrema for each outline, regardless of where they are located along
the contour. The number of extrema to be selected (and the corresponding number of
inflections) is determined by the number of salient points used in experiment 4. This
enables a direct comparison between a mathematical selection criterion (extrema with
highest absolute curvature) and a perceptual one (visual salience as judged by a large
group of independent subjects).4.2 Methods
Only aspects of the methods that are unique to this experiment are described here
(see also section 2 and table 1).4.2.1 Subjects. 50 participants (10 male, 40 female, mean age 19.1 years) were tested in
two sessions with a maximum number of 30 participants in each session.258J De Winter, J Wagemans4.2.2 Stimuli. On the basis of the results of an independent study, in which 161 subjects
were asked to mark salient points on the contours of all 260 stimuli (De Winter and
Wagemans 2008; see also De Winter and Wagemans 2004), we selected the most salient
points to be connected with straight-line segments in experiment 4 (see below). For all
stimuli in experiment 2, we selected curvature extrema with the highest absolute curva-
ture until we had the same number of points as in experiment 4 (mean (cid:136) 27:4 points).
In contrast to experiment 1, where all inflections were used, the selection of inflections
was less obvious in this experiment because there is no simple criterion to determine
which ones are most important. To make the selection comparable to that of the
extrema, we ranked all inflections by the average absolute curvature of the two selected
neighbouring extrema, and selected those with the highest values until the criterion
number was reached as closely as possible (there were a few cases where not enough
were available; mean (cid:136) 24.9 points). As in all the other experiments, the selected points
(either E or I) were then connected by straight-line segments to have E versions and
I versions of all 184 stimuli (see figures 4, 7, and 8).4.2.3 Procedure. Each subject received all 184 stimuli (half in E version and half in
I version, with stimulus assignment counterbalanced across subjects); each stimulus
was thus presented to 25 subjects per condition.4.3 Results and discussion
For the most important results, see tables 2, 3, and 4 and figure 5b. As in experi-
ment 1, identification was still reasonable to good for the E versions, whereas it was
poor for the I versions: mean and median identifications were 53.4% and 50.0% for
E versions and 14.2% and 0.0% for I versions. A t-test on the averages revealed a large
statistical difference between the two conditions (t366 (cid:136) 12:25, p 5 0:001). The differ-
ence between E and I versions has become even bigger than in experiment 1. This
increased difference may be due to the average number of selected extrema and inflec-
tions, which differ slightly here (27.4 or 24.9, respectively), whereas they were equal in
it may be due to some properties of the selected
experiment 1 (29.7). In addition,
points: first, the selection of extrema was probably better in this experiment because
the largest extrema were now selected (regardless of their location along the contour),
and, second, the selection of inflections was probably worse in this experiment (because
their selection was derived from the curvature values of the neighbouring extrema
rather than being evenly distributed along the contour as in experiment 1).As in experiment 1, we distinguished three groups of stimuli (see figure 4 for
examples and table 3 for statistics). Again, the first group (E 4 I) was clearly the largest
group, with 154 stimuli (83.7% of the stimuli), with a mean and median difference in
identification of 12.5% and 46.0%, respectively. The second group (E (cid:136) I) now consisted
of only 19 stimuli (10.3% of the stimuli), 18 of which had 0% identification in both
conditions. In the last group (E 5 I), with only 11 stimuli (6.0%), the I versions were
easier to identify than the E versions, and the difference was somewhat larger than in
experiment 1 (mean (cid:136) (cid:255)15:3%, median (cid:136) (cid:255)12:0%). The correlations between the relative
area difference and the identification difference (compared to the original silhouette)
were lower in this experiment (r (cid:136) 0:28 for E and r (cid:136) 0:26 for I; both ps 5 0:001).5 Experiment 3: Salient curvature singularities
5.1 Introduction
In this experiment, we start again from curvature singularities but, instead of selecting
them on the basis of their absolute curvature values, we now ask an independent group
of subjects to select the most salient curvature singularities. Because this is probably
a more valid selection criterion, we expect the identification rates to increase in this
experiment.Straight-line versions of object outlines2595.2 Methods
Only aspects of the methods that are unique to this experiment are described here
(see also section 2 and table 1).5.2.1 Subjects. 206 participants (44 male, 162 female, mean age 19.0 years) were tested
in seven sessions with a maximum number of 30 participants in each session.5.2.2 Stimuli. Before we could create new straight-line versions with empirically derived
salient curvature singularities, we needed to run another experiment, asking an inde-
pendent sample of 394 subjects (also first-year psychology students at the University
of Leuven) to select the most salient curvature singularities of each contour from the
260 outlines derived from the Snodgrass and Vanderwart set. The whole set was
subdivided into ten groups of 26 stimuli each (matched for several possibly relevant
variables; see section 2) and each subject received only 26 stimuli (half in E version
and half in I version, with stimulus assignment counterbalanced across subjects). On
average, each stimulus was thus presented to 20 subjects per condition. In the E ver-
sions, all of the local curvature extrema were shown as small black dots superimposed
on the contour, and likewise for all of the inflections in the I versions. A computer
program assisted the subjects in selecting the most salient dots superimposed on the
contour: a blue cross was always shown on the contour, superimposed on the curvature
singularity nearest to the cursor; a point could be selected by clicking the left mouse
button, and the small black dot then turned into a larger blue dot; it could be removed
from the selection by moving over it again (the blue cross then turned into a red one)
and clicking the left mouse button again, etc. The subjects needed to look at the whole
contour first for 1 s before they could begin selecting points. The contour remained
on the screen for as long as the subject wished (but at least for 5 s); the subjects could
indicate that they were finished by pressing the ‘ENTER’ key, and then all of the
selected points were written to a data file.For all of the stimuli in experiment 3, we selected the curvature extrema and the
inflections that were marked by at least 5 subjects from the preceding experiment
(this does not guarantee an equal number of extrema and inflections; see table 4). As
in all the other experiments, the selected points (either E or I) were then connected
by straight-line segments to produce E versions and I versions of all 184 stimuli (see
figures 4, 7, and 8 for examples).5.2.3 Procedure. The total set of 184 stimuli was subdivided into four groups of 46
stimuli each (matched for several possibly relevant variables; see section 2) and each
subject received only 46 stimuli (half in E version and half in I version, with stimulus
assignment counterbalanced across subjects). On average, each stimulus was thus pre-
sented to 26 subjects per condition.5.3 Results and discussion
For the most important results, see tables 2, 3, and 4 and figure 5c. As in experiments
1 and 2, identification was still reasonable to good for the E versions, whereas it was
poor for the I versions: mean and median identifications were 60.7% and 71.7% for
E versions and 20.0% and 3.8% for I versions. A t-test on the averages revealed a large
statistical difference between the two conditions (t366 (cid:136) 9:53, p 5 0:001). As expected,
identification was better for the E versions than in experiments 1 and 2, because the
most visually salient extrema were now selected (based on empirically established sali-
ence measures). It cannot be due to the mean number of selected extrema, because
this number is now lower than in experiments 1 and 2 (24.2 versus 29.7 and 27.4,
respectively). It is just a matter of a better selection. For the I versions, the difference
was not significant (somewhat larger than in experiment 2 but virtually identical to
that in experiment 1). We will return to this issue in section 8.260J De Winter, J WagemansAs in experiments 1 and 2, we distinguished three groups of stimuli (see figure 4
for examples and table 3 for statistics). As before, the overwhelming majority of the
stimuli (166 or 90.2%) were in the first group (E 4 I), with an average and median
difference in identification of 45.6% and 39.9%, respectively. The second group (E (cid:136) I)
now consisted of only 11 stimuli (6.0% of the stimuli), 9 of which were not identified
at all; the last group (E 5 I) now had only 7 stimuli (3.8%) and the difference was
not big (mean (cid:136) (cid:255)11:5%, median (cid:136) (cid:255)10:2%). The correlations between the relative
area difference and the identification difference (compared to the original silhouette)
were r (cid:136) 0:14 for E ( p (cid:136) 0:066) and r (cid:136) 0:33 for I ( p 5 0:001).Comparison of the results of the first three experiments reveals a striking pattern:
with the improved selection criterion for curvature extrema, the identification rates
clearly increase for the E versions (for all comparable points across the whole range:
mean, median, first and third quartile (cid:246)see table 2). The correlation with the area
measure clearly decreases (from 4 0:50 in experiment 1 to 5 0:15 in experiment 3). For
the I versions, the identification rates do not vary so strongly (experiment 2 is some-
what lower) and neither do the correlations with the area measure (against lowest in
experiment 2). We will return to this observation in section 8.6 Experiment 4: Salient points and midpoints
6.1 Introduction
In contrast to the preceding three experiments, in which the points to be connected
were always mathematically defined curvature singularities (selected according to math-
ematically defined criteria, as in experiments 1 and 2; or based on empirically defined
criteria, as in experiment 3), we now select the points to be connected in a completely
empirical way. We have asked another independent sample of 161 subjects to mark
salient points along the contours of our 260 stimuli (De Winter and Wagemans 2008;
see also De Winter and Wagemans 2004) and we have taken the most popular ones
as points of departure for our new straight-line versions.6.2 Methods
Only the aspects of the methods that are unique to this experiment are described here
(see also section 2 and table 1).6.2.1 Subjects. 108 participants (18 male, 90 female, mean age 19.0 years) were tested
in four sessions with a maximum number of 30 participants in each session.6.2.2 Stimuli. Before we could create new straight-line versions with empirically
derived salient points, we needed to run another experiment, asking an independent
sample of 161 subjects (also first-year psychology students at the University of Leuven)
to select the most salient points along each contour from the 260 outlines derived
from the Snodgrass and Vanderwart set. The whole set was subdivided into four groups
of 65 stimuli each (matched for several possibly relevant variables) and each subject
received one set of 65 stimuli. On average, each stimulus was thus presented to 40 sub-
jects per condition. For more details of the data acquisition and data analysis of this
study, see De Winter and Wagemans (2008; see also De Winter and Wagemans 2004).
In essence, the selection of the most salient points proceeded as follows. First, the
raw frequency data were smoothed by a Gaussian function (with an SD of 5 pixels)
and then the local maxima from this salience distribution were selected if their value
was higher than a particular threshold. Because the contours differed widely in how
distributed the salience values were, the threshold was set adaptively. It was determined
as the integer value of the mean smoothed salience (eg 7 for mean smoothed salience
of 7.93).Straight-line versions of object outlines261We now have all of the salient points to be connected by straight-line segments in
the condition SP100 (for 100% of the salient points selected according to the procedure
described above). In the comparison condition, we used the points half-way inbetween
these salient points [measured on the original outline as the Euclidean distance in
pixels from point to point and then accumulated along the outline; see also appendix 1
in De Winter and Wagemans (2006)]. We call the straight-line versions connecting
these midpoints the MP100 versions. Because we want to know how fast identification
decreases when fewer points are connected, we have also created a condition in which
the 75% most salient points of the previously determined salient points are used
(SP75 condition). Likewise, we have also determined new midpoints between those
75% salient points and connected these by straight-line segments to create the MP75
condition (see figures 4, 7, and 8 for examples).6.2.3 Procedure. The total set of 184 stimuli was subdivided into four groups of 46
stimuli each (matched for several possibly relevant variables; see section 2). Each
subject received all four groups of 46 with a counterbalanced assignment of stimuli
to conditions across subjects (group A to SP100, B to MP100, C to SP75, D to MP75,
for subject 1; group B to SP100, C to MP100, D to SP75, A to MP75, for subject 2;
etc). Hence, each subject saw all of the 184 only once and, on average, each stimulus
was presented to 27 subjects per condition.,,,6.3 Results and discussion
For the most important results, see tables 2, 3, and 4 and figures 5d and 5e. As
expected, the mean identification rates for the SP versions were much higher than for
the MP versions (68.9% versus 34.4%, for SP100 and MP100, respectively). The medians
differed even more (85.2% versus 25.9%, respectively). A similar difference was obtained
for the 75% versions [54.7% versus 18.0%, for SP75 and MP75, respectively (medians:
59.3% versus 3.7%, respectively)]. An ANOVA revealed a significant effect of point type
(SP versus MP) (F1 183 (cid:136) 309:70, p 5 0:001), and of the number of points (100% versus
75%) (F1 181 (cid:136) 144:03, p 5 0:001), but no interaction effect (F1 183 5 1). Compared to
experiment 2, where each straight-line version was based on the same number of
curvature singularities as the present number of salient points, the identification rates
are higher here (for all comparable points across the whole range: mean, median, first
and third quartile(cid:246)see table 2). For example, for the difference between the means
t366 (cid:136) 4:20, p 5 0:001. The same is true for the comparison between inflections and
midpoints (t366 (cid:136) 6:74, p 5 0:001), where this difference is less obvious: the midpoints
between selected salient points are by no means guaranteed to be close to inflections
(whereas salient points are often close to extrema, see Dr Winter and Wagemans 2008).
The extent to which MP versions are still relatively well-identifiable seems to depend
on the distribution of MPs along the contour. By definition, MPs are located midway
between salient points and, hence,
they are relatively evenly distributed, whereas
the location of inflections may be more erratic (especially in experiment 2, where their
locations depend on the average absolute curvature of their neighbouring extrema).
The likelihood of having an MP version that is similar to an SP version (and thus
easier to identify) is higher in the case of a rather complex shape, with a long out-
line, a large number of points, and relatively short distances between the points.
This observation is confirmed by a calculation of these parameters: compared to
the 25% most-difficult-to-identify stimuli, the 25% easiest-to-identify stimuli have a
longer outline (1564 versus 1179 pixels, t45 (cid:136) 3:302, p 5 0:002), more selected points
(36 versus 22, t45 (cid:136) 4:416, p 5 0:001), and a shorter average distance between them
(35 versus 53 pixels, t45 (cid:136) 5:132, p 5 0:001). We will return to such object differences
in section 8.262J De Winter, J WagemansAs in the preceding experiments, we distinguished three groups of stimuli (see
figure 4 for examples and table 3 for statistics). As before, the overwhelming majority
of the stimuli (163 or 88.6%) were in the first group (SP100 4 MP100), with a mean and
median difference in identification of 39.6% and 33.0%, respectively. The second group
(SP100 (cid:136) MP100) now consisted of only 14 stimuli (7.6% of the stimuli), 6 of which
were not identified at all and 5 of which were identified perfectly in both conditions.
Finally, the third group (SP100 5 MP100) had only 7 stimuli (3.8%), with a mean
and median difference of (cid:255)14:8% and (cid:255)15:0%. The same distinction was also made
for the 75% versions. Here too, the majority of the stimuli (152 or 82.6%) were in
the first group (SP75 4 MP75), with a mean and median difference in identification
of 44.9% and 44.4%, respectively. The second group (SP75 (cid:136) MP75) now consisted of
24 stimuli (13.0% of the stimuli), 17 of which were not identified at all. Finally, the
third and smallest group (SP75 5 MP75) had only 8 stimuli (4.3%), with a mean and
median difference of (cid:255)10:2% and (cid:255)9:3%, respectively.The correlations between the relative area difference and the identification differ-
ence (compared to the original silhouette) were rather low (even negative) for the
100% versions, r (cid:136) (cid:255)0:09 ( p (cid:136) 0:360) for SP100 and r (cid:136) (cid:255)0:11 for MP100 ( p (cid:136) 0:150),
and positive for the 75% versions but significant only for SP75, r (cid:136) 0:24 ( p 5 0:001), not
for MP75, r (cid:136) 0:02 ( p (cid:136) 0:812).7 Experiment 5: Midpoints with tangent lines
7.1 Introduction
In all of the experiments so far, the straight-line versions in which inflections (experi-
ments 1, 2, and 3) or midpoints (experiment 4) were connected by straight-line segments
were much harder to identify than the corresponding versions connecting extrema or
salient points. Despite Lowe’s (1985) demonstration and Biederman’s (1988) empirical
confirmation that the location of the selected points does not matter for Attneave’s
sleeping cat (compare figure 1c to 1b), this major difference between E and I versions,
or SP and MP versions, should not surprise us. Contour segments around inflections
have generally very little curvature and the same tends to be true for segments around
midpoints, because they are located far away from the most salient points (usually points
with high absolute curvature values, if not curvature extrema). When connecting I or
MP by straight-line segments, they become corner points, whereas originally they were
located in contour segments where curvature did not change much, far away from strong
curvature changes. In other words, removing continuous curvature changes in creating
straight-line versions usually implies replacing shallow curvature changes by straight-
line segments with the same local orientation and replacing strong curvature changes
by corners in the same location in the case of E and SP versions. In contrast, shallow
curvature changes might become corners and strong curvature changes might be
replaced by straight-line segments in the case of I and MP versions, and the original
orientation of the contour segments surrounding I or MP is usually changed quite
dramatically. In this new experiment, we ask how difficult it is to identify MP versions
when no spurious corners are introduced at the original location of the MPs and local
contour orientations are preserved at MPs.7.2 Methods
7.2.1 Subjects. 24 participants (4 male, 20 female, mean age 18.8 years) were tested in
one session in a room with 24 PCs.7.2.2 Stimuli. In this experiment, we used only one version of each stimulus. We created
new straight-line versions starting from the same midpoints as in experiment 4. Instead
of connecting the selected points by straight-line segments, as we did in all of the
preceding experiments, we now fitted a tangent line through each of the midpoints andStraight-line versions of object outlines263then had new corners where neighbouring tangent lines intersected. We call this new
version MPT for midpoint tangents. Some of these MPT versions were problematic
because the intersections created X-crossings or the intersection points were sticking
out too far. We eliminated these from the stimulus set, retaining 142 stimuli to be tested
(see figures 4, 7, and 8 for examples and our website for a complex list of the selected
stimuli).7.2.3 Procedure. All subjects received the 142 stimuli in a new random order, so we
have identification rates per stimulus that are based on 24 subjects each.7.3 Results and discussion
For the most important results, see tables 2, 3, and 4 and figure 5f. As expected, the
mean identification rate for these new MPT versions was much higher (mean 60.2%,
median 62.5%) than for the MP100 versions from experiment 4 (34.4% and 25.9%, respec-
tively) (t324 (cid:136) 8:37, p 5 0:001, between the means), but still somewhat lower than for the
SP100 versions from experiment 4 (68.9% and 85.2%) (t324 (cid:136) 2:31, p (cid:136) 0:02 between
the means). Restricting the comparisons to the same 142 stimuli from experiment 4
confirms these trends: identification is clearly better than for the MP100-142 versions
(t282 (cid:136) 11:4, p 5 0:001), and no longer much worse than for the SP100-142 versions
(t282 (cid:136) 1:50, p (cid:136) 0:13). In other words, preserving the local orientation around the
midpoints, instead of introducing spurious corner points at these locations, removes a
great deal of the identification cost. Hence, the fact that corners are located where no
strong curvature changes were present in the original outlines has probably contributed
a lot to the difficulty in identifying straight-line versions based on I or MP in the
previous experiments.As in the preceding experiments, we distinguished three groups of stimuli, based
on the sign of the difference between the present MPT versions and the corre-
sponding SP100-142 versions (see figure 4 for examples and table 3 for statistics). The
group with SP100-142 4 MPT was still the largest group, containing 73 stimuli (51.4%),
but it was clearly smaller than in all of the preceding experiments. The average and
median difference was also not that big (22.3% and 20.8%, respectively). The second
largest group (48 stimuli, 33.8%) now was the group with the reversed difference
(SP100-142 5 MPT). All of the stimuli
in the last group with SP100-142 (cid:136) MPT
(21 stimuli, 14.8%) were either perfectly identified (18) or not at all (3). Examples of
each group are given in figure 4.As for the MP versions in experiment 4, the correlation between the relative area
difference and the identification difference (compared to the original silhouette) was
very low for the present MPT versions (r (cid:136) 0:08, p (cid:136) 0:200).8 General discussion
The research reported in this paper started from Attneave’s (1954) sleeping cat demon-
stration. It is useful to distinguish between two aspects of this demonstration: first,
that continuous curvature along the contour is not important for object identification
and, second, that the critical information about shape is located at curvature extrema.
We have tested these two aspects by asking a large number of subjects to try to
identify a much larger set of better-controlled stimuli. All of our stimuli are modified
outlines derived from line drawings of everyday objects (Snodgrass and Vanderwart
1980). They do not contain internal features as did Attneave’s drawing of a sleeping cat
but that is not an invalidating limitation because we compare the identification rates
of the modified stimuli with those of the smoothly curved outline contours, not the orig-
inal line drawings. It just allows for much better control of where along the contour
we select points to be connected by straight-line segments. In doing this, we can exam-
ine differences between different ways of selecting points and between different objects.264J De Winter, J WagemansThe results provide partial support for Attneave’s original ideas but also interesting
additional insight in how shape is specified by contour information.Addressing the first aspect of Attneave’s demonstration (cid:246)is it possible to identify
objects based on contours consisting of straight-line segments only? (cid:246)the answer is a
balanced yes: identification was still possible in many cases but the variation between
stimuli and conditions was very large (between 0% and 100% identification in all
of the experiments). There are a number of stimuli for which continuous curvature
along the contour is not important but for others it does seem to play an important
role. Addressing the second aspect of Attneave’s demonstration (cid:246)is the critical infor-
mation about shape located at curvature extrema?(cid:246)the answer is again a balanced
yes: in all of the experiments, identification was considerably easier when curvature
extrema (E) rather than curvature inflections (I) were connected by straight lines.
However, in many cases straight-line versions could also be identified when they were
connecting other points and,
for the straight-line versions connecting curvature
extrema, the particular selection of extrema played an important role as well (again,
from 0% to 100% variation). Moreover, identification was highest when visually salient
points (SP, as marked by independent subjects) were connected and these do not neces-
sarily correspond to mathematical curvature extrema (see De Winter and Wagemans
2008). Furthermore, the relative identification cost for straight-line versions connecting
inflections or midpoints (MP) between salient points could often be removed by pre-
serving the local orientation around the midpoints,
instead of introducing spurious
corner points at these locations. In this sense, curvature extrema do not have such
a special status as corner points in straight-line versions. A different test of the role
of curvature extrema would be to present only points at their locations. We have
performed this test as part of our large-scale study on the identification of fragmented
outlines (Panis et al 2008).The strong variation in identifiability between stimuli and conditions cannot be
explained by a simple variable. An obvious candidate is the number of points con-
nected by straight-line segments. Indeed, within each experimental condition, there is a
significant correlation between the number of corner points in each stimulus and its
identification rate (varying between 0.18 and 0.48). However, there is also a consider-
able variation between conditions, which cannot be explained by the number of points.
For example, within experiment 1, the number of points was exactly the same in the E
and I conditions and the average identification was 46.4% versus 20.4%, respectively.
Experiments 2 and 4 were matched for number of points but identification appeared
easier when salient points or midpoints were connected (68.9% versus 34.4%, respec-
tively) than when extrema or inflections were connected (53.4% versus 14.2%, respectively).
Improving the criterion for selecting the extrema or salient points from experiments 1
to 4, making it more perceptually relevant than mathematically strict, had a strongly
beneficial influence on identification, although the number of selected points did not
increase (29.7, 27.4, 24.2, 27.6). All in all, the correlation between the average number
of points and the average identification rate across experiments was low and even slightly
negative (r (cid:136) (cid:255)0:06, p (cid:136) 0:847), and the same was true for the correlation between the
median values (r (cid:136) (cid:255)0:08, p (cid:136) 0:805).Another obvious candidate to explain the decrease in identifiability when going
from smoothly curved contours to straight-line versions is the deviation between the
stimuli. When the straight-line version approaches the original contour very well, it is
logical to expect that identification will not be lower. Across experimental conditions,
the correlation between the average size of the stimulus difference (cumulative area of
nonoverlapping stimulus parts) and the average identification rate as such was strongly
negative (r (cid:136) (cid:255)0:84, p 5 0:001) and the same was true for the medians (r (cid:136) (cid:255)0:88,
p 5 0:001). So, a small area difference clearly contributes to identifiability.Straight-line versions of object outlines265Looking at a finer scale within each experimental condition, there was a significant
positive correlation between the area difference and the drop in identification in six
experimental conditions (varying between 0.24 and 0.53). The correlation was highest
in the experiments where the selection was probably the least psychologically relevant
(one extremum per lob in experiment 1 and the largest absolute curvature in experi-
ment 2). In those experiments, large sections of the original contour are often missing
when selecting inappropriate points (see figure 6) and this causes a great variabil-
ity in identifiability. However, the correlation was quite low (even negative) in five
other experimental conditions where the average identification was either rather high
(eg experiment 3, E versions, mean identifiability (cid:136) 60:7%, r (cid:136) 0:14; experiment 4,
SP100 versions, mean identifiability (cid:136) 68:9%, r (cid:136) (cid:255)0:09) or rather low (eg experi-
ment 4, MP100 and MP75 versions, mean identifiability (cid:136) 34:4% and 18.0%, r (cid:136) (cid:255)0:11
and 0.02, respectively).This means that there is clearly more going on that determines whether the critical
shape information for object identification is preserved in the straight-line version of
the outline. A small deviation from the original outline (defined as the area of non-
overlap) is by no means a necessary or sufficient condition for identification. We
noticed that,
in the case of large average area differences (eg bigger pieces being
chopped off), the effect of the area difference on identifiability is usually substantial;
whereas, in the case of small average area differences (eg missing or deformed details),
the effect on identifiability can be small or large, depending on the diagnosticity of the
detail. We have quantified this impression by calculating the correlation between
the mean area difference for each experimental condition and the size of the corre-
lation between area difference and identification rate in that condition (r (cid:136) 0:639,
p (cid:136) 0:034; and similar but smaller for the medians, r (cid:136) 0:540, p (cid:136) 0:086).Let us have a closer look at the stimulus differences to try to understand what
the additional factors may be. There is a group of objects that appear quite robust
for the transformation from smoothly curved contours to straight-line versions, regard-
less of the specific selection criterion for the corner points, whereas another group
of objects cannot be identified in any of the straight-line versions (see figure 7).
Starting from the highly identifiable silhouettes (4 90%), we sorted the list of objects
(n (cid:136) 117) on the average identification rates for all straight-line versions (except SP75,
MP75, and MPT). We then distinguished between the top group of 25 objects that
remain pretty identifiable (between 95.5% and 69.5%) and the bottom group of
25 objects that become hardly identifiable (between 31.0% and 5.0%). The top group
includes mostly objects with relatively complicated shapes or global shape charac-
teristics (not local distinctive features) that are rather unique. This group contains
many animals with distinctive global shapes (eg giraffe, deer, seahorse, elephant, bear,
ostrich, spider, chicken, pig, swan, rhinoceros, squirrel; see figure 7a) but also other
biological objects or artifacts with a characteristic shape (eg anchor, flower, glasses,
leaf, carrot, windmill, watering can, kite, helicopter; see figure 7b). The bottom group
includes mostly objects with relatively simple shapes (with few curvature singu-
larities); these can be biological (eg lips,
lemon, banana, cherry, strawberry; see
figure 7c) as well as man-made (eg hat, pan, balloon, shoe, toothbrush, sock, boot;
see figure 7d).Zooming in on the subgroup for which the selection criterion does play a role
may be interesting to try to reveal necessary and sufficient conditions for identification
on the basis of straight-line versions. For several objects, identification is still relatively
good for straight-line versions based on E or SP but rather poor for those based on
I or MP. To obtain these objects in a systematic way, we again started from the
highly identifiable silhouettes (4 90%) and selected those with reasonable average iden-
tification for all E and SP100 versions (4 60%). We then sorted them according to theNumber
and
nameOriginal
silhouetteExperiment 1Experiment 2Experiment 3Experiment 4EIEIEISP100MP100100%96%25%100%60%96%15%100%93%98%100%89%68%84%92%70%100%41%93%0%0%20%0%0%0%56%30%(a)200Seahorse(b)48Carrot(c)135Lemon(d)179Pan92%4%0%12%0%48%0%44%15%Figure 7. (a) and (b) Examples of straight-line versions that can still be identified in almost all conditions. These are typically
objects with a highly distinctive global shape. (c) and (d) Examples of straight-line versions that are difficult to identify in
almost all conditions. These are typically objects with simple shapes where large parts are easily lost. The identification rate is
mentioned below each stimulus.2
6
6JD
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sNumber
and
nameOriginal
silhouetteExperiment 1Experiment 2Experiment 3Experiment 4EIEIEISP100MP100100%93%54%96%16%92%0%89%4%100%82%4%96%0%92%4%93%41%99%18%4%100%12%96%0%100%4%(a)65Comb(b)150Mushroom(c)258Wineglass(d)49Cat98%100%89%68%84%92%70%100%41%Figure 8. Examples of straight-line versions with a large difference between E/SP versions and I/MP versions. These are usually
moderately complex shapes. (a) An example of an object with a considerable degree of curvature variation along the contour
but a strikingly repetitive pattern that is preserved in E/SP versions but not in I/MP versions. (b) and (c) Examples of objects
with simpler shapes in which the characteristic global properties are preserved in E/SP versions but not in I/MP versions.
(d) Our versions of an outline drawing of a cat. The distinctive local features (ears) are preserved in E/SP versions but not in
I/MP versions. The identification rate is mentioned below each stimulus.iS
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7268J De Winter, J Wagemanssize of the difference with the average identification for all I and MP100 versions. The
majority of the objects with the biggest difference (4 60%) have moderately complex
shapes (see figure 8). Those with a considerable degree of curvature variation in the
original silhouette are characterised by a striking regularity such as a frequent repeti-
tion of a salient feature (eg comb, pineapple; see figure 8a). in the E/SP version, this
is maintained, while it usually disappeared in the I/MP version. Most of the objects
in this subset have simpler shapes that happen to be distorted strongly when the
corner points are selected badly (eg candle, mushroom, star, lamp, church, duck, pear;
see figure 8b). In many of these, the characteristic bilateral mirror symmetry is preserved
in the E/SP version but destroyed in the I/MP version (eg dress, wineglass, pants,
scissors, hand; see figure 8c). Symmetry is a salient regularity for the visual system
(eg Wagemans 1995, 1997) and it has been included as an important factor in theories
of shape representation (eg Biederman 1987; Kurbat 1994; Quinlan 1991). Note, however,
that symmetry is not a sufficient condition for identification (see figure 8c, ‘wineglass’
in experiment 4): the global shape characteristics (eg alternation of parts sticking out)
must be preserved as well. This corroborates the importance of convexities and con-
cavities in determining an object’s part-structure, as proposed in recent work on shape
perception (eg Barenholtz et al 2003; Bertamini 2001; Bertamini and Mosca 2004; Cohen
et al 2005; Lamote and Wagemans 1999; Vandekerckhove et al 2007).The more complex shapes (with more curvature variation) within this subgroup
for which the selection criterion plays a role, happen to have smaller parts or local
features that appear distinctive: when they are preserved in the straight-line version
(usually in the E/SP version), the objects can still be identified; however, when they are
not maintained (usually in the I/MP version), the objects can no longer be identified.
Many of the objects in this subset are animals (eg frog, rabbit, cat, fish, penguin,
duck, crocodile, kangaroo; see figure 8d) and the diagnostic features are often typical
body parts (eg paws, ears, beak, tail). It is quite striking that this damaging effect
can often be repaired by drawing tangent lines through the midpoints (see figure 9).
The MPT versions are usually a bit more ‘spiky’ or ‘jerky’ and may thus appear more
like cartoon versions, but at least their basic shape characteristics are maintained,Number
and
nameOriginal
silhouetteExperiment 4Experiment 5SP100MP100MPT100%96%0%92%100%100%0%96%78Dress100Frog126Kangaroo99%100%7%100%Figure 9. Examples of straight-
line versions that were hardly
identifiable as I/MP versions
but
that become identifiable
again when spurious corner
points at I/MP are avoided by
drawing straight lines through
them in the MPT versions. The
identification rate is mentioned
below each stimulus.Straight-line versions of object outlines269and hence they remain identifiable. This is again in line with recent work on the role
of concavities and convexities in an object’s part-structure (Barenholtz et al 2003;
Bertamini 2001; Bertamini and Mosca 2004; Cohen et al 2005; Lamote and Wagemans
1999; Vandekerckhove et al 2007). Despite substantial differences regarding the role of
different curvature singularities, similar differences between different object classes
(depending on their global shape characteristics) were obtained in the study of identi-
fication of fragmented outlines (Panis et al 2008).In summary, Attneave (1954) was right in pointing out that continuous curvature
along the contours is often not necessary for identification. However,
it is slightly
misleading to argue on the basis of the sleeping cat demonstration (see figure 1b) that
curvature extrema contain most of the information about the contour because con-
necting them with straight-line segments preserves identifiability. First, for sufficiently
complex objects without critical distinctive features at the level of small details, it does
not matter much which points are selected to be connected by straight-line segments
(see also figure 1c): they can be identified by their global shape which is preserved
regardless of the points being connected. Second, for relatively simple shapes with little
curvature variation (eg banana) or relatively few, rather large round sections (eg apple),
connecting only the global or largest curvature extrema by straight-line segments will
never retain the basic shape characteristics. Third, for the large majority of objects,
mostly with intermediate levels of complexity, the specific selection of points will
determine whether identification is still possible in the straight-line version: when the
global shape characteristics (eg repetition or mirror reflection of part structure)
or distinctive local features (eg typical body parts) are preserved, identification is good
and otherwise it is poor. Having a large and reliable benchmark data set with identi-
fication rates of a large number of everyday objects in different straight-line versions
will be useful to test future more specific proposals about critical shape information
in outline contours.Acknowledgments. This research was supported by a research grant from the University Research
Council (OT/00/007) and from the Research Foundation (FWO-Vlaanderen G.0189.02) to JW.
We would like to thank two anonymous reviewers for helpful comments on the previous draft
and Sven Panis for assistance with the data collection and for interesting discussions. After the
first submission of the manuscript, Joeri De Winter has died in a tragic accident.References
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