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Anim Cogn (2009) 12:809821

DOI 10.1007/s10071-009-0240-1

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ORIGINAL PAPER

The comparative psychophysics of complex shape perception

J. David Smith Joshua S. Redford Sarah M. Haas

Received: 26 April 2009 / Revised: 11 May 2009 / Accepted: 14 May 2009 / Published online: 3 June 2009 Springer-Verlag 2009

Abstract The authors compared the complex shape per-

ception of humans and monkeys. Members of both speciesparticipated in a SameDiVerent paradigm in which they

judged the similarity of shape pairs that could be variations

of the same underlying prototype. For both species, similar-

ity gradients were found to be steep going out from the

transformational center of psychological space. In contrast,

similarity gradients were found to be Xat going from the

periphery in toward the center of psychological space.

These results show that there are important common princi-

ples in the shape-perception and shape-comparison pro-

cesses of humans and monkeys. The same general

organization of psychological space is obtained. The same

quantiWable metric of psychological distance is applied.

Established methods for creating controlled shape variation

have the same eVect on both species similarity judgments.

The member of the to-be-judged pair of shapes that is

peripheral in psychological space controls the strength of

the perceived similarity of the pair. The results have

broader implications for the comparative study of percep-

tion and categorization.

Keywords Shape perception Similarity

Psychophysics Primate cognition Monkeys

Introduction

The relation between objective stimuli and their percep-

tual representations is a fundamental issue in the study of

perception. Many elegant studies have explored these psy-

chophysical relations in nonhuman animals, conWrming

basic perceptual laws, measuring sensitivities and thresh-

olds, examining criterion-setting processes, and so forth

(Berkley and Stebbins 1990; Moore 1997; Rilling and

McDiarmid 1965; Schusterman and Barrett 1975;

Stebbins 1970). Our research owes a substantial debt to

this literature.

In these studies, researchers naturally focused on the

simpler, low-dimensional psychological spaces, especially

single-dimensional perceptual continua like pitch or wave-

length. Indeed, the detailed nature of the psychophysical

measurements and correspondences sought by these studies

often dictated this approach. Consequently, scant research

has considered the psychophysical relationships among

complex objects and the organization of psychological

spaces of high dimensionality. Yet, in the study of complex

objects there also arise important questionsfor example,

about the interaction of stimulus attributes, about the conW-

gural features that can be produced by particular combina-

tions of stimulus attributes, and about the mechanisms of

selective attention that organisms use to navigate stimulus

complexes. Moreover, animals frequently encounter

objects of high complexitythat is, the natural kinds in

their worlds. Accordingly, the principal purposes of our

research were to examine how nonhuman animals respond

to the relationships among complex shapes, and to examine

the distance metric that determines similarity relationships

within the psychological space that contains those shapes.

To our knowledge, these psychophysical principles had not

been well established with stimuli at high dimensionality,

J. D. Smith (&) J. S. Redford S. M. HaasDepartment of Psychology, University at BuValo,

The State University of New York, 346 Park Hall,BuValo, NY 14260, USAe-mail: [email protected]


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810 Anim Cogn (2009) 12:809821

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while careful controls were preserved over the nature and

degree of stimulus variability.

In addition, we focused on a fundamental structural

property of the psychological spaces that contain animals

natural-kind categories. That is, these psychological spaces

often obey a principle that Rosch and others (e.g., Rosch

and Mervis 1975) called family resemblance. The principle

of family resemblancethat has motivated hundreds ofstudies in perception and categorizationcan be explained

in two ways. First, it means that members of natural-kind

categories have complex, variable, and probabilistic simi-

larity relationships to one another. A pair of members will

share some but not all features in common, and the sources

of similarity will change depending on which category

members are compared. In the same way, some members of

a family resemble each other for some reasons, and others

look alike for other reasons. Second, Rosch and others

found utility in noting that family-resemblance or natural-

kind categories often have a graded structure, with a hypo-

thetical prototypical item in the center as a transformational

focus from which category members can be thought of as

being derived. From that center, moving outward in a

graded fashion, one would Wnd close in highly typical items

that are low-level distortions of the prototypes, and farther

out more peripheral, less typical items that are higher-level

distortions of the prototype. One of the central images in

the human categorization literature is of this cloud of exem-

plars, centered on a prototype with a typicality gradient

running through it.

Consequently, our research was designed to analyze the

similarity relationships among items that diVered probabi-

listically in this way, that were derived from a transforma-

tional center or focus, and that showed the graded typicality

structure of many family-resemblance categories. This

structure may be a fundamental one for animals as they

construct psychological and behavioral equivalence classes

(i.e., categories) that help them navigate their worlds. For

example, many of monkeys important categories (e.g., rap-

tors, seeds, trees, big cats, and so forthprobably have this

family-resemblance or natural-kind structure. We wanted to

understand the nature of the psychological space underly-

ing these kinds of categories, the distance metric that deter-

mines perceived similarity among objects, and the

perceptual principles underlying typicality gradients in a

family-resemblance psychological space. We believed that

these data would provide a useful additional basis for

studying categorization comparatively. These data could

ground further research in how monkeys learn and use cate-

gories, abstract prototypes, and process peripheral and

exceptional category members.

To make this exploration, we needed a complex stimulus

domain that allowed the construction of inWnite complexly

varying stimuli, with probabilistic similarity relationships

in which we could still control and measure the strength of

similarity among items and the distance of items from their

transformational focus. These requirements were met with

the dot-distortion methodology that grounded early studies

of similarity and shape perception in humans (e.g.,

Attneave and Arnoult 1956) and that is an inXuential meth-

odology in research on humans perceptual categorization

(Blair and Homa 2001; Knowlton and Squire 1993;Nosofsky and Zaki 1998; Palmeri and Flanery 1999; Posner

et al. 1967; Posner and Keele 1968; Smith 2002; Smith and

Minda 2001).

The dot-distortion paradigm supported our general

approach in several ways. It oVered us widely used stimulus

materials in categorization research that have Wgured prom-

inently in the study of family resemblance. It allowed us to

present stimuli indeWnitely without any stimulus repetition,

so to rule out speciWc-token strategies and focus instead on

general perceptual strategies. It gave us a psychological

space of high dimensionality, allowing us to capture the

complex stimulus variability and similarity relationships

that may be found in real-world perceptual classes. Thus,

the dot-distortion methodology was well suited for explor-

ing the issues of this article.

Given our comparative goals, we included both

human and monkey participants in our research. In this

respect, our approach followed on the cross-species psy-

chophysical research in Shields et al. (1997) and Fagot

et al. (2001). Cross-species comparisons are still surpris-

ingly uncommon in comparative research, but are often

fruitful when they occur (e.g., Cook and Smith 2006;

Smith et al. 2004). Thus, Experiments 1A and 1B con-

sider the psychophysics of complex-shape perception by

humans, using, respectively, a similarity-rating task and

a SameDiVerent (SD) task. We used these two

approaches to bridge from the similarity-rating approach

that has been used historically in this area to the SD

approach that is more felicitous for use with animal par-

ticipants. In a complementary study, Tomonaga and

Matsusawa (1992) used the same two converging meth-

ods with humans in their cross-species research. The

human studies in the present article conWrm the psycho-

physics of shape perception established by Posner et al.

(1967) and extended by Smith and Minda (2001, 2002),

in the sense of relating an objective, quantiWable mea-

sure of interstimulus distance to humans behavioral

responses. Then, Experiment 2 considers the psycho-

physics of complex shape perception by rhesus mon-

keys, asking whether there are continuities and common

principles across species in the perception of high-

dimensional stimuli. In this respect, our research extends

the approach of Tomonaga and Matsusawa, who found

similarities of shape perception between humans and

chimpanzees.


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Experiment 1A: humans

Experiment 1A explored the structure of the psychological

similarity space that organizes similarity-based families of

dot-distortion shapes. Using a similarity-rating task, we

measured the rated similarity by humans between pair-wise

combinations of diVerent-level distortions of the transfor-

mational centers of categories. This experiment conWrmsthe psychophysics of these shapes that has been established

for humans. It also conWrms the usefulness of an estab-

lished measure of the psychological distance between com-

plex shapes. It describes the similarity gradient for shape

pairs that are either anchored to the transformational center

of a family-resemblance category or anchored to peripheral

members of a category. Subsequently, we ask whether

these measures and gradients extend usefully to analyzing

the complex-shape perception of monkeys.

Methods

Participants

Participants were 22 undergraduates from the University at

BuValo, the State University of New York (UB) who partic-

ipated in a 50-min session to fulWll a course requirement.

Our participants were drawn randomly from a subject pop-

ulation containing slightly more females than males. Partic-

ipants were in their late teens or early twenties with

apparently normal or corrected-to-normal visual acuity.

Dot-pattern stimuli

The stimulus materials for the similarity-rating task were

created using a method that generates families of shapes

from prototypes. By this method, nine points or dots are

selected randomly from within the central 30 30 area of a

50 50 grid. These nine dots together deWne a prototype.

Then distortions of the prototype are produced by applying

a series of probabilities that determine how far (if at all)

each dot will be moved from its position in the prototype.

DiVerent series of probabilities let one produce dot patterns

at diVerent distortion levels of the prototype. In some simi-

larity-rating trials, we presented two distortions of one pro-

totype. This produced trials with a range of stimulus

disparities depending on the particular distortion levels

used. For lower- or higher-level distortions, respectively,

the shapes were more similar or more diVerent. In other

similarity-rating trials, we presented distortions that were

derived from two diVerent prototypes, always producing a

large-disparity trial.

SpeciWcally, distortions were built from prototypes by

probabilistically moving each dot into one ofWve areas

that covered the 20 20 grid of pixels around it. For

Area 1, the dot did not move. For Area 2, the dot moved

to one of the eight pixel positions in the shell immedi-

ately around its original position. For Area 3, the dot

moved to one of the 16 pixel positions in the second

shell of pixels around it. For Area 4, the dot moved into

one of the 75 pixel positions in the third, fourth, and half

of the Wfth pixel shell around it. For Area 5, the dot wasmoved into one of the remaining 300 pixel positions in

the surrounding 20 20 pixel grid (i.e., to the Wfth,

sixth, seventh, eighth, ninth, or tenth shell of pixels

around its original position).

DiVerent levels of distortion were arranged by adjusting

the probabilities that dots had of moving into each of the

Wve areas. For Level 0 distortions, the probabilities that

dots would move to each area were 1.0, 0.0, 0.0, 0.0, and

0.0, respectively. Dots in Level 0 distortions never

movedthese patterns reproduced the prototype. For Level

1 distortions, the Wve probabilities were 0.88, 0.1, 0.015,

0.004, and 0.001. These distortions included mostly

unmoved or barely moved dots. The Wve probabilities were

0.59, 0.2, 0.16, 0.03, and 0.02 for Level 3 distortions, 0.2,

0.3, 0.4, 0.05, and 0.05 for Level 5 distortions, and 0.0,

0.24, 0.16, 0.3, and 0.3 for Level 7.7 distortions (henceforth

Level 7 distortions). These probabilities were those used in

Posner et al. (1967, Table 1, p 31) (Posner also used other

distortion levels, and other sets of probabilities, that were

not included here.). The present studies also included stim-

ulus pairs in which the two shapes were derived from two

diVerent prototypes. In these cases, the second member of

the pair was a Level 7 distortion of its prototype. These

shape pairs were universally distant from each other in psy-

chological space and perceptually dissimilar. As a conve-

nience in this article, we refer to Level 7 distortions of an

unrelated prototype as a Level 9 distortion.

With the dot positions chosen for a pattern, the pattern

was magniWed as follows. Each pixel position in the distor-

tion algorithm was mapped to a 3 3 pixel square on the

screen, and the dot was placed in the center of the appropri-

ate 9-pixel cell on the screen. In this way, the stimulus pat-

terns were magniWed threefold, from the virtual 50 50

coordinate space to being shown on an actual 150 150

space on the screen. Finally, Turbo Pascals (7.0) DrawPoly

procedure connected successive dots by lines and Wlled the

resulting polygon shape in red with a white outlining bor-

der. This followed the common practice of presenting dot-

distortion patterns as polygon shapes (Homa et al. 1979;

Homa et al. 1981).

Figure 1 shows pairs of stimuli that are Levels 1, 3, 5, or

7 distortions of the same prototype (rows 14 in the Wgure,

respectively) or Level 7 distortions of unrelated prototypes

(row 5).


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Similarity-rating task

Each trial consisted of two distortions presented side by

side in the center of an 11.5-inch computer screen against a

black background. Below each pair of shapes was centered

the question: How diVerent are these two shapes? Below

this a 16 scale was shown with the 1 labeled no diVer-

ence and the 6 labeled big diVerence.

Thirty-six types of pairs were presented, representing

every pairwise combination of distortion levels (0, 1, 3, 5,

7, and 9) in the two orders in which they could occur (0-1,

1-0, 0-3, 3-0, etc.). The six same-level pair types (e.g., 1-1)

were also presented in two orders (3-3, 3-3) to ensure that

these kinds of trials were sampled just as often as were the

other pair types. This made for 42 trial types in all. Each

type was presented for rating 15 times to each participant,

so each pairwise combination of distortion levels was rated

30 times. The 42 trial types were presented in 15 successive

random permutations without any apparent structure or

break to participants. Each participant received 630 pairs in

all. The prototype or prototypes used for a trial were chosen

at random on each of 630 trials for each of the 22 partici-

pants. Thus, this similarity-scaling experiment represents a

comprehensive sample of dot-distortion space.

Participants were given these instructions. In this

experiment you will see two red polygon shapes on each

trial. Your job is to look at each pair and decide how diVer-

ent they are. If there is no diVerence between them, give

them a rating of 1. If there is a big diVerence between

them, give them a rating of 6. Use intermediate ratings for

intermediate diVerences. Use the number keys at the top of

the keyboard to make your response. Make sure to use the

whole range of the scale from 1 to 6.

Results and discussion

Table 1 (column 4) gives the average dissimilarity rating

for every pairwise combination of two distortion levels.

Each entry in the table summarizes 660 observations.Humans dissimilarity ratings are discussed now.

Similarity gradients moving out from the transformational

center

Rows 16 of Table 1 (column 4) show rated dissimilarity

when the center of a family-resemblance shape category (a

Level 0 distortion or prototype) was compared successively

to greater levels of distortion (Levels 09). Clearly, the

increasing distortion levels had a powerful eVect on

humans perception, and the gradient of increasing dissimi-

larity was steep moving out from the transformational cen-

ter of the category to the periphery.

Similarity gradients moving in toward the transformational

center

The remaining rows of Table 1 examine the opposite case,

when a shape that is itself a distortion of the prototype that

lies more or less at the periphery of psychological space is

compared to shapes that move from that periphery into the

transformational center of the category. Clearly, the

decreasing distortion level of the comparison or inner shape

aVected humans perception minimally. The gradients of

changing dissimilarity were Xat moving in from the periph-

ery of the space to the transformational center. Figure 2

shows these Xat gradients.

The peripheral pair member controls similarity

One guiding principle behind humans dissimilarity ratings

in Table 1 is that the member of the to-be-judged pair that

is peripheral in psychological space controls the rated dis-

similarity of the pair almost completely. With a referent

prototype, dissimilarity increased sharply as the peripheral

comparison item increased in distortion level. With a refer-

ent peripheral item, though, dissimilarity hardly changed as

the comparison item decreased in distortion level.

A metric of psychological distance

Another guiding principle behind the dissimilarity ratings in

column 4 of Table 1 is that a simple, theoretically neutral

measure of psychological distance explains humans

dissimilarity ratings almost perfectly. Column 3 in Table 1

Fig. 1 Examples of pairs of dot-distortion shapes. Rows 14, respec-tively, show two Level 1, Level 3, Level 5, and Level 7 distortions of

the same underlying prototype. Row 5 shows Level 7 distortionsderived from two unrelated prototypes


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gives the natural logarithm of 1 + the average Pythagorean

distance that was moved by corresponding dots between pat-

terns of each pair type. The addition of 1 to the Pythagorean

distance ensures that 0 Pythagorean distance maps to 0 loga-

rithmic distance. This logarithmic-distance measure can be

estimated well for any two distortions of one prototype,

because then one knows which were the corresponding dots

and how far each moved between patterns. These distances

cannot be calculated precisely for two distortions from

diVerent prototypes, because in that case one cannot know

which dots correspond across the patterns. This explains

why not all the distances are entered in the table. However,

in practice the distance between patterns from two diVerent

prototypes is always largephysically and psychologi-

callyno matter how the dot correspondence is taken. For

smaller stimulus disparities involving two distortions of one

prototype, the psychological-distance calculation is precise.

The psychological-distance calculation is also psycho-

logically meaningful in the sense of predicting perfectly

humans response patterns. In Table 1, for the 15 unique

data rows for which the distance calculations could be

made (rows 1226), there was a 0.99 productmoment cor-

relation between the logarithmic psychological-distance

measure and humans dissimilarity ratings. Objective stim-

ulus distance completely explained subjective dissimilarity.

We note that this psychological-distance yardstick does not

necessarily represent some universal aspect of similarity

spaces. Other domains might have their own similarity

metric (e.g., Huber 2001; Huber and Lenz 1993). But the

logarithmic-distance metric is highly useful within the

Table 1 Logarithmic interdot distance (Ln Dist, columns 3, 5, 7, 9)for pairs of random-dot polygons at diVerent distortion levels (DL), theaverage dissimilarity rating (Dissim Rating, column 4) given byhumans in Experiment 1A, and the average proportion of diVerent

judgments (Propor DiV) given by humans in Experiment 1B (column6) and by two rhesus macaques (Macaca mulatta) in Experiment 2(columns 8, 10)

DL DL Experiment 1A: humans Experiment 1B: humans Experiment 2: Murph Experiment 2: Lou

Ln (Dist) Dissim Rating Ln (Dist) Propor DiV Ln (Dist) Propor DiV Ln (Dist) Propor DiV

Comparisons out from the transformational center0 0 0.000 1.306 0.000 0.019 0.000 0.175 0.000 0.145

0 1 0.164 1.604 0.160 0.306 0.161 0.179 0.161 0.146

0 3 0.648 2.396 0.655 0.807 0.642 0.269 0.640 0.202

0 5 1.112 3.067 1.089 0.945 1.098 0.376 1.096 0.301

0 7 1.771 4.327 1.753 0.990 1.758 0.652 1.753 0.580

0 9 5.185 0.995 0.935 0.867

Comparisons in toward the transformational center

9 7 5.153 0.995 0.925 0.880

9 5 5.114 0.993 0.940 0.884

9 3 5.196 0.988 0.927 0.888

9 1 5.146 0.996 0.937 0.903

9 0 5.185 0.995 0.935 0.867

7 7 2.090 4.756 2.099 0.989 2.100 0.803 2.092 0.753

7 5 1.873 4.486 1.865 0.993 1.863 0.723 1.866 0.634

7 3 1.806 4.392 1.805 0.994 1.812 0.706 1.814 0.605

7 1 1.763 4.288 1.762 0.995 1.757 0.686 1.749 0.582

7 0 1.771 4.327 1.753 0.990 1.758 0.652 1.753 0.580

5 5 1.419 3.629 1.416 0.982 1.430 0.468 1.406 0.423

5 3 1.250 3.368 1.253 0.957 1.244 0.438 1.262 0.334

5 1 1.120 3.035 1.126 0.944 1.126 0.403 1.114 0.313

5 0 1.112 3.067 1.089 0.945 1.098 0.376 1.096 0.301

3 3 0.969 2.918 0.965 0.922 0.937 0.318 0.976 0.305

3 1 0.703 2.492 0.712 0.843 0.696 0.252 0.710 0.2353 0 0.648 2.396 0.655 0.807 0.642 0.269 0.640 0.202

1 1 0.301 1.809 0.293 0.466 0.282 0.188 0.303 0.177

1 0 0.164 1.604 0.160 0.306 0.161 0.179 0.161 0.146

0 0 0.000 1.306 0.000 0.019 0.000 0.000 0.000 0.145

The four dependent measures are indicated in bold


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dot-distortion domain of complex shapes, and one can use

it to ask ifin this domainmonkeys express the same

metric in their behavioral responses as humans do.

Experiment 1B: humans

Experiment 1B shows that the Wndings of Experiment 1A

replicate using a paradigm that we could and did use with

monkeys in Experiment 2. In this sense, Experiment 1B is a

bridge experiment between Experiments 1A and 2. Using a

SD task, we measured the proportion of DiVerent responses

given by humans for pairwise combinations of diVerent-level

distortions of the transformational centers of categories.

Methods

Participants

Participants were 60 UB undergraduates, drawn randomly

from the same participant pool, who participated in a 50-

min session to fulWll a course requirement. Two partici-

pants were excluded from analysis. One participant did not

complete the required 630 trials. One was below chance on

both Same and DiVerent trials.

Dot-distortion materials

The stimulus materials for the SD task were created using

the methods already described. In each SD trial, we pre-

sented either two identical distortions of one prototype

(a Same trial), distortions from two diVerent prototypes (a

deWnite DiVerent trial), or two diVerent distortions of one

prototype (producing a diVerent trial but with a range of

stimulus disparities depending on the distortion levels

used).

SD trials

Each trial consisted of two distortions presented above and

below in the top center of an 11.5-inch computer screen

against a black background. Below each pair of shapes

appeared screen icons reminding participants about their

response optionsS (for Same) and D (for DiVerent).

These responses were selected by choosing labeled key-

board keys that reXected the spatial layout of the response

icons on the screen. The humans task was to respond Same

when the shapes were identical, but DiVerent when the

shapes were even minimally dissimilar. Participants heard a

0.5-s computer-generated reward whoop and gained a point

for each correct response. Participants heard a 4-s com-

puter-generated penalty sound and lost a point for each

error. After each trial, participants also received a scorecard

textbox on the screen that gave them a +1 or 1 for that

trial and told them how many points they had currently in

the task. After the feedback, the screen cleared and a new

shape pair was presented.

SD task

The following 65 types of pairs were presented. There were

DiVerent trials that presented each pair-wise combination

of Level 0, Level 1, Level 3, Level 5, and Level 7 distor-

tions of a single underlying prototype, except that the Level

0-Level 0 pair was not included in this group because it was

really a Same trial (24 trial types). These trial types system-

atically varied in the extent of stimulus disparity the trial

presented to the participant. There were DiVerent trials that

involved pairwise combinations of distortions from one

prototype (Level 0, 1, 3, 5, 7) with a Level 7 distortion from

another, unrelated prototype (11 trial types). These trials

always presented obvious disparities. Finally, there were

Same trials that presented a Level 0, 1, 3, 5, or 7 distortion

and its exact shape match (30 trial types). Overall, DiVerent

trials slightly predominated over Same trials (52.6 and

47.4%, respectively). In all, the 58 humans completed

36,540 SD trials. The 65 pair types were presented in suc-

cessive full permutations that had no structure or apparent

break to participants, and each participant continued per-

forming until reaching 630 trials. The prototypes to be used

for building distortions for a trial were chosen at random on

each of the 630 trials for each of the 58 participants. Thus,

the SD task represented a comprehensive survey of dot-dis-

tortion space.

Fig. 2 The mean dissimilarity rating provided by human observers inExperiment 1A when shapes at diVerent distortion levels (labeled lines

9, 7, 5, 3, and 1) were compared to shapes at equal or lower levels ofdistortion (Levels 7, 5, 3, 1, and 0) as plotted along theXaxis

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Comparison Distortion Level

Dissimilarity

Rating

Humans

7

9

3

5

1


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Instructions

Entering Experiment 1Bs SD task, participants read the

following: In this experiment you will see two red polygon

shapes on each trial. Your job is to look at each pair and

decide if they are same or diVerent. If they are the same,

then press the S key. If they are diVerent, even by a small

amount, then press the D key. You will GAIN ONEPOINT if you are correct and you will LOSE ONE POINT

if you are incorrect. This week we are giving $10 prizes to

the participants who score the highest. You may win a prize

if you carefully compare the shapes before responding.

The cash prizes were awarded to every top-performing

participant who responded to the laboratorys attempts to

contact them.


Table 1 (column 6) gives the proportion of DiVerent

responses for every pairwise combination of two distortion

levels (together within column 5the logarithmic-dis-

tance measure already described). Humans SD perfor-

mance is discussed now.


center

Rows 16 of Table 1 show the proportion of DiVerent

responses when the center (prototype) of a family-resem-

blance shape category is compared to successively greater

distortion levels. As in Experiment 1A, the gradient of

increasing dissimilaritynow measured as increasing

DiVerent judgmentswas steep moving out from the trans-

formational center of the category to the periphery.


center

The rest of Table 1 examines the case of peripheral mem-

bers of the shape family compared to shapes successively

closer to the prototype. Clearly, the decreasing distortion

level of the comparison or inner shape aVected humans

perception only slightly. As in Experiment 1A, the gradi-

ents of similarity were Xat moving in from the periphery of

the space to the transformational center.


Here, too, the results demonstrate the principle that the

member of the to-be-judged pair that is peripheral in psy-

chological space controls the perceived Sameness for the

pair. With a referent prototype, DiVerent judgments

increased sharply as the peripheral comparison item

increased in distortion level. With a referent peripheral

item, though, DiVerent judgments changed only slightly as



The results also conWrm the second principle that objective

stimulus distance explained humans DiVerent judgmentsalmost perfectly. In this case, the form of the function relat-

ing DiVerent judgments to distance was logarithmic,

because DiVerent responses increased rapidly at Wrst as dis-

tance increased, but then Xattened as they approached their

ceiling at 1.0. Humans data pattern was Wt with a logarith-

mic function, yielding a sum of the squared deviations of

0.004 and an average absolute deviation of 0.013, with

0.998 of the variance in DiVerence proportions accounted

for by the regression. As in Experiment 1A, objective stim-

ulus distance predicted humans DiVerent judgments per-

fectly.

Experiment 2: monkeys

Experiment 2 explores the structure of the psychological

similarity space that organizesfor rhesus monkeyssim-

ilarity-based families of complex shapes. Using the SD

task, we measured the proportion of DiVerent responses

given by monkeys for pairwise combinations of diVerent-

level distortions of the transformational centers of catego-

ries. This experiment establishes for the Wrst time a psycho-

logical-distance metric of complex shape perception for

nonhuman primates. It provides an objective measure of

psychological similarity between complex shapes that can

be used in other studies of primate perception, categoriza-

tion, and cognition. It describes for animals the shapes of

the typicality gradients for shape pairs that are either

grounded in the transformational center of a family-resem-

blance category or grounded in peripheral members of a

category.

Methods

Participants

Rhesus monkeys (Macaca mulatta) Murph (12-year-old)

and Lou (12-year-old) were tested. They had been trained,

using procedures described elsewhere (Rumbaugh et al.

1989; Washburn and Rumbaugh 1992), to respond to com-

puter-graphic stimuli using a joystick. They had been tested

in a variety of other computer tasks. They had also had

experience with a wide variety of computer tasks, including

a related categorization paradigm (Smith et al. 2008b).

They had also had experience with an unrelated SD task


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816 Anim Cogn (2009) 12:809821

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involving colored clip-art images from a CD-Rom contain-

ing 100,000 examples (Fleming et al. 2007). There is no

reason why this experience should have aVected their per-

formance in the basic, shape-comparison paradigm used in

the present research, any more than humans lifetime of

diverse cognitive experience aVected their performance in

the shape-comparisons of Experiment 1. Indeed, the results

to be discussed shortly will conWrm the lack of diVerentialimpact from the diVerent cognitive experiences and testing

history of the two species. The monkeys were tested in their

home cages at the Language Research CenterofGeorgia

State University. They were housed in single-housing cages

in rooms with up to four macaques, with outdoor access.

Monkeys were given access to the test apparatus fre-

quently for long sessions of several hours. They had contin-

uous access to water during testing, and they were not food

deprived or weight reduced for the purposes of testing.

Monkeys worked at their own discretion and at their own

pace, working or resting as they chose. We did not control

the number of trials they completed in any given time

period, except that we set the maximum number of trials

completed in a session to be 1,300.

Apparatus

The monkeys were tested using the Language Research

Centers Computerized Test SystemLRC-CTS(described

in Rumbaugh et al. 1989; Washburn and Rumbaugh

1992)comprising a Compaq DeskPro computer, a digital

joystick, a color monitor, and a pellet dispenser. Monkeys

manipulated the joystick through the mesh of their home

cages, producing isomorphic movements of a computer-

graphic cursor on the screen. Contacting appropriate com-

puter-generated stimuli with the cursor brought them a

94-mg fruit-Xavored chow pellet (Bioserve, Frenchtown,

NJ, USA) using a Gerbrands 5120 dispenser interfaced to

the computer through a relay box and output board (PIO-12

and ERA-01; Keithley Instruments, Cleveland, OH, USA).

Correct responses were accompanied by a computer-gener-

ated whooping sound that bridged the animals to their

reward. On incorrect responses, the screen froze with the

wrong response visible, and there was a computer-gener-

ated buzzing sound. Generally, the timeout period was 20 s

during training, and it was shortened to 15 s during psycho-

physical testing to increase data collection.

Training

Nonhuman primates often succeed on SD and related tasks

(Katz et al. 2002; Shields et al. 1997; Wasserman et al.

2001; Wright et al. 1984, 1989, 1990, 2003). However,

they do Wnd these tasks diYcult to learn (i.e., experimenters

Wnd these tasks diYcult to train). For example, Shields

et al. (1997) observed that rhesus macaques responded

strongly and for hundreds of trials to the absolute cues in an

SD task before Wnally achieving successful, two-item SD

performance. Fagot et al. (2001) found a similar result for

baboons. Primates SD concepts show other fallibilities

compared to those of humans, including some reported fail-

ures of transfer, and some emphasis on response strategies

based in speciWc-item memory and associations (DAmatoand Columbo 1989; DAmato et al. 1985; Katz et al. 2002;

see also Fleming et al. 2007).

Our monkeys also demonstrated this diYculty in

responding abstractly to the SD relation embodied by the

shape pairs. At Wrst, we addressed monkeys haphazard

responding by correcting response biases. We did this by

giving more trials of the opposite trial type proportionally

to their overuse of the biased response. This did not help

them learn the SD task. Next, we tried to instill the SD con-

cept using geometric shapes (triangle, square, diamond, and

circle) instead of 18-dimensional polygons. This approach

was also unsuccessful.

Our third and successful approach built on the intriguing

work showing that the SD concept can be presented more

clearly to animals if arrays of same objects and arrays of

diVerent objects are contrasted (Fagot et al. 2001; Wasserman

et al. 2001; Young et al. 1997). Thus, we gave monkeys

training with ten on-screen shapes that were either all iden-

tical to one another (Same) or all clearly diVerent from one

another (DiVerent). In the former case, the ten shapes were

ten copies of one level 7 distortion of a randomly chosen

prototype. In the latter case, the ten shapes were ten level 7

distortions of ten diVerent randomly chosen prototypes.

Once the monkeys reached 8090% accuracy with 10-item

arrays, training continued with 8-, 6-, and 4-item arrays

until the criterion was reached. Finally, when the monkeys

reached 7080% correct with clearly Same and clearly

DiVerent item pairs (i.e., 2-item arrays), they entered the

phase of mature psychophysical scaling including stimulus

disparities of all levels. The lower criterion at this last

phase of training reXected the common Wnding that SD

judgments on item pairs are more diYcult for animals than

are SD judgments for larger arrays that also contain a

visual-entropy cue that can support correct Same or DiVer-

ent responding. The issue of the visual-entropy cue in SD

responding is discussed in Fagot et al. (2001), Wasserman

et al. (2001), and Young et al. (1997).

It is natural that our animals had diYculty in mastering

the present SD task, because it is one of the most sophisti-

cated SD performances achieved by a nonhuman primate. It

was a simultaneous SD discrimination, not the successive

matching-to-sample task that has been controversial. There

were only two objects presented on each trial. So, the cue of

visual entropy was minimized relative to other recent stud-

ies of pigeon and primate SD performance. In fact, in recent


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Anim Cogn (2009) 12:809821 817

123

studies, primates SD performance deteriorated in the

absence of this entropy cue, and they were not fully able to

sustain the discrimination when making a judgment about

only two shapes (Fagot et al. 2001). In addition, in the pres-

ent SD task every trial was unique, and every stimulus pair

was used once and then discarded. Thus, monkeys were in a

perpetual state of transfer and generalization to new stimuli,

and their SD discrimination was continually forced to gen-eralize broadly. Finally, the present task ruled out any spe-

ciWc-item association or speciWc-item memorization

strategies because items never repeated. Given the sophisti-

cation of this SD performance, some of the data in the pres-

ent article were re-analyzed in Smith et al. (2008a).

Murph completed 5,166, 1,883, 7389, 5,059, and 2,604

training trials at 10, 8, 6, 4, and 2 shapes, respectively. Lou

completed 1,842, 5,990, 1,730, 3,231, and 4,797 training

trials at 10, 8, 6, 4, and 2 shapes, respectively.

The training history of the animals makes it plain that we

did not perfectly equalize the procedures between humans

and monkeys. Humans received instructions that facilitated

their task learning and acclimation. For that reason (and

because of class-period constraints on our testing), humans

completed fewer trials than the monkeys. Given the results

that emerge from the present humanmonkey comparison,

these diVerences in methodology probably only strengthen

the articles conclusions about the common principles in

complex-shape perception across species. Nonetheless, one

should bear these diVerences in methodology in mind.

SD trials

As with humans, each trial consisted of two distortions pre-

sented above and below in the top center of an 11.5-inch

computer screen against a black background. Below each

pair of shapes appeared screen icons reminding subjects

about their response optionsS (for Same) and D (for

DiVerent). The monkeys used an analog joystick to move a

cursor to touch the response icon of their choice. Monkeys

received food rewards and trial-less timeout periods as

already described, and these consequences were associated

with computer generated whoops and buzzes, respectively.

SD task

The 65 trials types described in Experiment 1B were pre-

sented in Experiment 2, in successive full permutations that

had no structure or apparent break to subjects. Once again,

the prototypes to be used for building distortions for a trial

were chosen at random on every trial given to each mon-

key. Thus, the SD task represented a comprehensive survey

of dot-distortion space. Murph completed 12,643 Same

trials (47.3%) and 14,066 DiVerent trials (52.7%). Lou

completed 10,223 Same trials (47.3%) and 11,400 DiVerent

trials (52.7%).


Table 1 (columns 8 and 10 for Murph and Lou, respec-

tively) give the average level of DiVerent responses for

every pairwise combination of two distortion levels(together within columns 7 and 9, respectivelythe log-

arithmic-distance measure already discussed). The mon-

keys SD responding is discussed now.


center

Rows 16 of Table 1 show the proportion of DiVerent

responses when the center (prototype) of a family-resem-

blance shape category is compared successively to higher

distortion levels. As with humans, the gradient of increas-

ing dissimilarity was steep moving out from the transfor-

mational center of the category to the periphery.


center

The rest of Table 1 examines the possible comparisons

between more or less peripheral shapes in psychological

space compared to shapes that are successively closer to the

transformational center. As with humans, the gradients of

changing dissimilarity were Xat moving in from the periph-

ery toward the prototype. Figure 3 shows these Xat gradi-

ents for both monkeys.


The monkeys data also conWrmed the guiding principle

that the member of the to-be-judged pair that is peripheral

in psychological space controls the level of DiVerent

responses for the pair. With a referent prototype, DiVerent

judgments increased sharply as the peripheral comparison

item increased in distortion level. With a referent peripheral

item, though, DiVerent judgments changed only slightly as



The monkeys data also conWrmed the second guiding prin-

ciple that objective stimulus distance predicts precisely the

level of DiVerent responses. For Murph, for the 15 unique

data rows in Table 1 for which the distance calculations

could be made, there was a 0.971 productmoment correla-

tion between the logarithmic-distance measure and the


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818 Anim Cogn (2009) 12:809821

123

level of DiVerent responses observed. Squaring the correla-

tion coeYcient, one sees that objective distance explained

94.3% of the variance in DiVerent responding. For Lou, for

the 15 unique data rows in Table 1 for which the distance

calculations could be made, there was a 0.960 product

moment correlation between the logarithmic-distance mea-

sure and the level of DiVerent responses observed. Squaring

the correlation coeYcient, one sees that objective distance

explained 92.2% of the variance in DiVerent responding.

Both levels of explanatory power are remarkable given the

a priori, stimulus-based, and objective nature of the loga-

rithmic measure. The agreement between the monkeys in

their ratings was remarkable, too, with a productmoment

correlation of 0.99 across the 15 data rows.

General discussion

In this article, we compared the complex shape perception

of humans and monkeys. Members of both species judged

the dissimilarity or diVerence of shape pairs that could be

variations of the same underlying prototype. There were

strong continuities in the perception of an inXuential

domain of complex shapes. The SD judgments of the twomonkeys in Experiment 2, for example, had product

moment correlations of 0.98 and 0.97 with the dissimilarity

ratings of humans in Experiment 1A (see Figs. 2, 3).

One important convergence was that the same metric of

psychological distance applied. In every case, we found

that the logarithmic distance that corresponding polygon

vertices were moved between shapes allowed us to predict

more than 90% of the variance in dissimilarity ratings or

diVerence judgments. The simplicity of this measure is

remarkable given that it has no weighting principle to

emphasize some among the nine dots so that it incorporates

no selective-attention process in the organism that deter-

mines perception. The generality of this measure could

make it applicable in other areas of research touching on

the perception and categorization of complex shapes. The

objective character of this measure has the advantage of

ensuring that it is unbiased toward any theory of perception

or categorization.

However, we must carefully delimit the convergence

and similarity between the shape perception of humans and

monkeys. The similarity and convergence are behavioral

reXected in the behavioral-response curves of the two

species. We cannot conclude from this that humans and

monkeys converge or are alike in all aspects of their mental

experience of these shapes, or in their consciousness about

the underlying similarity relationships, and so forth. Indeed,

these response curves cannot reXect fully and directly the

latent/underlying mental experiences of our subjects,

though in our view they probably do reXect important

aspects of humans and animals perceptual-representation

systems. This limitation is important to keep in mind when

human and animal psychological metrics and psychophysi-

cal data patterns are being compared (see also Dittrich

1994).

The shape domain tested here also allowed us to evaluate

in a controlled setting the psychological organization of

family-resemblance stimulus spaces. The shapes tested

were mainly controlled statistical distortions of underlying

prototypes. Consequently, these shapes can be viewed as

lying within the cloud of exemplars surrounding and

derived from a transformational center or prototype, with a

typicality gradient from typical items near the clouds cen-

ter (Level 1 and 3 distortions) to atypical items near its

periphery (Level 5 and 7 distortions). Within these spaces,

additional common principles emerged between humans

Fig. 3 The proportion of DiVerent responses given by monkeys Mur-ph (a) and Lou (b) in Experiment 2 when shapes at diVerent distortionlevels (labeled lines 9, 7, 5, 3, and 1) were compared to shapes at equalor lower levels of distortion (Levels 7, 5, 3, 1, and 0) as plotted alongtheXaxis

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7


Proportion

DifferentResponses

Proportion

Different

Responses

Monkey

7

9

3

5

1

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7


Monkey

7

9

3

5

1

B

A


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Anim Cogn (2009) 12:809821 819

123

and monkeys shape perception. For both species, similar-

ity gradients were steep going out from the transforma-

tional center into the periphery of psychological space. For

both species, similarity gradients were Xat going in from

the periphery to the transformational center of psychologi-

cal space. From either perspective, the general consequence

of this was that the member of the to-be-judged pair that

was peripheral in psychological spaceand especially thedistance of that member from the transformational center

controlled for both species the perceived dissimilarity or

diVerence of the pair.

Op de Beeck et al. (2003) found a converging result. In a

temporally successive SD task involving two-dimensional

stimuli, rhesus monkeys showed stimulus asymmetries of

the following kind. They perceived and responded to stimu-

lus diVerences more accurately when the Wrst stimulus was

the more prototypical of the pairthat is, when it was

nearer to the center of the psychological space encompass-

ing the stimuli. This asymmetry is consistent with the idea

that prototype-centered similarity gradients are steep (so

that subsequent stimuli diVerent from the prototypical item

will clearly be perceived as such). In an additional study,

Op de Beeck et al. found the same asymmetry in humans

SD responding. Fabre-Thorpe et al. (1998) and Sigala et al.

(2002) reported additional similarities between the percep-

tual/categorization strategies of humans and monkeys.

Similarities like those in the present research and others

are important for expressing a basic continuity between

humans and animals complex-shape perception. However

else humans diVer from monkeys, in the language coding

they uniquely apply to objects, in the conceptual overlays

they bring to objects, in the rule-based nature of their cate-

gorization strategies, the perceptual systems of the two spe-

cies are similar at this basic level of shape perception,

similarity judgment, and the psychological organization of

high-dimensional stimulus spaces as they are reXected in

the behavioral responses of humans and monkeys.

These results could be used to ground additional studies

in comparative categorization. For one thing, the psycho-

logical-distance measure could be useful in other domains

as a general yardstick of inter-stimulus distance. For

another thing, the venerable domain of dot-distortion cate-

gorization has gone almost unresearched in nonhuman ani-

mals, though the dot-distortion paradigm has the potential

to answer important comparative questions about the nature

of categorization (Smith 2002; Smith and Minda 2002).

As an example, a perennial question concerns whether

human and animal category learners blend or average their

exemplar experiences to form a prototype, compare new

items to it, and accept the items as category members if

they are similar enough to the prototype. Early descriptions

of categorization were prototype-based in this way (Homa

et al. 1981; Posner and Keele 1968; Reed 1972; Rosch and

Mervis 1975). However, a contrasting theory is that cate-

gory learners store the category exemplars they experience

as independent, individuated memory traces, compare new

items to these, and accept the items as category members if

they are similar enough to the exemplars (e.g., Medin and

SchaVer 1978; Nosofsky 1987).

The present results show why the dot-distortion para-

digm is useful for resolving this issue with nonhuman ani-mals. If animals store the transformational center of the

family-resemblance space (i.e., the prototype) as the refer-

ent standard for categorization, the present results allow

this clear prediction. Animals should show a steep categori-

zation gradient across prototypes, low-level distortions,

high-level distortions, and so forth, just as the monkeys

showed steep dissimilarity gradients in the present article

when they made SD judgments anchored to the prototype

center of the psychological space. But, if animals store the

training exemplars that lie in the periphery of the family-

resemblance space, the present results allow this contrast-

ing prediction. Animals should show a Xat categorization

gradient, just as monkeys showed Xat dissimilarity gradi-

ents here when they made SD judgments anchored in the

periphery of the psychological space.

In fact, this technique has produced strong evidence of

prototype abstraction in humans (Smith 2002; Smith and

Minda 2001, 2002). Very recently, this technique was

extended to show strong evidence of prototype abstrac-

tion in monkeys (Smith et al. 2008b). The study of Smith

et al. (2008b) stands in an interesting relationship to the

present research. Here we showed how animals compare

and contrast pairs of shapes, when there is no category

training and when every pair of shapes is trial unique.

The present study established the basic psychophysics of

shape perception, in the sense of relating an objective,

quantiWable measure of interstimulus distance to the

behavioral responses of humans and animals. The study

also illustrated the basic perceptual gradients that ani-

mals might harness in the service of categorization.

Smith et al. (2008a, b) followed up the present demon-

stration to show that animals, just as humans, do actually

bring those gradients into categorization situations, when

a single item is presented, and they must compare it to a

second, virtual pair membertheir mental representation

of the category.

The present results also suggest some interesting proper-

ties of family-resemblance concept spaces that have been

insuYciently appreciated. For example, the Xatness of the

periphery-based similarity gradients points out that it is in

principle impossible for an item to be similar simulta-

neously to all the members of a family-resemblance cate-

gory. One will always move away from some exemplars in

psychological space as one moves toward others. For this

reason, shape similarity does not change much moving


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820 Anim Cogn (2009) 12:809821

123

from the periphery into the middle of the category, because

one is in a steady state of approaching some exemplars and

moving away from others. In contrast, one will be able to

approach the prototype indeWnitely closely. For this reason,

shape similarity changes dramatically as items move from

the periphery to approach the prototype in psychological

space. These intuitions about family-resemblance psycho-

logical spaces underlie the observed asymmetry in the dis-tance and similarity relationships in these spaces, the

diVerent character of similarity gradients grounded from

the prototype out or from the periphery in, and the powerful

control exerted on similarity by the peripheral member of

the to-be-compared pair. These results embody a set of

psychological, or psychophysical, rules of the road for fam-

ily-resemblance category structures that may be generally

useful in theory and research regarding family-resemblance

and natural-kind categories. It is our hope that these rules of

the road might be constructively applicable and construc-

tively applied to other interesting lines of research on non-

human primates natural-kind categorization (Vonk and

MacDonald 2004; Vonk and Povinelli 2006). Indeed, our

work might even have constructive correspondences to

comparative research on more distant species. For example,

Dittrich et al. (1993) carried out an intriguing psychophysi-

cal study of pigeons perceptions of wasp and mimic

hoverXy photographs. They used image analysis to derive

an objective measure of the psychological distance between

stimuli. They also found close correspondences between

their objective distance measures and pigeons behavioral

responses. In combination, the present study and that of

Dittrich et al. show that the same basic continuities exist

between objective psychological distance and behavioral

responses, across species, and across the use of carefully

controlled experimental materials and rich, ecological

materials (see also Green et al. 1999).

In fact, the results from Dittrich et al. (1993) show why

the present study has an interesting ecological application

and suggest a possible aVordance available to the develop-

ment of categorization systems through evolution. In the

family-resemblance stimulus spaces under consideration

here, typicality gradients anchored in the prototype were

steepthat is, increasing perceived dissimilarities to the

prototype reXected clearly and sharply the objective mea-

sure of psychological distance. In contrast, typicality gradi-

ents anchored in peripheral exemplars were Xatthe

perceived similarity to the referent exemplar hardly

changed as one moved closer in or farther from the proto-

type. Regarding prototype-centered gradients, this means

that an organism would get a beautiful read on category

belongingness if it represented the prototype of the cate-

gory, and used this to classify (and approach or avoid)

novel, to-be-classiWed objects. Items strongly inside and

outside the category would register highly contrastively,

and could be strongly discriminated in the behavioral

response they produced. In contrast, regarding exemplar-

centered gradients, the Xat gradient means that the organ-

ism would get a poor read on category belongingness,

because similarity comparisons with this referent would

hardly distinguish close-in, typical members from atypical,

peripheral members. It is possible that there would arise,

therefore, a Wtness advantage toward the organismsabstracting the prototypes of family-resemblance categories

and navigating the world armed with these central tenden-

cies. This does not mean that the organism would or should

suYce only with a prototype-abstraction ability in its over-

all categorization capacity. Other capabilities might be nec-

essary to allow category learning in cases that did not

provide a well-behaved, family-resemblance cloud of

exemplars. Nonetheless, it is an intriguing possibility that

one answer to the prototype-exemplar debate may be found,

not in the elaborate formal mathematical models where it

has universally been sought, but in an optimality and Wtness

assessment of what animals should do to thrive in their

environment of natural kinds, given the structure of those

natural-kind similarity spaces that is suggested by the pres-

ent results.

Acknowledgments This research was supported by National Insti-tutes of Health Grant HD-38051 and by Grant BCS-0634662 from theNational Science Foundation.

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