Salient material properties and haptic volume perception: The influenceof surface texture, thermal conductivity, and compliance

Wouter M. Bergmann Tiest, Mirela Kahrimanovic, Ilona Niemantsverdriet, Kassahun Bogale, andAstrid M. L. Kappers

Physics of Man, Helmholtz Institute, Utrecht University

We investigated the influence of surface texture, thermal conductivity, and compliance on thehaptic perception of the volume of small cubes. It was hypothesized that an object containinghighly salient material properties would be perceived as larger in volume than the same objectwithout these properties. Blindfolded subjects were asked to explore pairs of cubes differingin their material properties and to select the one with the larger volume. The results showedthat, counterintuitively, a smooth cube was perceived as being significantly larger than a roughcube of the same physical volume, with average biases of about 19 %. Furthermore, cubes witha higher thermal conductivity were perceived as significantly larger than cubes with a lowerthermal conductivity (average bias of about 7 %). In addition, the magnitude of the bias inthis condition was not changed by increasing or decreasing the temperature of the test objects,suggesting that the effect of thermal conductivity could not be attributed directly to the heatflow. Finally, a hard cube was perceived as significantly larger than a soft cube of equal physi-cal volume, with an average bias of about 25 %. These results reveal that the studied materialproperties have a significant and consistent influence on the haptic perception of volume. Theobserved biases provide an indication about the level at which processing of haptic informationon volume and material properties occurs.

Introduction

Objects that we encounter in our environment can differalong a number of dimensions, like shape, size and mate-rial. Each dimension contributes in its own way to the per-cept of the object and the perception of one particular di-mension may be influenced by the presence of other physicalobject properties. The present study focuses on the influ-ence of salient material properties on haptic perception ofthe volume of objects. Previous studies have shown that vol-ume perception is not veridical. We have shown that small3-dimensional objects with the same physical size (i.e. vol-ume) but differing in shape are perceived as being different insize (Kahrimanovic, Bergmann Tiest, & Kappers, 2010). Inthat study, blindfolded subjects had to explore tetrahedrons,cubes and spheres by touch. On each trial, they were askedto compare two differently shaped objects and to indicate theone they perceived as larger in volume. The largest effectof shape on volume perception was found for the compar-ison of tetrahedrons and spheres. A tetrahedron was per-ceived as equal in volume to a sphere that was on averageabout 48 % larger in volume than the tetrahedron. Similarly,tetrahedrons were perceived as being larger than cubes of thesame physical volume, and cubes were perceived as beinglarger in volume than spheres. Additional analyses of theseresults showed that the occurrence of these volume biasescould be explained by the subjects’ tendency to base theirvolume judgement on the surface area of the objects. Hence,

during the volume discrimination task subjects perceived twoobjects with the same physical surface area as being the samein volume.

In order to explain these findings, we have proposed thatthe effect of surface area on the volume judgement may berelated to the saliency of that property during exploration ofthe objects. When an object is enclosed, the cutaneous re-ceptors in the skin are stimulated mainly by the surface ofthe object, resulting in more attention being directed towardsthat property. As a consequence, the judgement of the sub-jects is based on that salient property. Previous studies onvolume perception of objects differing along the height-to-width ratio (e.g. different cylinders) have also suggested thatthe volume judgement was influenced by the most salient di-mension, which has been shown to be the length of objectsduring visual judgements and the width of objects duringhaptic judgements (e.g. Frayman & Dawson, 1981; Holm-berg, 1975; Krishna, 2006; Stanek, 1968, 1969).

Inspired by these findings, we wondered whether the vol-ume percept would also be influenced by other object dimen-sions that may be salient to the haptic sense as well. Thesaliency of object properties has been investigated by wayof search tasks, in which a subject had to search for a targetobject between a number of distractor objects. These stud-ies have shown that the presence of specific object proper-ties can make objects stand out among other objects that donot possess that property, i.e. that specific property is indi-

2 WOUTER M. BERGMANN TIEST, MIRELA KAHRIMANOVIC, ILONA NIEMANTSVERDRIET, KASSAHUN BOGALE, AND ASTRID M. L. KAPPERS

cated as very salient. Examples of properties that are salientfor the haptic sense and that could be used to discriminateeasily between objects are a rough surface (Lederman &Klatzky, 1997; Plaisier, Bergmann Tiest, & Kappers, 2008),the presence of edges (Lederman & Klatzky, 1997; Plaisier,Bergmann Tiest, & Kappers, 2009), a compliant material(Lederman & Klatzky, 1997; Van Polanen, Bergmann Tiest,& Kappers, under review), a large difference in thermal prop-erties (Ho & Jones, 2006), and differences in actual objecttemperature (Plaisier & Kappers, 2010). The present studyfocuses on the influence of three salient material propertieson haptic perception of the volume of objects, by means ofthree experiments. In the first experiment, the influence ofthe surface texture of objects was investigated. The sec-ond experiment investigated the influence of objects’ thermalproperties on haptic volume perception. Lastly, the third ex-periment was concerned with the objects’ compliance. Thethree experiments employed similar methods, which are dis-cussed first.

General methods

Our basic objective was to measure perceptual volume bi-ases between objects that either do or do not have a particularsalient feature. This was done by repeatedly presenting sub-jects with two objects with different material properties: areference object of constant size and a test object of varyingsize, and asking which is the larger in volume. By fitting apsychometric curve to the data, the point of subjective equal-ity (PSE) can be determined, i.e. the sizes of the two stimulithat are perceived to be equal in volume. From the PSE, thedirection and magnitude of the perceptual bias can be calcu-lated.

Procedure

Subjects were blindfolded and seated themselves at a flattable. Two 12-cm-high stands were fixed on the table, 40 cmin front of the subject, with a centre-to-centre distance be-tween the stands of 10 cm. The experimenter placed the ref-erence stimulus on one stand and a test stimulus on the other.The position of the reference and test stimuli was randomisedand counterbalanced. The subject was asked to explore firstthe stimulus on his/her left-hand side, and then the stimu-lus on the right-hand side. Subsequently, a two-alternativeforced-choice task was conducted; the subject had to indicatewhich of the two stimuli was larger in volume. The subjectwas only allowed to use the dominant hand and was asked toexplore the stimuli by enclosure, which has been shown to bethe stereotypical exploratory strategy for volume perception(Lederman & Klatzky, 1987). Moving the stimulus was notallowed; otherwise mass information would become avail-able. The subjects were allowed to explore the stimuli onlyonce, but the exploration time for each individual explorationwas not restricted.

Data collection and analyses

The stimuli were presented by means of the method ofconstant stimuli. For each experiment, there was a singlereference stimulus and nine test stimuli of increasing vol-ume. Each combination of reference and test stimuli waspresented ten times in a random order, resulting in 90 trialsper subject. From these data, the fraction was calculated withwhich each test stimulus was selected as being larger in vol-ume than the reference stimulus. Subsequently, a cumulativeGaussian distribution ( f ) as a function of the volume (x) wasfitted to the data using the equation

f (x) = 12 + 1

2 erf(

x − µ√

2σ

),

where the parameter σ is a measure of the 84 % discrimina-tion threshold, which is the sensitivity of the subject to per-ceive volume differences between two objects, and the pa-rameter µ is a measure of the PSE, which indicates the vol-ume of the test stimulus that is perceived as being equivalentto the reference stimulus. The bias is defined as the volumeof the reference stimulus minus the volume of a test stim-ulus µ that has the same perceived volume. This value wasthen expressed as a percentage of the volume of the referencestimulus, resulting in relative biases, which were used for thestatistical analysis.

Experiment 1: surface texture

The pupose of the first experiment was to see whether asalient material property has an influence on volume percep-tion, similar to the effect that a salient geometric property hasbeen shown to have (Kahrimanovic et al., 2010). It has beenshown that roughness is a very salient feature for the hapticsense that can be detected very fast and efficiently (Plaisieret al., 2008). Here, the question is whether the presence ofa rough surface also has an influence on haptic perceptionof volume. Blindfolded subjects were asked to compare twocubes of which one had a smooth surface and the other arough surface, and they had to indicate which of the two wasthe larger in volume. If the previously proposed positive rela-tionship between the salience of an object property and vol-ume perception holds and if we assume that a rough cube ismore salient than a smooth cube, then it can be hypothesizedthat the volume of a rougher cube should be overestimated.

Methods

Subjects. A group of seven subjects (two male, five fe-male) participated in the experiment. Their mean age was 29years. All subjects were right-handed. All subjects excepttwo were entirely naïve as to the purposes of the experiment.These two subjects had only some basic information aboutthe experiment, but were naïve as to the exact methods that

HAPTIC VOLUME PERCEPTION 3

Figure 1. The stimulus set with the upper row showing thestimuli for the surface texture experiment, and the lower rowshowing the stimuli for the thermal conductivity experiment.The stimulus at the left of each row is the reference stimulus.

were used. Nevertheless, their data did not differ systemati-cally from the data of the naïve subjects.

Stimuli. The stimuli were cubes manufactured on acomputer-controlled milling machine out of a synthetic,resin-filled polyurethane board material (Ebaboard S-1,Ebalta Kunststoff GmbH). In each cube, a small cylindricalhole (diameter of 1 mm) was made in the center of one plane,creating the possibility to place the cubes on stands for ex-ploration. The volume of the test cubes ranged from 3 to11 cm3 in steps of 1 cm3. In addition to these rather smoothtest stimuli, a cube with a rough surface was used as the ref-erence stimulus. This stimulus was made out of the samematerial as the test stimuli but was subsequently covered byrelatively coarse sandpaper (grit number P40). Pilot experi-ments showed that this cube indeed felt rougher than the testcubes. The volume of the reference stimulus was 6.9 cm3.This volume was calculated by multiplying the height, width,and depth of the cube, rather than raising one length to thethird power. The lengths used for this calculation were thedistances between the tops of two grits on two opposite sides.The lengths could also be expressed as the distance betweenthe bases of two grits on two opposite sides. This would re-sult in an about 1.5 % smaller volume than the one calculatedwith the first method. The complete stimulus set is shown infigure 1 (top row).

Procedure. The experiment was executed together withthe three main conditions of Experiment 2 (see below). Theconditions for individual subjects were presented in differ-ent sessions and in a randomized order. The sessions wereperformed on different days or on the same day with at leasta 1-hour break between them. One condition took about 20minutes.

Results

Figure 2 shows the data of a representative subject and thebest-fit function fitted to the data points. The biases werepositive for all subjects, as shown in figure 3. A positive biasindicates that the test objects were overestimated in volume.The average bias was 19 % (SE 1 %), meaning that the roughreference cube of 6.9 cm3 was on average perceived as be-ing equal in volume to a smooth test cube of about 5.6 cm3.

Σ = 0.85 cm3

Μ = 5.7 cm3

3 4 5 6 7 8 9 10 110.0

0.2

0.4

0.6

0.8

1.0

test volume Hcm3L

frac

tion

ùtest

larg

er÷

Figure 2. A representative example of the data from a singlesubject in the surface texture experiment together with thefitted psychometric curve. The solid line indicates the vol-ume of the reference stimulus. The dashed lines indicate thepoint of subjective equality. The values of the threshold (σ)and the PSE (µ) are also shown in the figure.

1 2 3 4 5 6 7 mean0

5

10

15

20

25

subject

bias

H%L

Figure 3. Relative volume biases (in percent) in the surfacetexture experiment for seven subjects, and their average. Theerror bar indicates the standard error of the mean.

The average bias was significantly different from zero (one-sample t-test, t6 = 13, p = 1.1 × 10−5). In addition to thePSE, the 84 % discrimination thresholds could also be ex-tracted from the fits. The average threshold was 0.7 cm3 (SE0.1 cm3).

Discussion

Concerning the influence of surface texture on volumeperception, the present experiment showed that a cube witha smooth surface was perceived as significantly larger thana cube with a rough surface, with an average bias of about19 %. The results seem very consistent between subjects,with only small inter-subject variability, as visible in figure

4 WOUTER M. BERGMANN TIEST, MIRELA KAHRIMANOVIC, ILONA NIEMANTSVERDRIET, KASSAHUN BOGALE, AND ASTRID M. L. KAPPERS

3.Although the measured bias was large and highly signifi-

cant, its direction was not in accordance with our hypothesis.We predicted that the rough surface would be more salientthan the smooth surface, which should result in an overes-timation of the volume of the rough cube. The finding thatthe volume of smooth cubes was overestimated may be in-terpreted in two different ways. First, it may contradict thepositive relationship between the saliency of material prop-erties and the volume percept. Second, it may imply that aspecific property of the smooth cubes was even more salientthan the texture of the rough cube. Due to the thickness of thesandpaper glued to the rough cube, its edges were less pro-nounced than those of the smooth cube. Plaisier et al. (2009)already concluded that edges are salient object features. Fur-thermore, it has been shown that objects with edges (cubes,tetrahedrons) are overestimated in volume compared to edge-less objects (spheres) (Kahrimanovic et al., 2010). Perhaps,the overestimation of the smooth cubes may be related to thesaliency of the edges. It might be that covering the referencecube with the abrasive paper resulted in a decrease of thesaliency of the edges for this cube compared to the cube thatwas not covered with the paper. Consequently, this may haveresulted in the observed overestimation of the volume of thesmooth cube.

Experiment 2: thermal conductivity

The second experiment investigated the influence of ob-jects’ thermal properties on haptic volume perception. Dur-ing each trial, subjects had to compare a cube made out ofbrass to a cube made out of a synthetic material, and to selectthe one with the larger volume. These objects differ highlyin their thermal conductivity, which is the ability of a ma-terial to conduct heat. During the contact between the skinand an object, the object extracts heat from the skin result-ing in a decrease of the skin temperature: The higher thethermal conductivity the faster the heat flow. Brass has ahigher thermal conductivity than the synthetic material, andthe skin temperature will therefore decrease at a higher ratewhen exploring brass objects. As a result, the brass objectswill be perceived as colder. Although thermal conductivityhas been shown to be a less salient feature than properties likeroughness and the presence of edges (Lederman & Klatzky,1997), it has been shown that subjects can use thermal cuesappropriately to discriminate between objects when the dif-ferences in the thermal properties are large (Bergmann Tiest& Kappers, 2008; Ho & Jones, 2006). For the present study,an influence of the thermal properties on volume perceptionwas expected because the difference in thermal conductivitybetween the used materials was rather large. We hypothe-sized that the relatively faster heat flow when exploring thebrass cubes will make the brass cubes more salient than thesynthetic cubes, resulting in an overestimation of the volume

of the brass cubes.Assuming this, it would be interesting to test whether the

proposed effect could be attributed directly to the heat flowduring enclosure. In order to test this, we conducted twoadditional conditions in which the temperature of the brassobjects was manipulated. In the first condition, the temper-ature of the brass objects was increased from room temper-ature to a value around skin temperature. This manipulationwas assumed to result in a decrease of the heat flow betweenthe warm brass objects and the hand, and therefore in a de-crease of the difference between the heat flow when enclos-ing the warm brass objects and the heat flow when enclos-ing the room-temperature synthetic objects. If the effect ofthermal conductivity on perceived volume were determinedby the heat flow, then we may hypothesize that the percep-tual bias for comparing the warm brass objects with the syn-thetic objects will be smaller than the bias when comparingthese objects without a manipulation of the temperature. Inthe second condition, the temperature of the brass objectswas decreased below room temperature. The cold brass ob-jects will extract heat faster from the hand than the brass ob-jects at room temperature. This was assumed to result in anincreased difference between the heat flow when enclosingthe cold brass objects and the heat flow when enclosing theroom-temperature synthetic objects. Consequently, a largerperceptual bias is expected in this condition than in the con-dition with the brass objects at room temperature.

In these conditions, two aspects are manipulated at thesame time: the two objects that are compared in each trialare different in thermal conductivity, but also in temperature.If a bias in volume perception were found, it is not read-ily attributable to either one of the manipulations. In orderto remedy this confound, two additional control conditionswere performed, in which the objects’ material was the sameand only the temperature of one of the objects was manipu-lated. If any volume bias were based on differences in ther-mal conductivity, we would not expect to find such a biasin these control conditions. These conditions can be seen asthe counterpart of the main condition of this experiment, inwhich the objects’ temperature was the same and only thematerial, and therefore the thermal conductivity, of one ofthe objects was manipulated.

Methods

This experiment consisted of three main conditions andtwo control conditions. In the main conditions, the subjectswere the same as in Experiment 1, with one additional sub-ject, bringing the total number to eight. The test cubes weremade out of brass, which has a thermal conductivity of about111 W/K/m. The volume of the test stimuli ranged from 4to 12 cm3 in steps of 1 cm3. The reference stimulus was acube of 8 cm3 made out of Ebaboard S-1, the same mate-rial as used for the test cubes in Experiment 1. The ther-

HAPTIC VOLUME PERCEPTION 5

mal conductivity of this material was not specified by themanufacturer, but the thermal conductivity of polyurethaneis about 0.20 W/K/m, substantially smaller than that of brass.The edges of the cubes were of comparable sharpness, withthe brass cubes having a corner radius of 0.6 mm and theEbaboard cube having a corner radius of 0.5 mm. The stimuliare shown in figure 1, bottom row.

The procedure was identical to that of Experiment 1. Inthe first condition, the stimuli were presented at room tem-perature (about 22°C). In the two other conditions the samestimuli were used but the temperature of the brass objectswas now manipulated while the temperature of the syntheticreference stimulus remained at room temperature. The teststimuli could either be cooled to a temperature of about 5°Cor they could be heated to a temperature of about 35°C. Thetemperature of the stimuli was decreased by placing the ob-jects on an ice pack covered with a piece of cloth to pre-vent the stimuli from becoming wet, and increased with atemperature-controlled box that could be set to the requiredtemperature. The temperature of the objects was held con-stant during the experiment. Subjects were instructed totouch the objects only briefly to avoid changing their tem-perature too much.

The two control conditions were basically the same as thesecond and third main conditions, respectively, except thatthe reference object was also made of brass. Since this stim-ulus was taken from the series of test stimuli, there was no8 cm3 test stimulus in the control conditions. For this reason,not 90 but 80 trials per subject were performed in both con-trol conditions. Eight new right-handed subjects (four male,four female) with a mean age of 26 years participated in thecontrol conditions.

Results

Figure 4 shows the average relative biases measured in thesecond experiment. The average bias in the room tempera-ture condition was 6.2 % (SE 0.9 %), indicating that a brassobjects is perceived as being larger in volume than a syntheticobject of the same size. The biases in the other two main con-ditions were 8 % (SE 2 %) for the condition with the cold teststimuli and 7 % (SE 2 %) for the condition with the warm teststimuli. Hence, the brass objects were perceived as larger involume than the synthetic objects independent of their tem-perature. All biases were significantly different from zero,as tested by one-sample t-tests (t7 ≥ 3.7, p ≤ 0.007). Arepeated-measures ANOVA performed on the relative biasesrevealed no effect of condition (F2,14 = 0.39, p = 0.69).

The discrimination thresholds in the three main condi-tions were 1.0 cm3 (SE 0.1 cm3), 0.7 cm3 (SE 0.1 cm3), and0.61 cm3 (SE 0.09 cm3) for the neutral, the cold and the warmconditions, respectively. A repeated-measures ANOVA per-formed on the thresholds revealed a significant effect of con-dition (F2,14 = 4.6, p = 0.029). Bonferroni-corrected pair-

neutral cold warm cold warm0

2

4

6

8

10

condition

bias

H%L

Figure 4. The relative biases (in percent) for the thermalconductivity experiment. From left to right: the conditionsin which the temperature of the test objects was either keptat room temperature (neutral), decreased (cold), or increased(warm), and the two control conditions (cold and warm). Er-ror bars indicate the standard error of the mean.

wise comparisons showed that only the difference betweenthe neutral and warm conditions was statistically significant(p = 0.014).

In the two control conditions, no biases were found for anysubject, except for one in the control condition with the coldtest stimuli. In all other cases, discrimination performancewas perfect, meaning that the subjects’ judgements alwayscorresponded to the physical relation between the two stim-uli in a trial. For this reason, no discrimination thresholdscan be reported.

Discussion

The present experiment showed a significant influence ofthermal properties of objects on the perception of their vol-ume. In the first condition, subjects compared two cubesmade out of materials with different thermal conductivities(brass versus synthetic material), which were both presentedat room temperature. The results showed that the cubes witha higher thermal conductivity were perceived as larger in vol-ume than equally sized cubes with a lower thermal conduc-tivity (bias of 6.2 %). We propose that this effect might berelated to the increased saliency of the perceived ‘coldness’that is caused by heat being extracted from the skin duringcontact with the object, hypothesizing that with a higher heatflow the object would be perceived as larger.

In order to investigate this hypothesis further, two addi-tional conditions were conducted in which the temperatureof the brass objects was manipulated in order to increase ordecrease the difference between the heat flow when exploringbrass objects and the heat flow when exploring the syntheticobject. In these conditions, subjects were asked to compare

6 WOUTER M. BERGMANN TIEST, MIRELA KAHRIMANOVIC, ILONA NIEMANTSVERDRIET, KASSAHUN BOGALE, AND ASTRID M. L. KAPPERS

the volume of cold and warm brass cubes to that of a syn-thetic cube that was at room temperature. If the measuredeffect of thermal conductivity on volume perception couldbe related to the heat flow, then increasing the temperature ofthe brass objects would result in a smaller bias than the onemeasured during the condition with the brass objects at roomtemperature, and a decrease of the temperature of the brassobjects would result in an increase of the perceptual bias.

The results showed that the brass cubes, both cooled andheated, were perceived as being larger in volume than thesynthetic cubes. The magnitudes of the biases in these twoconditions (8 % and 9 %) did not differ significantly fromeach other and also not from the magnitude of the bias mea-sured in the condition with both test and reference stimuli atroom temperature. The failure to observe the predicted pat-terns in these conditions suggests that the perceptual biasescould not be explained directly by the heat flow between theskin and the objects. Independent of the temperature of theobjects, the object with a higher thermal conductivity wasperceived as larger in volume than the object with a lowerthermal conductivity. The idea that temperature did not playa role was confirmed by the two control conditions, in whichonly the objects’ temperature was manipulated and no biaseswere observed. This suggests that observers are influencedby the perceived ‘coldness’ of objects, which is associatedwith a higher thermal conductivity, but automatically correctfor temperature differences when perceiving this ‘coldness’.The observation that the effect of temperature could not mod-ify the influence of the thermal conductivity is interesting,because a comparison of the results from Plaisier and Kap-pers (2010) and Lederman and Klatzky (1997) showed thatdifferences in temperature were more salient than differencesin thermal conductivity. Apparently, when both features dif-fer, as in the present experiment, the influence of thermalconductivity cues is stronger than the influence of tempera-ture cues.

Experiment 3: compliance

The third experiment was concerned with the objects’compliance. Hardness, the inverse of compliance, has beenfound to be a salient feature (Lederman & Klatzky, 1997;Van Polanen et al., under review). A hard object stands outamong softer ones. The question is, whether this saliencyleads to the harder object being perceived as larger than thesofter one. In a magnitude estimation experiment, no ef-fect of softness has been found on perception of object size(Berryman, Yau, & Hsiao, 2006). However, this experimentwas performed with simulated objects, consisting of rubberplates mounted on linear motors, that were grasped betweenthe thumb and index finger. It is unknown whether real com-pliant objects, that can deform in other ways than just beingsqueezed in one direction, produce the same result. It mightbe that enclosing the objects, as opposed to squeezing be-

tween thumb and index finger, leads to a different percept ofthe objects’ size. It could also be that it is not so much thehardness itself, but the corners and edges that feel more pro-nounced in the harder object, are the relevant salient features.To investigate this, volume biases were measured in two con-ditions. In the first condition, the objects were enclosedin the same manner as in the first two experiments. In thesecond condition, the objects were squeezed between thumband index finger, similar to the method used by Berrymanet al. (2006). In this latter case, the corners and edges wereavoided. If a bias were found in this condition, it cannot bedue to the influence of the edges, but should be due to thedifference in compliance between the objects.

Methods

This experiment was very similar to the previous experi-ments, except that a 8.7 cm3 soft polyether foam cube wasused as a reference stimulus. The stiffness (spring constant)of the cube was measured using an Instron 5542 Univer-sal Material Testing machine. This machine compresses thestimulus between two parallel plates and measures force anddisplacement. The relation between these two was found tobe nonlinear in the range between 0–1 N. In the lower part ofthe range, which subjects encounter first upon touching thestimulus, the slope (stiffness) was found to be 0.35 N/mm. Inthe higher part, the slope was 0.069 N/mm. The test stimuliwere made of the same incompressible material as in Ex-periment 1 (Ebaboard S-1) and ranged in volume from 4 to12 cm3 in steps of 1 cm3. The same eight subjects as inthe control conditions of Experiment 2 participated in thisexperiment.

There were two conditions: in the enclosure condition,subjects were asked to enclose the stimuli entirely with theirhand, as in experiments 1 and 2. In the pinch condition,subjects were asked to grasp the stimuli between thumb andindex finger, in the same manner as used by Berryman etal. (2006). The order of the conditions was counterbalancedover subjects. Subjects were instructed to base their judge-ment on their perception of the uncompressed volume.

Results

In both conditions, hard cubes were perceived as largerthan soft cubes of equal physical volume. The average biaseswere 26 % (SE 2 %) and 23 % (SE 3 %) for the enclosure andpinch conditions, repectively. These are shown in figure 5.Both biases were significantly larger than zero (one-samplet-tests, t7 = 38; p = 2.4 × 10−9 and t7 = 22; p = 9.4 × 10−8,respectively). They were not significantly different from eachother (paired-samples t-test, t7 = 0.71, p = 0.50).

The discrimination thresholds for the two conditions were1.5 cm3 (SE 0.2 cm3) and 1.1 cm3 (SE 0.2 cm3). Thesewere also not significantly different from each other (paired-samples t-test, t7 = 1.7, p = 0.14).

HAPTIC VOLUME PERCEPTION 7

enclosure pinch0

5

10

15

20

25

30

condition

bias

H%L

Figure 5. The relative biases (in percent) for the complianceexperiment for the condition with the hand enclosing the ob-jects (left) and the condition with the object grasped betweenthumb and index finger. Error bars indicate the standard errorof the mean.

Discussion

The influence of hardness on volume perception was mea-sured for two situations: In the first, the stimuli were en-closed by the subject’s hand. In the other, the subject graspedthe stimuli between thumb and index finger. In both cases,substantial biases were found, indicating that hard cubes areperceived as larger than soft ones. The reason for this canagain be sought in the saliency of object features. The hard-ness of the hard objects makes them stand out compared tosoft objects (Van Polanen et al., under review). At the sametime, the edges and corners of the hard objects are also morepronounced than those of the soft objects. These featureshave also been shown to be salient (Plaisier et al., 2009).However, in the pinch condition, where subjects only touchthe object’s faces and do not come into contact with the edgesand corners, the bias is of the same magnitude as in the en-closure condition. This indicates that the hardness itself, andnot necessarily the presence of edges and corners, is respon-sible for the observed biases. The edges could still play a mi-nor role in this experiment, perhaps being responsible for the(statistically insignificant) difference between the two con-ditions. Since the contribution in volume bias due to edgesand corners, as found in experiment 1, is of a smaller magni-tude than that of hardness, the latter dominates in the presentexperiment and the former is not enough for the differencebetween the two conditions to reach statistical significance.

An important question presents itself: could it be that thesofter objects are perceived as smaller because they are ac-tually smaller when compressed? Although subjects wereinstructed to base their judgement on the uncompressed vol-ume as encountered when first touching the object, theymight have been influenced by its smaller size when some

pressure was applied. In the pinch condition, the task ofcomparing 3-dimensional volume reduces to judging dif-ferences in the 1-dimensional distance between the fingerswhen grasping the stimulus. The bias of 23 % in volumethat was found corresponds to a difference of 1.9 mm in dis-tance between the fingers. Compressing the soft stimulusthis amount requires a force of ∼ 0.6 N. A force of only∼ 0.1 N is sufficient to establish contact. Therefore, thisamount of compression seems overly large for judging theuncompressed size. Thus, it seems more likely that the biasis not the result of the stimulus being compressed that much,but rather of a perceptual process under the influence of hard-ness as a salient material property. This idea is confirmed bythe result of the enclosure condition, in which the stimulusis contacted in a very different way but a bias of the samemagnitude is found.

The results seem to contradict the findings by Berrymanet al. (2006), who found no effect of hardness on size per-ception. However, the softest material they used was a foamrubber with a Shore durometer rating of 50 on the OO scale.Although this is not readily converted to a stiffness value,an estimate can be made based on the specifications of theShore hardness measurement. A rating of 50 on the OOscale means that a spherical indentor with a diameter of 3/32"(2.4 mm) is pushed 0.050" (1.3 mm) into the material whena force of 4 oz (1.1 N) is applied. The ratio between thisforce and indentation is 0.88 N/mm. Considering the factthat the stiffness of our stimulus (0.35 N/mm) was measuredby compressing the entire side of the cube (441 mm2), it isclear that our stimulus material is much softer than the softestmaterial used by Berryman et al.. It could be that their failureto observe an effect of softness on size perception is due tothe relative hardness of their materials. When the contrastbetween hard and soft material is greater, as in the presentexperiment, the hardness becomes more salient and has aneffect on volume perception.

General discussion and conclusions

The present study investigated the influence of salient ma-terial properties on the haptic perception of the volume ofcubes that could fit in one hand and had to be explored uni-manually. Significant perceptual biases were observed, re-vealing a robust influence of the studied material propertieson volume judgement. Roughness leads to an underestima-tion of the object’s volume, whereas ‘coldness’ (higher ther-mal conductivity) and hardness lead to an overestimation ofthe object’s volume. Moreover, the effect of thermal conduc-tivity could not be changed by a manipulation of the temper-ature of the test objects. So, in general, salient material prop-erties appear to influence volume perception, as have salientgeometric properties been shown to do earlier. However, thespecific property of surface texture seems to have an effectthat is in the opposite direction to what was expected. This

8 WOUTER M. BERGMANN TIEST, MIRELA KAHRIMANOVIC, ILONA NIEMANTSVERDRIET, KASSAHUN BOGALE, AND ASTRID M. L. KAPPERS

is thought to be due to the saliency of the geometric propertyof edges dominating over the material property of roughness.Also, perceived coldness (thermal conductivity) was shownto have a small but significant effect, even though the saliencyof this property was found to be limited in a speeded searchtask (Lederman & Klatzky, 1997). It might be that because acertain amount of heat transfer needs to be established beforecoldness can be experienced, it takes some time before thisproperty becomes salient. This might be the reason why thisproperty is not identified as salient in speeded search tasks.

In earlier work, we have shown that haptic volume esti-mation is most likely based on perception of other geometricproperties such as surface area (Kahrimanovic et al., 2010).The question is now whether the salient material propertiesinfluence the volume percept directly, or whether their influ-ence works through the perception of these geometric prop-erties. In the latter case, we would expect material propertiesthat are related to the surface, such as roughness, to have alarger effect than properties that are related to the bulk ofthe material, such as compliance. This was not observed,implying that the salient material properties might influencethe volume percept directly. To investigate this, one couldmeasure the influence of the salient material properties onthe perception of geometric object properties such as edgelength or surface area. However, these measurements are be-yond the scope of the present paper.

For a better understanding of the mechanisms involved inthe effect of material properties on volume perception, it maybe interesting to compare the magnitude of the biases ob-served in the three experiments. This comparison may pro-vide some suggestions about the level at which the effectsmay be manifested. The present study showed that the biasin the thermal conductivity experiment was smaller than thebiases in the roughness experiment and the compliance ex-periment. It may be that information of mechanical naturehas a stronger effect on the volume percept than informationof a thermal nature, due to the level of processing at whichthe effect manifests itself. Previously, we have shown that theshape of 3-dimensional objects has a weaker effect on hap-tic bimanual volume perception of large objects than on uni-manual volume perception of small objects (Kahrimanovic,Bergmann Tiest, & Kappers, 2011). Volume processing ofthe small stimuli may occur already in the primary sensorycortex, which contains cortical areas that receive informationfrom receptors in the skin as well as areas that receive in-formation from receptors in muscles and joints. In contrast,bimanual volume perception requires integration of informa-tion from the two hands, and this integration is shown to takeplace in the posterior parietal cortex (Kandel, Schwartz, &Jessell, 2000). Bimanual perception of the large objects isassumed to be less prone to systematic distortions becauseof the deeper processing of information. This reasoning mayalso be applied to the present study. In the roughness and

compliance experiments, the relevant information about theobjects is transmitted mainly by mechanoreceptors and couldbe processed already at an early stage. In the thermal conduc-tivity experiment, the relevant information is coming fromboth mechanoreceptors and thermal receptors. These differ-ent cues are processed separately at the peripheral level butconverge at the thalamus and the orbitofrontal cortex (Kandelet al., 2000). Consequently, the effect of thermal cues onthe volume percept may manifest itself at a higher level ofprocessing than the effect of mechanical cues. This deeperprocessing of information may result in a weaker effect ofthe salient feature.

The present study revealed large and consistent overesti-mations of the smooth cubes compared to the rough cubes,of the brass cubes (either at room temperature or with a de-creased or increased temperature) compared to the syntheticcubes, and of the hard synthetic cubes compared to the softpolyether foam cube: all subjects showed substantial positivebiases. Apparently, material properties have a consistent in-fluence on haptic perception of the volume of 3-dimensionalobjects. The present study speculated about the mechanismsunderlying these effects, but further research is required fora more detailed understanding of the origin of the observedeffects.

Acknowledgments

This work has been partially supported by the Nether-lands Organisation for Scientific Research (NWO) and theEuropean Commission with the Collaborative Project no.248587, “THE Hand Embodied”, within the FP7-ICT-2009-4-2-1 program “Cognitive Systems and Robotics”.

References

Bergmann Tiest, W. M., & Kappers, A. M. L. (2008). Thermosen-sory reversal effect quantified. Acta Psychologica, 127, 46–50.

Berryman, L. J., Yau, J. M., & Hsiao, S. S. (2006). Representationof object size in the somatosensory system. Journal of Neuro-physiology, 96, 27–39.

Frayman, B. J., & Dawson, W. E.(1981). The effect of object shapeand mode of presentation on judgments of apparent volume. Per-ception & Psychophysics, 29(1), 56–62.

Ho, H., & Jones, L. A. (2006). Contribution of thermal cuesto material discrimination and localization. Perception & Psy-chophysics, 68(1), 118–128.

Holmberg, L. (1975). The influence of elongation on the percep-tion of volume of geometrically simple objects. PsychologicalResearch Bulletin, 15, 1–18.

Kahrimanovic, M., Bergmann Tiest, W. M., & Kappers, A. M. L.(2010). Haptic perception of volume and surface area of 3-Dobjects. Attention, Perception& Psychophysics, 72(2), 517–527.

Kahrimanovic, M., Bergmann Tiest, W. M., & Kappers, A. M. L.(2011). Characterization of the haptic shape-weight illusion with3-dimensional objects. IEEE Transactions on Haptics, 4(4),316–320.

HAPTIC VOLUME PERCEPTION 9

Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principlesof neural science (4th ed.). McGraw-Hill.

Krishna, A. (2006). Interaction of senses: The effect of vision ver-sus touch on the elongation bias. The Journal of Consumer Re-search, 32(4), 557-566.

Lederman, S. J., & Klatzky, R. L. (1987). Hand movements: Awindow into haptic object recognition. Cognitive Psychology,19(3), 342–368.

Lederman, S. J., & Klatzky, R. L. (1997). Relative availabilityof surface and object properties during early haptic processing.Journal of Experimental Psychology: Human Perception andPerformance, 23(6), 1680–1707.

Plaisier, M. A., Bergmann Tiest, W. M., & Kappers, A. M. L.(2008).Haptic pop-out in a hand sweep. Acta Psychologica, 128, 368–377.

Plaisier, M. A., Bergmann Tiest, W. M., & Kappers, A. M. L.(2009).Salient features in three-dimensional haptic shape perception.Attention, Perception & Psychophysics, 71(2), 421–430.

Plaisier, M. A., & Kappers, A. M. L. (2010). Cold objects popout! In A. M. L. Kappers, J. B. F. van Erp, W. M. BergmannTiest, & F. C. T. van der Helm (Eds.), Haptics: Generating andperceiving tangible sensations (Vol. 6192 of Lecture Notes onComputer Science, pp. 219–224). Berlin/Heidelberg: Springer.

Stanek, R. J. (1968). Surface and volume judgments of 3-dimensional shapes. Psychonomic Science, 11(4), 121–122.

Stanek, R. J. (1969). A parametric study of volume and surfacejudgements. Perception & Psychophysics, 6(1), 16–18.

Van Polanen, V., Bergmann Tiest, W. M., & Kappers, A. M. L. (un-der review). Haptic search for hard and soft spheres.