Objects that we encounter in our environment can differ along a number of dimensions, like shape, size, and material. Each dimension contributes in its own way to the percept of the object, and the perception of one particular dimension may be influenced by the presence of other physical object properties. The present study focuses on the influence of salient material properties on haptic perception of the volumes of objects. Previous studies have shown that volume perception is not veridical. We have shown that small three-dimensional objects with the same physical size (i.e., volume) but differing in shape are perceived as being different in size (Kahrimanovic, Bergmann Tiest, & Kappers, 2010). In that study, blindfolded subjects had to explore tetrahedrons, cubes, and spheres by touch. On each trial, they were asked to compare two differently shaped objects and to indicate the one that they perceived as being larger in volume. The largest effect of shape on volume perception was found for the comparison of tetrahedrons and spheres. A tetrahedron was perceived as being equal in volume to a sphere that was on average about 48 % larger in volume than the tetrahedron. Similarly, tetrahedrons were perceived as being larger than cubes of the same physical volume, and cubes were perceived as being larger in volume than spheres. Additional analyses of these results showed that the occurrence of these volume biases could be explained by the subjects’ tendency to base their volume judgment on the surface areas of the objects. Hence, during the volume discrimination task, subjects perceived two objects with the same physical surface area as being the same in volume.

In order to explain these findings, we have proposed that the effect of surface area on the volume judgment may be related to the saliency of that property during exploration of the objects. When an object is enclosed, the cutaneous receptors in the skin are stimulated mainly by the surface of the object, resulting in more attention being directed toward that property. As a consequence, the judgments of the subjects are based on that salient property. Previous studies on volume perception of objects differing along the height-to-width ratio (e.g., different cylinders) have also suggested that volume judgments were influenced by the most salient dimension, which has been shown to be the lengths of objects during visual judgments, and the widths of objects during haptic judgments (e.g., Frayman & Dawson, 1981; Holmberg, 1975; Krishna, 2006; Stanek, 1968, 1969).

Inspired by these findings, we wondered whether the volume percept would also be influenced by other object dimensions that may be salient to the haptic sense, as well. The saliency of object properties has been investigated by way of search tasks, in which a subject had to search for a target object between a number of distractor objects. These studies have shown that the presence of specific object properties can make objects stand out among other objects that do not possess such a property—that is, that a specific property is indicated as being very salient. Examples of properties that are salient for the haptic sense and that could be used to discriminate easily 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, 2012), a large difference in thermal properties (Ho & Jones, 2006), and differences in actual object temperature (Plaisier & Kappers, 2010). The present study focused on the influence of three salient material properties on haptic perception of the volumes of objects, by means of three experiments. In the first experiment, the influence of the surface texture of objects was investigated. In the second experiment, we investigated the influence of objects’ thermal properties on haptic volume perception. Finally, the third experiment was concerned with the objects’ compliance. The three experiments employed similar methods, which we discuss first.

General methods

Our basic objective was to measure perceptual volume biases between objects that either did or did not have a particular salient feature. This was done by repeatedly presenting subjects with two objects with different material properties—a reference object of constant size and a test object of varying size—and asking which was the larger in volume. By fitting a psychometric curve to the data, the point of subjective equality (PSE) could be determined—that is, the sizes of the two stimuli that were perceived to be equal in volume. From the PSE, the direction and magnitude of the perceptual bias could be calculated.

Procedure

The subjects were blindfolded and seated themselves at a flat table. Two 12-cm-high stands were fixed on the table, 40 cm in front of the subject, with a center-to-center distance between the stands of 10 cm. The experimenter placed the reference stimulus on one stand and a test stimulus on the other. The positions of the reference and test stimuli were randomized and counterbalanced. Each subject was asked to explore first the stimulus on his or her left-hand side, and then the stimulus on the right-hand side. Subsequently, a two-alternative forced choice task was conducted: The subject had to indicate which of the two stimuli was larger in volume. Each subject was only allowed to use the dominant hand and was asked to explore the stimuli by enclosure, which has been shown to be the stereotypical exploratory strategy for volume perception (Lederman & Klatzky, 1987). Moving the stimulus was not allowed; otherwise, mass information would become available. The subjects were allowed to explore the stimuli only once, but the exploration time for each individual exploration was not restricted.

Data collection and analyses

The stimuli were presented by means of the method of constant stimuli. For each experiment, there was a single reference stimulus and nine test stimuli of increasing volumes. Each combination of reference and test stimuli was presented ten times in a random order, resulting in 90 trials per subject. From these data, the fraction was calculated by which each test stimulus was selected as being larger in volume than the reference stimulus. Subsequently, a cumulative Gaussian distribution (f) as a function of the volume (x) was fitted to the data, using the equation

$$ f(x) = \frac{1}{2} + \frac{1}{2}{\text{erf}}\left( {\frac{{x - \mu }}{{\sqrt {2} \sigma }}} \right) $$

where the parameter σ is a measure of the 84 % discrimination threshold, which is the sensitivity of the subject to perceive volume differences between two objects, and the parameter μ is a measure of the PSE, which indicates the volume of the test stimulus that is perceived as being equivalent to the reference stimulus. The bias is defined as the volume of the reference stimulus minus the volume of a test stimulus μ that has the same perceived volume. This value was then expressed as a percentage of the volume of the reference stimulus, resulting in relative biases that were used for the statistical analysis.

Experiment 1: Surface texture

The purpose of the first experiment was to investigate whether volume perception is influenced by a salient material property, in the same way as it has been shown to be influenced by a salient geometric property (Kahrimanovic et al., 2010). It has been shown that roughness is a very salient feature for the haptic sense that can be detected very quickly and efficiently (Plaisier et al., 2008). Here, the question is whether the presence of a rough surface also has an influence on haptic perception of volume. Blindfolded subjects were asked to compare two cubes, of which one had a smooth surface and the other a rough surface, and they had to indicate which of the two was the larger in volume. If the previously proposed positive relationship between the salience of an object property and volume perception holds, and if we assume that a rough cube is more salient than a smooth cube, then it can be hypothesized that the volume of a rougher cube should be overestimated.

Method

Subjects

A group of seven subjects (two male, five female) participated in the experiment. Their mean age was 29 years. All of the subjects were right-handed, and all except two were entirely naïve as to the purposes of the experiment. These two subjects had only some basic information about the experiment, but were naïve as to the exact methods that were used. Nevertheless, their data did not differ systematically from those of the naïve subjects.

Stimuli

The stimuli were cubes manufactured on a computer-controlled milling machine out of a synthetic, resin-filled polyurethane board material (Ebaboard S-1, Ebalta Kunststoff GmbH). In each cube, a small cylindrical hole (diameter of 1 mm) was made in the center of one plane, creating the possibility of placing the cubes on stands for exploration. The volumes of the test cubes ranged from 3 to 11 cm3, in steps of 1 cm3. In addition to these rather smooth test stimuli, a cube with a rough surface was used as the reference stimulus. This stimulus was made out of the same material as the test stimuli but was subsequently covered by relatively coarse sandpaper (grit number P40). Pilot experiments showed that this cube indeed felt rougher than the test cubes. 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 by raising one length to the third power. The lengths used for this calculation were the distances between the tops of two grits on two opposite sides. The lengths could also be expressed as the distance between the bases of two grits on two opposite sides. This would result in an about 1.5 % smaller volume than the one calculated by the first method. The complete stimulus set is shown in Fig. 1 (top row).

Fig. 1
figure 1

The stimulus set in the upper row shows the stimuli for the surface texture experiment, and the lower row shows the stimuli for the thermal conductivity experiment. The stimulus at the left of each row is the reference stimulus

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Procedure

The experiment was executed together with the three main conditions of Experiment 2 (see below). The conditions for individual subjects were presented in different sessions and in a randomized order. The sessions were performed on different days or on the same day with at least a 1-h break between them. One condition took about 20 min.

Results

Figure 2 shows the data of a representative subject and the best-fit function fitted to the data points. The biases were positive for all subjects, as is shown in Fig. 3. A positive bias indicates that the test objects were overestimated in volume. The average bias was 19 % (SE 1 %), meaning that the rough reference cube of 6.9 cm3 was on average perceived as being equal in volume to a smooth test cube of about 5.6 cm3. The average bias was significantly different from zero [one-sample t test: t(6) = 13, p = 1.1 × 10–5]. In addition to the PSE, the 84 % discrimination thresholds could also be extracted from the fits. The average threshold was 0.7 cm3 (SE 0.1 cm3).

Fig. 2
figure 2

A representative example of the data from a single subject in the surface texture experiment, together with the fitted psychometric curve. The solid line indicates the volume of the reference stimulus, and the dashed lines indicate the point of subjective equality (PSE). The values of the threshold (σ) and the PSE (μ) are also shown in the figure

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Fig. 3
figure 3

Relative volume biases (as percentages) in the surface texture experiment for seven subjects, and their average. The error bar indicates the standard error of the mean

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Discussion

Concerning the influence of surface texture on volume perception, the present experiment showed that a cube with a smooth surface was perceived as being significantly larger than a cube with a rough surface, with an average bias of about 19 %. The results seem very consistent between subjects, with only small intersubject variability, as is visible in Fig. 3.

Although the measured bias was large and highly significant, its direction was not in accordance with our hypothesis. We predicted that the rough surface would be more salient than the smooth surface, which should result in an overestimation of the volume of the rough cube. The finding that the volume of smooth cubes was overestimated may be interpreted in two different ways. First, it may contradict the positive relationship between the saliency of material properties and the volume percept. Second, it may imply that a specific property of the smooth cubes was even more salient than the texture of the rough cube. Due to the thickness of the sandpaper glued to the rough cube, its edges were less pronounced than those of the smooth cube. Plaisier et al. (2009) had already concluded that edges are salient object features. Furthermore, it has been shown that objects with edges (cubes, tetrahedrons) are overestimated in volume as compared to edgeless objects (spheres) (Kahrimanovic et al., 2010). Perhaps the overestimation of the smooth cubes may be related to the saliency of the edges. It might be that covering the reference cube with the abrasive paper resulted in a decrease of the saliency of the edges for this cube as compared to the cubes that were not covered with the paper. Consequently, this may have resulted in the observed overestimation of the volumes of smooth cubes.

Experiment 2: Thermal conductivity

The second experiment investigated the influence of objects’ thermal properties on haptic volume perception. During each trial, subjects had to compare a cube made out of brass to a cube made out of a synthetic material, and to select the one with the larger volume. These objects differ highly in their thermal conductivity, which is the ability of a material to conduct heat. During the contact between the skin and an object, the object extracts heat from the skin, resulting in a decrease of the skin temperature: The higher the thermal conductivity, the faster the heat flow. Brass has a higher thermal conductivity than does the synthetic material, and the skin temperature will therefore decrease at a higher rate when exploring brass objects. As a result, the brass objects will be perceived as being colder. Although thermal conductivity has been shown to be a less salient feature than properties like roughness and the presence of edges (Lederman & Klatzky, 1997), it has been shown that subjects can use thermal cues appropriately to discriminate between objects when the differences 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 perception was expected, because the difference in thermal conductivity between the materials we used was rather large. We hypothesized that the relatively faster heat flow when exploring the brass cubes would make the them more salient than the synthetic 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 flow during enclosure. In order to test this, we conducted two additional conditions in which the temperature of the brass objects was manipulated. In the first condition, the temperature of the brass objects was increased from room temperature to a value around skin temperature. This manipulation was assumed to result in a decrease of the heat flow between the warm brass objects and the hand, and therefore in a decrease of the difference between the heat flow when enclosing the warm brass objects and the heat flow when enclosing the room-temperature synthetic object. If the effect of thermal conductivity on perceived volume was determined by the heat flow, we might then hypothesize that the perceptual bias for comparing the warm brass objects with the synthetic object would be smaller than the bias when comparing these objects without a manipulation of the temperature. In the second condition, the temperature of the brass objects was decreased below room temperature. The cold brass objects would extract heat faster from the hand than the brass objects at room temperature. This was assumed to result in an increased difference between the heat flow when enclosing the cold brass objects and the heat flow when enclosing the room-temperature synthetic objects. Consequently, a larger perceptual bias was expected in this condition than in the condition with the brass objects at room temperature.

In these conditions, two aspects were manipulated at the same time: the two objects that were compared in each trial were different in thermal conductivity, but also in temperature. If a bias in volume perception were to be found, it would not be readily attributable to either one of the manipulations. In order to remedy this confound, two additional control conditions were performed, in which the objects’ materials were the same, and only the temperature of one of the objects was manipulated. If any volume bias were based on differences in thermal conductivity, we would not expect to find such a bias in these control conditions. These conditions can be seen as the counterpart of the main condition of this experiment, in which the objects’ temperature was the same and only the material, and therefore the thermal conductivity, of one of the objects was manipulated.

Method

This experiment consisted of three main conditions and two control conditions. In the main conditions, the subjects were the same as in Experiment 1, with one additional subject, bringing the total number to eight. The test cubes were made out of brass, which has a thermal conductivity of about 111 W/K/m. The volume of the test stimuli ranged from 4 to 12 cm3, in steps of 1 cm3. The reference stimulus was a cube of 8 cm3 made out of Ebaboard S-1, the same material used for the test cubes in Experiment 1. The thermal conductivity of this material was not specified by the manufacturer, but the thermal conductivity of polyurethane is about 0.20 W/K/m, substantially less than that of brass. The edges of the cubes were of comparable sharpness, with the brass cubes having a corner radius of 0.6 mm and the Ebaboard cube having a corner radius of 0.5 mm. The stimuli are shown in Fig. 1, bottom row.

The procedure was identical to that of Experiment 1. In the first condition, the stimuli were presented at room temperature (about 22 °C). In the two other conditions, the same stimuli were used, but the temperature of the brass objects was now manipulated while the temperature of the synthetic reference stimulus remained at room temperature. The test stimuli could either be cooled to a temperature of about 5 °C or heated to a temperature of about 35 °C. The temperature of the stimuli was decreased by placing the objects on an ice pack covered with a piece of cloth to prevent the stimuli from becoming wet, and increased with a temperature-controlled box that could be set to the required temperature. The temperature of the objects was held constant during the experiment. The subjects were instructed to touch the objects only briefly to avoid changing their temperature too much.

The two control conditions were basically the same as the second and third main conditions, respectively, except that the reference object was also made of brass. Since this stimulus was taken from the series of test stimuli, there was no 8-cm3 test stimulus in the control conditions. For this reason, not 90 but 80 trials per subject were performed in both control conditions. Eight new right-handed subjects (four male, four female) with a mean age of 26 years participated in the control conditions.

Results

Figure 4 shows the average relative biases measured in the second experiment. The average bias in the room-temperature condition was 6.2 % (SE 0.9 %), indicating that a brass object is perceived as being larger in volume than a synthetic object of the same size. The biases in the other two main conditions were 8 % (SE 2 %) for the condition with the cold test stimuli and 7 % (SE 2 %) for the condition with the warm test stimuli. Hence, the brass objects were perceived as being larger in volume than the synthetic objects, independent of their temperature. All biases were significantly different from zero, as tested by one-sample t tests [ts(7) ≥ 3.7, ps ≤ .007]. A repeated measures ANOVA performed on the relative biases revealed no effect of condition [F(2, 14) = 0.39, p = .69].

Fig. 4
figure 4

The relative biases (as percentages) for the thermal conductivity experiment. From left to right are the conditions in which the temperature of the test objects was either kept at room temperature (neutral), decreased (cold), or increased (warm), and the two control conditions (cold and warm). Error bars indicate the standard errors of the means

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The discrimination thresholds in the three main conditions were 1.0 cm3 (SE 0.1 cm3), 0.7 cm3 (SE 0.1 cm3), and 0.61 cm3 (SE 0.09 cm3) for the neutral, cold, and warm conditions, respectively. A repeated measures ANOVA performed on the thresholds revealed a significant effect of condition [F(2, 14) = 4.6, p = .029]. Bonferroni-corrected pairwise comparisons showed that only the difference between the neutral and warm conditions was statistically significant (p = .014).

In the two control conditions, no biases were found for any subject, except for one in the control condition with the cold test stimuli. In all other cases, discrimination performance was perfect, meaning that the subjects’ judgments always corresponded to the physical relation between the two stimuli in a trial. For this reason, no discrimination thresholds can be reported.

Discussion

The present experiment showed a significant influence of the thermal properties of objects on the perception of their volume. In the first condition, subjects compared two cubes made out of materials with different thermal conductivities (brass vs. synthetic material), which were both presented at room temperature. The results showed that the cubes with a higher thermal conductivity were perceived as being larger in volume than equally sized cubes with a lower thermal conductivity (bias of 6.2 %). We propose that this effect might be related to the increased saliency of the perceived “coldness” that is caused by heat being extracted from the skin during contact with the object, hypothesizing that with a higher heat flow, the object would be perceived as larger.

In order to investigate this hypothesis further, two additional conditions were conducted in which the temperature of the brass objects was manipulated in order to increase or decrease the difference between the heat flow when exploring brass objects and the heat flow when exploring the synthetic object. In these conditions, subjects were asked to compare the volume of cold and warm brass cubes to that of a synthetic cube that was at room temperature. If the measured effect of thermal conductivity on volume perception could be related to heat flow, then increasing the temperature of the brass objects would result in a smaller bias than the one measured during the condition with the brass objects at room temperature, and a decrease of the temperature of the brass objects would result in an increase of the perceptual bias.

The results showed that the brass cubes, both cooled and heated, were perceived as being larger in volume than equally sized synthetic cubes. The magnitudes of the biases in these two conditions (8 % and 9 %) did not differ significantly from each other, and also did not differ from the magnitude of the bias measured in the condition with both test and reference stimuli at room temperature. The failure to observe the predicted patterns in these conditions suggests that the perceptual biases could not be explained directly by heat flow between the skin and the objects. Independent of the temperature of the objects, the object with a higher thermal conductivity was perceived as being larger in volume than the object with a lower thermal conductivity. The idea that temperature did not play a role was confirmed by the two control conditions, in which only the objects’ temperatures were manipulated and no biases were observed. This suggests that observers are influenced by the perceived “coldness” of objects, which is associated with a higher thermal conductivity, but automatically correct for temperature differences when perceiving this “coldness.” The observation that the effect of temperature could not modify the influence of thermal conductivity is interesting, because a comparison of the results from Plaisier and Kappers (2010) and Lederman and Klatzky (1997) showed that differences in temperature were more salient than differences in thermal conductivity. Apparently, when both features differ, as in the present experiment, the influence of thermal conductivity cues is stronger than the influence of temperature cues.

Experiment 3: Compliance

The third experiment was concerned with the objects’ compliance. Hardness, the inverse of compliance, has been found to be a salient feature (Lederman & Klatzky, 1997; van Polanen et al., 2012): A hard object stands out among softer ones. The question is whether this saliency leads to the harder object being perceived as larger than the softer one. In a magnitude estimation experiment, no effect of softness has been found on the perception of object size (Berryman, Yau, & Hsiao, 2006). However, this experiment was performed with simulated objects consisting of rubber plates, mounted on linear motors, that were grasped between the thumb and index finger. It is unknown whether real compliant objects, which can deform in other ways than just being squeezed in one direction, would produce the same result. It might be that enclosing the objects, as opposed to squeezing between thumb and index finger, leads to a different percept of the objects’ size. It could also be that not so much the hardness itself, but the corners and edges, which feel more pronounced in a harder object, are the relevant salient features. To investigate this, volume biases were measured in two conditions. In the first condition, the objects were enclosed in the same manner as in the first two experiments. In the second condition, the objects were squeezed between thumb and index finger, in a manner similar to the method used by Berryman et al. In the latter case, the corners and edges were avoided. If a bias were to be found in this condition, it could not be due to the influence of the edges, but should be due to the difference in compliance between the objects.

Method

This experiment was very similar to the previous experiments, except that a 8.7-cm3 soft polyether foam cube was used as a reference stimulus. The stiffness (spring constant) of the cube was measured using an Instron 5542 Universal Material Testing machine. This machine compresses the stimulus between two parallel plates and measures force and displacement. The relation between these two was found to be nonlinear in the range between 0 and 1 N. In the lower part of the range, which subjects encounter first upon touching the stimulus, the slope (stiffness) was found to be 0.35 N/mm. In the higher part, the slope was 0.069 N/mm. The test stimuli were made of the same incompressible material as in Experiment 1 (Ebaboard S-1) and ranged in volume from 4 to 12 cm3, in steps of 1 cm3. The same eight subjects as in the control conditions of Experiment 2 participated in this experiment.

We ran two conditions: In the enclosure condition, subjects were asked to enclose the stimuli entirely with their hand, as in Experiments 1 and 2. In the pinch condition, they were asked to grasp the stimuli between thumb and index finger, in the same manner used by Berryman et al. (2006). The order of the conditions was counterbalanced over subjects. The subjects were instructed to base their judgments on their perception of the uncompressed volume.

Results

In both conditions, hard cubes were perceived as being larger than soft cubes of equal physical volume. The average biases were 26 % (SE 2 %) and 23 % (SE 3 %) for the enclosure and pinch conditions, respectively. These results are shown in Fig. 5. Both biases were significantly larger than zero [one-sample t tests: t(7) = 38, p = 2.4 × 10–9, and t(7) = 22, p = 9.4 × 10–8, respectively]. They were not significantly different from each other [paired-samples t test: t(7) = 0.71, p = .50].

Fig. 5
figure 5

The relative biases (as percentages) in the compliance experiment for the condition with the hand enclosing the objects (left) and the condition with the object being grasped between thumb and index finger. Error bars indicate the standard errors of the means

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The discrimination thresholds for the two conditions were 1.5 cm3 (SE 0.2 cm3) and 1.1 cm3 (SE 0.2 cm3). These were also not significantly different from each other [paired-samples t test: t(7) = 1.7, p = .14].

Discussion

The influence of hardness on volume perception was measured for two situations: In the first, the stimuli were enclosed by the subject’s hand. In the other, the subject grasped the stimuli between thumb and index finger. In both cases, substantial biases were found, indicating that hard cubes were perceived as being larger than soft ones. The reason for this can again be sought in the saliency of object features. The hardness of the hard objects makes them stand out as compared to soft objects (van Polanen et al., 2012). At the same time, the edges and corners of the hard objects were also more pronounced than those of the soft object. These features have also been shown to be salient (Plaisier et al., 2009). However, in the pinch condition, in which subjects only touched the object’s faces and did not come into contact with the edges and corners, the bias was of the same magnitude as in the enclosure condition. This indicates that the hardness itself, and not necessarily the presence of edges and corners, was responsible for the observed biases. The edges could still play a minor role in this experiment, perhaps being responsible for the (statistically insignificant) difference between the two conditions. Since the contribution to the volume bias of edges and corners, found in Experiment 1, is of a smaller magnitude than that of hardness, the latter dominated in the present experiment, and the former was not enough for the difference between the two conditions to reach statistical significance.

An important question presents itself: Could it be that softer objects are perceived as being smaller because they are actually smaller when compressed? Although subjects were instructed to base their judgment on the uncompressed volume encountered when first touching the object, they might have been influenced by its smaller size when some pressure was applied. In the pinch condition, the task of comparing three-dimensional volume was reduced to judging differences in the one-dimensional distance between the fingers when grasping the stimulus. The bias of 23 % in volume that was found corresponds to a difference of 1.9 mm in distance between the fingers. Compressing the soft stimulus this amount required a force of ~0.6 N. A force of only ~0.1 N was sufficient to establish contact. Therefore, this amount of compression seems overly large for judging the uncompressed size. Thus, it seems more likely that the bias was not the result of the stimulus being compressed that much, but rather of a perceptual process under the influence of hardness as a salient material property. This idea was confirmed by the result of the enclosure condition, in which the stimulus was contacted in a very different way, but a bias of the same magnitude was found.

The results seem to contradict the findings of Berryman et al. (2006), who found no effect of hardness on size perception. However, the softest material that they used was a foam rubber 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 on the basis of the specifications of the Shore hardness measurement. A rating of 50 on the OO scale means that a spherical indentor with a diameter of 3/32 in. (2.4 mm) is pushed 0.050 in. (1.3 mm) into the material when a force of 4 oz. (1.1 N) is applied. The ratio between this force and the indentation is 0.88 N/mm. Considering that the stiffness of our stimulus (0.35 N/mm) was measured by compressing the entire side of the cube (441 mm2), it is clear that our stimulus material was much softer than the softest material used by Berryman et al. It could be that their failure to observe an effect of softness on size perception was due to the relative hardness of their materials. When the contrast between hard and soft materials is greater, as in the present experiment, the hardness becomes more salient and has an effect on volume perception.

General discussion and conclusions

In the present study, we investigated the influence of salient material properties on the haptic perception of the volume of cubes that could fit in one hand and had to be explored unimanually. Significant perceptual biases were observed, revealing a robust influence of the studied material properties on volume judgments. Roughness leads to an underestimation of the object’s volume, whereas “coldness” (higher thermal conductivity) and hardness lead to an overestimation of the object’s volume. Moreover, the effect of thermal conductivity could not be changed by a manipulation of the temperature of the test objects. So, in general, salient material properties appear to influence volume perception, as salient geometric properties had been shown to do earlier. However, the specific property of surface texture seems to have an effect that is in the opposite direction to what would be expected. This is thought to be due to the saliency of the geometric property of edges dominating over the material property of roughness. Also, perceived coldness (thermal conductivity) was shown to have a small but significant effect, even though the saliency of this property was found to be limited in a speeded search task (Lederman & Klatzky, 1997). It might be that because a certain amount of heat transfer needs to be established before coldness can be experienced, it takes some time before this property becomes salient. This might be the reason why this property was not identified as salient in speeded search tasks.

In earlier work, we have shown that haptic volume estimation is most likely based on perception of other geometric properties, such as surface area (Kahrimanovic et al., 2010). The question is now whether salient material properties influence the volume percept directly, or whether their influence works through the perception of these geometric properties. In the latter case, we would expect material properties that are related to the surface, such as roughness, to have a larger effect than properties that are related to the bulk of the material, such as compliance. This was not observed, implying that salient material properties might influence the volume percept directly. To investigate this, one could measure the influence of the salient material properties on the perception of geometric object properties such as edge length or surface area. However, these measurements are beyond the scope of the present article.

For a better understanding of the mechanisms involved in the effect of material properties on volume perception, it may be interesting to compare the magnitudes of the biases observed in the three experiments. This comparison might provide some suggestions about the levels at which the effects may be manifested. The present study showed that the bias in the thermal conductivity experiment was smaller than the biases in the roughness and compliance experiments. It may be that information of a mechanical nature has a stronger effect on the volume percept than does information of a thermal nature, due to the level of processing at which the effect manifests itself. Previously, we have shown that the shape of three-dimensional objects has a weaker effect on haptic bimanual volume perception of large objects than on unimanual volume perception of small objects (Kahrimanovic, Bergmann Tiest, & Kappers, 2011). Volume processing of the small stimuli may occur early in processing, in the primary sensory cortex, which contains cortical areas that receive information from receptors in the skin as well as areas that receive information from receptors in muscles and joints. In contrast, bimanual volume perception requires integration of information from the two hands, and this integration is shown to take place in the posterior parietal cortex (Kandel, Schwartz, & Jessell, 2000). Bimanual perception of large objects is assumed to be less prone to systematic distortions because of deeper processing of the information. This reasoning may also be applied to the present study. In the roughness and compliance experiments, the relevant information about the objects is transmitted mainly by mechanoreceptors, and could be processed at an early stage. In the thermal conductivity experiment, the relevant information comes from both mechanoreceptors and thermal receptors. These different cues are processed separately at the peripheral level but converge at the thalamus and the orbitofrontal cortex (Kandel et al., 2000). Consequently, the effect of thermal cues on the volume percept may manifest itself at a higher level of processing than the effect of mechanical cues. This deeper processing of the information may result in a weaker effect of the salient feature.

The present study revealed large and consistent overestimations of smooth cubes as compared to rough cubes, of brass cubes (either at room temperature or with a decreased or increased temperature) as compared to synthetic cubes, and of hard synthetic cubes as compared to soft polyether foam cubes: All subjects showed substantial positive biases. Apparently, material properties have a consistent influence on haptic perception of the volumes of three-dimensional objects. In the present study we speculated about the mechanisms underlying these effects, but further research will be required for a more detailed understanding of the origin of the observed effects.