Abstract
Haptic object perception is still poorly understood up to now. This study investigated the ability of human fingers to discriminate the volume of objects by passive touch. Experiments measured the discrimination threshold of volume using three tasks: passive tactile volume perception, passive tactile area perception, and active tactile volume perception. In each trial, we utilized two plastic cubes to successively stimulate the fingers, and participants were instructed to make comparisons between the stimulus objects’ volume and area. Results showed that there was no significant difference in the discrimination thresholds of tactile volume perception between passive touch and active touch, whereas significant differences in the discrimination thresholds between fingertips, such as the thumb versus the pinky finger. In passive touch, the discrimination thresholds of volume perception were larger than that with surface area perception. We found that the discrimination of the volume of objects is more difficult than the discrimination of the area of the objects.
Keywords
Introduction
People obtain a great information involve in volume from visual and auditory sources because these sources make us aware of our surroundings (L. Y. Wang et al., 2017; Wu, Yan, Zhang, Jin, & Guo, 2012). Similar to vision and hearing, touch perception is also important for various cognitive functions (James, Kim, & Fisher, 2007). People who lose the ability to see, rely heavily on the sense of touch in their activities. Persons with vision loss show greater ability in the 2-point discriminative test than sighted individuals (Gazzaniga, Ivry, & Mangun, 2013). The sense of touch is complicated, and it can include various categories such as tactile sense, pressure, shape, and temperature perception (Crutch, Warren, Harding, & Warrington, 2005; Klatzky, Lederman, & Metzger, 1985; Stilla & Sathian, 2008). In particular, the three-dimensional (3D) shape feature is an important cue for recognizing objects (Kahrimanovic, Tiest, & Kappers, 2010, 2011; Plaisier, Tiest, & Kappers, 2009).
Previous studies have investigated the role of the tactile system recognition of objects (Kahrimanovic et al., 2010, 2011; Lederman & Klatzky, 2009a). The volume that describes the total size of object has been studied in tactile perception. Lederman and Klatzky (2009a) demonstrated that the enclosure procedure is a stereotypical exploratory procedure that was used by participants when asked to judge the volume of a 3D object. Kahrimanovic et al. (2010) studied the effects of shape, size, and weight when discriminating the volume of objects. They (Kahrimanovic et al., 2011) found a strong relationship between the surface area and the volume estimation of objects. On the other hand, various skin areas have different tactile sensitivity (Ackerley, Carlsson, Wester, Olausson, & Wasling, 2014; Ackerley et al., 2012; Ackerley, Saar, McGlone, & Wasling, 2014; Bjornsdotter, Gordon, Pelphrey, Olausson, & Kaiser, 2014). For example, the 2-point discrimination ability of fingers is better than that of the forearm (Lederman & Klatzky, 2009a; Weinstein, 1968). Bolanowski, Verrillo, and McGlone (2004) designed an experiment in which an experimenter rolled balls on the subject’s fingertip and several other body regions (e.g., thenar eminence, forearm). The results showed that there were differences in the volume perception of objects between the glabrous skin of the thumb or thenar eminence and the hairy skin of the forearm when each touched a surface (Bolanowski et al., 2004).
Perceiving the volume of an object is determined not only by the object’s physical volume but also by modes of touch. Previous study shows that active touch and passive touch have been widely investigated in humans using various tasks and techniques (Symmons, Richardson, & Wuillemin, 2004). In active touch, a body part is actively used to touch an object; however, in passive touch, the body part is touched by the object (Delhaye, Hayward, Lefevre, & Thonnard, 2012). Passive touch refers to perception mediated solely by variations in cutaneous stimulation (Bodegard et al., 2000; May, Stewart, Tapert, & Paulus, 2014; Savini et al., 2010). In contrast, active touch involves muscles, tendons, and joints sensations, and it is in an active rather than merely perceptive sense (Ackerley et al., 2012; Chatel-Goldman, Congedo, Jutten, & Schwartz, 2014; Gandevia, 1996; Lederman & Klatzky, 2009a; Taylor, 2009). It can be said that the passive tactile process more directly reflects tactile perception than the active touch process.
Symmons et al. (2004) reviewed the literature concerning active and passive touch in the exploration of two-dimensional stimuli and the results were equivocal: On some occasions, active touch was found to be superior in performance than passive touch; in some cases, passive exploration was better compared with active touch, and in some instances, there was no difference in the performance recognition of the objects. Some other studies regarding 3D stimuli revealed a similar conclusion to two-dimensional stimuli. For example, the difference was not statistically significant between active and passive touch with 3D stimuli (Symmons, Richardson, Wuillemin, & VanDoorn, 2005). The studies prove that the lack of better performance by active subjects could be attributed to the inferring effects of decisions about which way to move fingers. Although the difference between active touch and passive touch has been widely investigated, research linking the difference in volume perception of fingers has not been done until now. We investigate this question in this study.
Object recognition by touch is a complex and poorly understood process. It involves encoding of elementary microgeometric (roughness and surface texture) and macrogeometric (edges and shape) features, integration of sensorimotor information, and association with other multimodal sensory information to create a tactile representation of a semantically defined object (Savini et al., 2010). Lederman and Klatzky (1987) demonstrated that the enclosure behavior is a stereotypical exploratory procedure that was used by participants with their hands when they were asked to judge the volume of a 3D object in an active touch experiment. In terms of passive touch, there seems to be some primal connection between volume perception and area perception: Humans often rely on the surface area of objects to perceive volume and not on their physical volume (Kahrimanovic et al., 2010). People can identify the volume of objects by passive touch with fingers. Therefore, the present experiment examined the difference between volume perception and area perception by passive touch.
In this study, we investigate the abilities of human fingertips by passive touch with tactile volume perception. To investigate the passive volume perception of fingertips, we first adopted a discrimination task in which subjects identify the volume of a cube on five fingertips. Second, we compared active versus passive tactile performance for volume perception. Finally, using passive tactile technique, we investigated the relationship between the tactile volume and area perceptions.
Methods
Participants
Twenty-three participants (10 females, mean age = 23.5 years, standard deviation = ±2.6 years) from the university student body were included in this study. All participants took part in all tasks of the three experiments. All participants were right-handed, as examined by the Edinburgh handedness questionnaire (Oldfield, 1971) and had normal or corrected-to-normal sight and no psychiatric or neurological history. They were naive to the purpose of the study and were paid for their participation. The individuals provided written informed consent for participation in this study, which was previously approved by the ethics committee of Capital Medical University.
Stimuli
Cubes that made of polyethylene were used as stimuli. The volumes of stimuli were determined by a preliminary experiment, (see Figure 1 in Supplemental material) with volumes ranging from 0.2 to 0.8 cm3. The stimuli consisted of a reference and 10 experimental stimuli, and the volume of the reference stimulus was 0.5 cm3 (Figure 1, reference stimulus was framed by square).

A set of 11 different plastic cubes were used for assessing tactile spatial resolution. Ten cubes were arranged for the experimental stimuli (volume: 0.2, 0.3, 0.35, 0.4, 0.45, 0.55, 0.6, 0.65, 0.7, and 0.8 cm3; area: 0.34, 0.45, 0.50, 0.54, 0.59, 0.67, 0.71, 0.75, 0.79, and 0.86 cm2). The other cube is the standard stimulus, which is 0.5 cm3/0.63 cm2. To measure the edges of the cubes, we used Vernier calipers and then calculated the volume of the cubes (volume: 0.203, 0.303, 0.356, 0.405, 0.455, 0.504, 0.553, 0.599, 0.651, 0.703, and 0.804 cm3). The maximum measuring error was estimated to be less than 2%.
Conditions and Procedures
Experiment 1: passive tactile volume perception
Five different conditions were designed in this experiment. Each participant was passively stimulated to their five fingers of right hand using cube objects. The subjects were asked to distinguish the volumes of paired objects. It is worth noting that the three experiments in our research involved a total of nine experimental conditions, which were mixed together and performed in a random order. Each condition lasted for approximately 15 minutes, resulting in over 2 hours per participant for completing Experiment 1. Each participant was assigned 2 days to complete the experiment. In the first day, participants got familiar with the experiment process and completed four experimental conditions. In the second day, the participants performed the remaining five experimental conditions.
During the experiment, participants sat comfortably in a chair and were blindfolded (Figure 2(a)). With regard to the conditions for passive tactile volume perception, the participant placed their right arm on the desk, palm upward. To start a trial, 3 seconds were given to prepare. Then, the test stimulus was rotated on a fingertip of the participant for 4 seconds (Figure 2(b)). The cube was rotated on the first fingertip pulp in a clockwise direction, ensuring a full contact between the skin and the surface of the cube. After 2 seconds, the reference stimulus was rotated on the same finger for 4 seconds in the same way. In the following 4 seconds, the participant had to indicate which of the two stimuli was larger in volume. During the experiment, the right hand of the participant was not allowed to move. Stimulus 1 and Stimulus 2 are randomly ordered in the reference and test conditions, and the Stimulus 1 numbers of the reference conditions and that of the test condition are the same in one session. The volume of the reference stimulus cube was unchanged throughout the experiment.

(a) Cube stimulus during passive tactile volume perception and (b) the experimental sequence.
Experiment 2: passive tactile versus active tactile volume perception
Four different conditions were used in Experiment 2. The task factor consisted of two different tasks: passive tactile volume perception and active tactile volume perception. The first task condition is the same as Experiment 1, but only the index finger and pinky finger of the right hand were used. For active tactile volume perception, the participants were asked to actively explore the stimulus (Figure 3). In Experiment 2, the participants rotated the stimuli with their fingertip on the desk, while the finger was freely moving.

Cube stimulus during active tactile volume perception.
When examining active tactile volume perception, the participants were asked to actively explore the stimulus and indicate which of the two stimuli was larger in volume.
Experiment 3: volume versus area perception by passive touch
Four different conditions were designed in Experiment 3. The task factor consisted of two different tasks: passive tactile volume perception and passive tactile area perception in which participants were asked to distinguish the areas by passive touch. These two tasks involved using the index finger and pinky finger of the right hand. The order of the four different conditions was randomized. Each condition lasted for approximately 15 minutes, resulting in about 1 hour per participant for completion of Experiment 3.
For passive tactile area perception, the hand gesture of the participant and experimental stimulation sequence was set similarly to the conditions of passive tactile volume perception. During this experiment, the experimenter pressed one fingertip of participant with a stimulus cube (Figure 4). The task for participants compared the area of the stimuli and answered which one was bigger. We only evaluated the volume of cubes in the response in all experimental conditions because the values of the volume were not affected in all experimental conditions.

Cube stimulus during passive tactile area perception.
Data Analysis
Data were analyzed using a method that consisted of two parts (Kahrimanovic et al., 2011; Zhang et al., 2017). In the first part of the experiment, the stimuli were given to all participants to get a rough estimation of each participant’s discrimination threshold. Stimuli were provided step-by-step, increasing by 0.1 cm3 each time. Each combination (test and reference stimuli) was done 4 times. Next, the accuracy of each subject’s discrimination threshold was calculated in the first part. According the accuracy, we determine which set of wide- or narrow-range stimuli was used in the second part. So we defined a criterion (85%), what was determined with a computer simulation. If the estimated accuracy was less than 85%, a similar stimulus range as the first part was utilized. Each combination of reference and test stimuli was provided 6 times and was continued up to 10 repetitions for each combination in order to obtain the exact response. If the accuracy was greater than 85%, a small number of test stimuli were applied in steps of 0.05 cm3, and a new stimulus combination was added, which finally totaled 10 stimuli. The data from both parts were combined for the analyses.
To compare each combination of reference and test stimuli in the different conditions, the probability was calculated for each participant the data for which was selected on the test stimulus result to be among larger volume/area. A weighted cumulative Gaussian distribution (f) as a function of the volume of stimuli (V) was fitted to the data with the least squares procedure, using the following equation:
In this equation, erf is the Gauss error function:

Two examples of collected data: (a) a wide-range stimuli data and (b) a narrow-range stimuli data. The light-gray bars indicate the trials data. The dark-gray bars are trials from the second part of the experiment. The curve shows the fitted function through the measured data points (left vertical scale). The dashed line indicates the place of the 84% threshold. The value of this discrimination threshold, σ, is shown in the right top corner of the figure. Note: Please refer to the online version of the article to view the figures in colour.
Results
Experiment 1: Passive Tactile Volume Perception
Figure 6 shows the average discrimination thresholds and the standard deviations of five fingers in the passive tactile volume perception task: 0.087 ± 0.030 (thumb), 0.090 ± 0.021 (index finger), 0.092 ± 0.031 (middle finger), 0.136 ± 0.059 (ring finger), and 0.159 ± 0.041 (pinky finger) cm3. A one-way repeated measures analysis of variance (ANOVA) was performed on the discrimination thresholds and revealed a significant difference of among fingers, F(4, 88) = 23.066, p < .001. The result showed that discrimination thresholds of the thumb finger, index finger, and middle finger were significantly different compared with the ring finger and the pinky finger, respectively. However, a post hoc paired t test showed that there was no significant difference among the thumb finger, index finger, and middle finger as the same as that between ring and pinky fingers.

Average discrimination threshold of passive tactile volume perception for the five fingers. The error bars represent the standard deviation. **p < .01.
Experiment 2: Passive Tactile Versus Active Tactile Volume Perception
Figure 7 shows the average discrimination thresholds and the standard deviations of the four different conditions: 0.090 ± 0.021 (index finger used in passive tactile), 0.103 ± 0.024 (index finger used in active tactile), 0.159 ± 0.041 (pinky finger used in passive tactile), and 0.172 ± 0.059 (pinky finger used in active tactile) cm3. A 2 (Fingers) × 2 (Perception Tasks) repeated measures ANOVA performed concerning the discrimination thresholds revealed a highly significant effect of the fingers, F(1, 22) = 118.136, p < .001. However, the task effect has no significant difference, F(1, 22) = 2.274, p = .146. There was no significant interaction between finger and perception modality, F(1, 22) < 0.001, p > .998.

Average discrimination threshold for the four conditions (index and pinky finger in the passive and active tactile volume perception tasks). The error bars represent the standard deviation. Note: Please refer to the online version of the article to view the figures in colour.
Experiment 3: Passive Tactile Volume Perception Versus Area Perception
Figure 8 shows the average discrimination thresholds and the standard deviations of the four different conditions: 0.090 ± 0.021 (index finger used in volume perception), 0.085 ± 0.023 (index finger used in area perception), 0.159 ± 0.041 (pinky finger used in volume perception), and 0.141 ± 0.047 (pinky finger used in area perception) cm3. A 2 (Finger) × 2 (Tasks) repeated measures ANOVA performed on the discrimination thresholds revealed a significant effect of the task (volume vs. area), F(1, 22) = 4.919, p < .05. The main effects of finger were significant, F(1, 22) = 62.229, p < .001. There was no significant interaction between finger and task, F(1, 22) = 1.105, p = .304.

Average discrimination threshold for the four conditions (index and pinky finger in passive tactile volume perception and passive tactile area perception). The error bars represent the standard deviation. *p < .05. Note: Please refer to the online version of the article to view the figures in colour.
Discussion
Comparing with our previous study (Zhang et al., 2017), which was conducted using perception by active touch only, the volume discrimination threshold of current experiment was larger than that of the previous (two fingers exploring the volume of objects).We considered that this method of exploration might raise the threshold of discrimination because it does not really involve enclosure. However, the accuracy of volume perception showed that it still be able to perceive the information of enclosure. Moreover, we found no differences in Experiment 2 regarding the perception ability between active and passive touch. However, as mentioned earlier, passive touch is sometimes similar or superior to active touch. Therefore, we summarized the recent data for passive touch perception in this article.
Our results in Experiment 1 showed that the volume discrimination of objects was significantly influenced by the fingers used. The discrimination thresholds of the thumb finger, index finger, and middle finger were significantly less than those of the ring finger and the pinky finger (Figure 6). This is almost the same result as traditional testing models (2-point touch threshold; Lederman, 1991; Weinstein, 1968) and active touch (Zhang et al., 2017). Experiments 2 and 3 showed similar results as Experiment 1, in that there was a significant difference in the discrimination threshold between the index and pinky finger (Figures 7 and 8).
We suppose this effect may be related to tactile experience of fingers because the thumb, the index finger, and the middle finger are frequently used in daily life activities. For example, people pick up a small object or discard materials using these three fingers. Previous research has shown that tactile perception of the dominant hand has advantages over the nondominant hand. Ozcan, Tulum, Pinar, and Baskurt (2004) found that pressure pain threshold assessment in right-handed participants revealed significantly lower pressure pain threshold in the dominant hand than in the nondominant hand. The 2-point discrimination distance differs in dominant and nondominant limbs in healthy adults (Thukral & Bhatia, 2014). Moreover, people with loss of vision obtain geometrical information by touch and have more experience with touch than sighted individuals. Legge, Madison, Vaughn, Cheong, and Miller (2008) found that persons with vision loss showed high tactile spatial acuity, which did not decline with age and was not limited to the fingers used for Braille reading. It is worth mentioning that they attributed this intriguing finding to central neuronal plastic changes arising from the regular use of active touch in daily life. Another study demonstrated that blindness does lead to an enhancement of tactile abilities for 3D shape discrimination (Norman & Bartholomew, 2011). Goldreich and Kanics (2003) and Legge et al. (2008) also found that the fingers of blind people have enhanced touch sensation.
The related causes of different discrimination thresholds for fingers were also investigated by neuroimaging techniques. Many studies showed that the touch using different fingers activated different subareas of the primary somatosensory cortex (Besle, Sanchez-Panchuelo, Bowtell, Francis, & Schluppeck, 2014; Overduin & Servos, 2008). Besle, Sanchez-Panchuelo, Bowtell, Francis, and Schluppeck (2013) found that not only area but also intensity of subareas activated was different for the different fingers; the extension of activated area and intensity by the thumb, the index, and the middle finger was more significant than the ring and the pinky finger. The index finger is perceived to be the most sensitive digit and has the best 2-point discriminative capacity (Lederman, 1991; Weinstein, 1968) and the largest primary somatosensory area representation in the cerebral cortex (Besle et al., 2013). This shows that different abilities of human fingers to discriminate volume may be related in different brain area functions and connection.
Passive perception mainly obtains information from skin tactile receptors. The type and amount of tactile receptors greatly affect the tactile sensation ability of fingers. Studies have found that there are four main sensory corpuscles in fingers: Meissner’s corpuscles, Merkel cells, Pacinian corpuscles, and Ruffini’s corpuscles (Gardner, Martin, & Jessell, 2000). Meissner’s corpuscles and Merkel cells are the most useful for object perception. The result of a similar density of Meissner’s corpuscles in the index, and ring fingers does not correlate with the findings that the index finger has superior 2-point discrimination over the ring finger (Weinstein, 1968). By dissecting the skin, Lacour, Dubois, Pisani, and Ortonne (1991) found that the mean numbers of Merkel cells from thumb to pinky were 71.5, 83.5, 103.5, 83.2 and 61.2 per mm2, respectively. We did not find strong correlation between the density of the corpuscles and the volume discrimination threshold in Experiment 1. These results demonstrate that the difference in volume discrimination thresholds between fingers may not be due to peripheral (i.e., tactile receptors) of fingers.
The results of Experiment 2 showed that the volume discriminability of objects by passive tactile perception was not significantly different from active tactile perception (Figure 7). Symmons et al. (2004) reviewed the relevant literature that included 73 comparisons of active and passive tactile research. Forty-two studies showed that active touch is superior to passive touch; however, 11 studies indicated that passive showed a better result, and 20 studies suggested that there is no significant difference between the two conditions. This review shows that there is much research proving that passive touch is better than active touch in some cases. In addition, Richardson, Wuillemin, and Mackintosh (1981) tested the performance of active and passive touch of subjects through a tactile maze test. They showed that active subjects made more errors and took a greater number of trials to reach criterion than did passive subjects. Symmons et al. (2005) designed an experiment in which active subjects’ movements were applied to guide a passive subject over the same stimuli in three dimensions. The results showed that the difference in accuracy was not statistically significant between active and passive touch. Therefore, the studies showing a lack of better performance by active subjects could be attributed to the inferring effects of making decisions about which way to move. However, the haptic brain function for movement had no effect on the final performance. It is highly likely that the results reflect limits to the neuronal cognitive system not the haptic system. Through experimental analysis, Schwartz, Perey, and Azulay (1975) and Cronin (1977) also found that the motor component of the active touch was not necessarily a decisive factor for tactile perception. Moreover, Simoes-Franklin, Whitaker, and Newell (2011) investigated the neuronal substrates of these exploratory procedures using a rough categorization task by functional magnetic resonance imaging. Participants either actively explored a surface (active touch) or the surface was moved under the participant’s stationary finger (passive touch). The results revealed that active touch elicited greater and more distributed brain activity compared with passive touch in areas activated by field extent but not in those cortexes associated with motor components. In this study, we infer that active touch has no more advantage than passive touch when the stimulus is a simple abstract shape. In general, the advantage of active touch is that spatial position information can be obtained from muscles, joints, and so on. When passive touch was adopted, most of the information is obtained from the tactile receptors. But the resolution of information from muscles, joints, and so on is lower than from the tactile receptors (Lederman & Klatzky, 2009b; Taylor, 2009). The smallest difference in the volume of the stimulus was only 0.05cm2 in our study. For this abstract, small stimulus, the discrimination threshold for muscle may be greater than the difference in the volume. The motion part of the active touch experiment only plays a role that changes the object’s orientation, and the value of the information provided by motion part to the participants to perceive object was much less than the value from the skin. Moreover, during the experiment, the subjects were blindfolded. As a result, the direction control of the participants was not very accurate during the active touch. To complete the task of rolling stimulus as best as possible, some attention of participants needed to be directed. On the contrary, participants were stimulated by the experimenter during the passive touch, so they could pay almost all attention to object perception. Therefore, the experimental paradigm of this study may limit the advantages of active touch.
Our research aim is to study the perception of object area and volume in combination with different exploration modes. The area and volume of the same object are not independent of each other, but the object perception can be changed by altering the exploration modes. Kahrimanovic et al. (2011) confirmed that the availability of mass information contributed to a more accurate volume judgment and resulted in a decrease of the volume biases with different exploration methods. Moreover, the other studies investigated that the differences exist between the length perceptions resulting from the use of two different haptic exploration modes to know the same object (Arthur, Daniel, & Howard, 1976; S. Wang, 1981). A study by Hubel and Wiesel (1968, 1977) showed that visual object recognition first identifies the primary feature and reencodes the complex shape of the recognizable unit. However, little is known about the cognitive process of passive tactile volume perception. A study by Plaisier et al. (2009) reported that edges and vertices are also important components and structural features of 3D object recognition by touch. The Kahrimanovic et al.’s (2010) study showed that the haptic volume judgments were biased by the objects’ shape because the judgments were based on the surface area of objects, instead of the volume itself. They (Kahrimanovic et al., 2010) also suggested that to determine the object volume, the object surface area is more accurate than the side length, diagonal, and so on. Another investigation was also done by Kahrimanovic et al. (2011) to study the relationship between the recognition of volume and area. The results showed that the estimated volume of the object depends on the surface area. In this experiment, the information can only be obtained through the finger characteristics, which can be converted to area directly. We suppose that the volume of passive tactile perception is more complex than area perception and length perception. Moreover, we conjectured this difference between volume and area perception may be due to the effects of exploration methods. Although area perception and volume perception are both passive tactile methods, differences in exploration methods may affect object perception. During the passive volume perception, the stimulus was rolled on the participants’ fingertips. To unify the stimulation frequency and time, the participants were pressed on the same place of the fingertips skin 3 times for area perception. The area where the stimulus was rolled was greater than the pressed area. When the participants were stimulated 3 times intermittently by passive area perception, they had more opportunities to perceive size of the area than volume. This might also lead to lower discrimination thresholds for area perception. Moreover, in light of previous research (Panday, Tiest, & Kappers, 2011, 2012), edges could disrupt the perception of size and volume. In the passive volume perception experiment, only a single edge of the stimulus touched the participant’s finger during the roll. The feature of edges helped in distinguishing different shapes, but the information about the volume was not contained by edges and had a big disruptive influence (Panday et al., 2012). So the exploration method could actually be responsible for the increased threshold in the volume task. On the whole, the passive tactile area perception is more accurate than passive tactile volume perception.
Conclusion
This study revealed that fingers have the ability to estimate the volume of 3D objects by passive touch. The volume perception abilities of the thumb, index finger, and middle finger were higher than the ring finger and pinky finger. In addition, passive or active touch had no significant influence on volume perception. Finally, comparison of discrimination thresholds for volume and area revealed that the discrimination thresholds for volume were high, which indicates that discrimination of the volume of objects is more difficult than area perception.
Supplemental Material
PEC878560 Supplemental Material - Supplemental material for Discrimination Thresholds for Passive Tactile Volume Perception by Fingertips
Supplemental material, PEC878560 Supplemental Material for Discrimination Thresholds for Passive Tactile Volume Perception by Fingertips by Jian Zhang, Zhilin Zhang, Ritsu Go, Chunlin Li and Jinglong Wu in Perception
Footnotes
Acknowledgements
The authors thank Mirela Kahrimanovic and Kewei Chen for their invaluable help during the preparation of the manuscript.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was financially supported by grants from the National Key Research and Development Program of China under grant 2018YFC0115400, the National Natural Science Foundation of China (grant numbers 81671776, 61727807, 61633018, and 81771909) and the Beijing Municipal Science and Technology Commission (grant number Z161100002616020 and Z181100003118007), and the Beijing Nova Program (grant number Z171100001117057).
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References
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