Previous research on the interaction between vision and touch has employed static visual and continuous tactile stimuli, and has shown that two kinds of multimodal interaction effect exist: the averaging effect and the contrast effect. The averaging effect has been used to explain several kinds of stimuli interaction while the contrast effect is associated only with the size-weight illusion (A. Charpentier, 1891). Here, we describe a novel visuotactile interaction using visual motion information that can be explained with the contrast effect. We show that the magnitude of tactile force perception (MTFP) from an impact on the palm is significantly modified by the visual motion information of a virtual collision event. Our collision simulator generates visual stimuli independently from the corresponding tactile stimuli. The results show that visual speed modified MTFP even though the actual contact force remained constant: higher visual pre- and post-collision speeds induced lower tactile force perception. Finally, we propose a quantitative model of MTFP in which MTFP is expressed as a function of the visual velocity difference, suggesting that the gain of the tactile perception in the human brain is altered via MTFP modulation.

^{1}Figure 2 shows the average results for Experiment 1. The horizontal axis represents collision speeds of the virtual ball and the vertical axis represents MTFP. Plotted points indicate averaged values of MTFPs from 13 subjects. Figure 2 shows that the MTFPs were influenced by the speed of the visual stimulus both before and after the collision. When the post-collision speed was kept constant, higher pre-collision speeds induced significantly lower MTFP values. Similarly, when the pre-collision speed was kept constant, higher post-collision speeds induced significantly lower MTFPs (two-way repeated measures ANOVA; pre-collision speed, 8 and 64 cm/s, × post-collision speed, 8 and 48 cm/s). For pre-collision speed,

*F*[1, 12] = 19.5,

*p*= 0.001,

*η*

_{ p}

^{2}= 0.62. For post-collision speed,

*F*[1, 12] = 9.7,

*p*= 0.009,

*η*

_{ p}

^{2}= 0.45. In addition, there was no interaction effect (

*F*[1, 12] = 0.26,

*p*> 0.1,

*η*

_{ p}

^{2}= 0.02).

*t*-test;

*t*[12] = 3.44,

*p*= 0.005) and 64/48 collision speed condition (

*t*[12] = 2.39,

*p*= 0.034). On the other hand, there were no significant differences with the 8/48 speed condition (

*t*[12] = 0.90,

*p*= 0.39) and 64/8 speed condition (

*t*[12] = 1.87,

*p*= 0.085).

*t*-test;

*t*[9] = 1.93,

*p*= 0.09) ensuring that there was no artifact effect caused by the apparatus or the tactile stimulus timing and the subject's response timing.

^{2}) and with an initial speed of 32 cm/s; i.e., the visual collision speed was set to 8, 16, 48, or 64 cm/s. In all conditions, the restitution coefficient of the visual stimuli was 0.5 and no acceleration was added after collision. For example, if the collision speed was 48 cm/s, then the post-collision speed was 24 cm/s.

*F*[3,18] = 23.24,

*p*< 0.001,

*η*

_{ p}

^{2}= 0.80), but not between the uniform motion and accelerated motion conditions (

*F*[1,6] = 3.72,

*p*= 0.1,

*η*

_{ p}

^{2}= 0.38). In addition, there was no significant acceleration × collision speed interaction (

*F*[3,18] = 0.12,

*p*> 0.1,

*η*

_{ p}

^{2}= 0.02). We conclude that the collision speed was a critical parameter in the estimation of MTFP, but the visual acceleration and the initial speed of the visual stimulus were not. By combining the results of Experiments 1 and 2, it is suggested that MTFP for a constant contact force can be predicted using a formula as a function of visual pre-collision and post-collision speeds.

*V*(a vector quantity) between the visual pre-collision velocity

*V*_{ pre}and the visual post-collision velocity

*V*_{ post}. In our experiments,

*V*_{ pre}becomes a positive value and

*V*_{ post}is a negative value in vector quantity because the visual object (ball) reversed direction after collision. Thus, Δ

*V*becomes the summation of pre-collision velocity and post-collision velocity absolute values (i.e., differential velocity will become 48 in the 32/16 cm/s condition). Theoretically, Δ

*V*is related to the impulse

*I*in collision phenomena. Therefore, their relationship can be formulated as

*I*=

*m*· Δ

*V*∝ Δ

*V,*where

*m*represents the mass of the ball. We assume that

*m*can be represented as a constant value because the same virtual ball was used in all our experiments. No significant difference was detected between the MTFP from the 32/16 condition and the MTFP from the 8/48 or 64/8 speed condition in Experiment 1, supporting the differential velocity hypothesis because all the conditions have similar Δ

*V*( Figure 4).

*V,*demonstrating that larger velocity differences induced lower MTFPs. Therefore, we assume that MTFP can be described by the following formula:

*K*represents the gain factor as a function of visual velocity difference, Δ

*V,*and

*f*represents a function of contact force,

*CF*. The absolute magnitude of tactile force perception in the reference phase

*MTFP*

_{ ref}can be derived as

*K*

_{ ref}and Δ

*V*

_{ ref}represent the gain factor and differential velocity in the reference phase, respectively. Similarly, the absolute magnitude of tactile force perception in the test phase

*MTFP*

_{ test}can be represented as

*K*

_{ test}and Δ

*V*

_{ test}represent the gain factor and differential velocity in the test phase, respectively. Since we used a magnitude estimation method, the subjects estimated the

*MTFP*

_{ test}in comparison with the

*MTFP*

_{ ref}. Therefore, the subject's response (

*res*) can be described as a ratio of the two MTFPs as follows:

*res*can be described as

*K*using the following formula

*n*represents a power constant that accounts for the nonlinearity between perception and physical dimensions. For describing the contrast effect,

*K*was defined by the reciprocal of visual differential velocity.

*n*as 0.059. The determination coefficient was 0.92. Although the results from Experiment 2 were not used to determine the regression curve, their magnitude coincided well with the curve (the determination coefficient for the data from Experiment 2 was 0.95 using this curve).

*K*as a function of the reciprocal of visual differential velocity was able to explain our results for MTFP. This suggests that the gain factor

*K*optimizes the resolution of the tactile perception, which is allocated depending on the dynamic visual stimuli information. In the real world, a larger Δ

*V*yields a greater impact on the palm. Therefore, the gain factor

*K*is lowered to compress the perceptual response and to expand the range of pressure force perception when a larger Δ

*V*is presented visually. Conversely, a lower Δ

*V*makes the gain factor

*K*higher to take into account a low contact force in high resolution level.

*W*represents the estimated weight,

*H*

_{test}represents the physical weight of the test objects, and

*VO*

_{test}represents the physical volume of the test objects. In their experimental settings,

*H*

_{test}was 350. Thus, the formula can be calculated as

*VO*

_{ref}, formula (10) can be described as

*n*in formula (11), we obtain

^{1}The two excluded subjects had high variability from 5 repeated measures on each condition. Thus, we decided that those two subjects were unsuitable to use in our analysis. However, if the two subjects were included in the two-way repeated measures ANOVA (pre-collision × post-collision), significant effect of pre-collision speed & post-collision speed and no interaction effect are shown, the same results as presented in Experiment 1.