The Cutaneous Rabbit Effect: Phenomenology and saltation
|Jack Brooks and Jörg Trojan (2017), Scholarpedia, 12(12):52363.||doi:10.4249/scholarpedia.52363||revision #184883 [link to/cite this article]|
The Cutaneous Rabbit Effect: Phenomenology and saltation
Frank Geldard and Carl Sherrick first described the Cutaneous Rabbit Effect (CRE) in 1972 (Geldard and Sherrick, 1972). This version of the illusion entailed five quick taps at the wrist, then at the middle of the forearm, and then at the elbow (see figure). Participants felt the taps uniformly along the arm as if “a tiny rabbit were hopping from wrist to elbow” (Geldard and Sherrick, 1972). The CRE demonstrates the perceptual interdependence of space and time and gives us insight into how the spatiotemporal properties of touch are processed.
Discovery of the Cutaneous Rabbit Effect
The Cutaneous Rabbit Effect was first discovered in the Cutaneous Communication Laboratory at Princeton University when Frank Geldard and his colleagues were testing cutaneous perception and realized that under some conditions of timing touches were wildly mislocalized. The basic configuration described in the first published account of the phenomenon (Geldard and Sherrick, 1972) consisted of a series of briefly presented tactile stimuli presented in direct succession at two positions along the forearm. In that particular setup, 5 stimuli each were presented at two positions 10 cm apart in direct succession with stimulus durations of 2 ms and temporal intervals of 40–80 ms and without any temporal gap between the two positions. Strikingly, these stimuli were not perceived at their veridical positions but rather spread out between them, reminiscent of a hopping rabbit. This led to the name of the effect, which is still widely used today, even though Geldard (1975, p. 30) tried to introduce “saltation” as a more scientific term early on.
Geldard and colleagues were at first fascinated by the complex perceptual patterns evoked by multiple stimuli and positions. For instance, they quickly realized that the hops were perceived to traverse longer distances if they reduced the number of taps at each location. Vice versa, increasing the number of taps at each location shortened perceived hop distance. Furthermore, adding more stimulus positions extended the range of the effect, so that the “rabbit” could jump along the whole arm, from wrist to shoulder (Geldard and Sherrick, 1972). The lab went on to document the preconditions and limitations of the CRE by varying the stimuli parameters, but many of these studies remained unpublished (see here: http://tactileresearch.org/).
The original CRE consisted of a series of multiple taps presented at two or more positions. This general setup can be varied in respect to number and distance of stimulus positions, number of stimuli, and inter-stimulus intervals. In order to yield a clearer view of specific mechanisms of the illusion, however, subsequent studies mainly focused on simpler stimulus configurations consisting of just two or three taps presented at two positions.
The simplest variant—originally termed the “utterly reduced rabbit” by Geldard (Geldard, 1975) —consists of just two taps presented at two positions, typically 10 cm apart. The “reduced rabbit” is an extension of the “utterly reduced rabbit” with an additional reference stimulus presented at the first position well before the two-tap pattern. In most published research, CRE is used synonymously with either the two-tap or the three-tap variant.
CRE and saltation
The major phenomenological property of the CRE is that the perceived position of the first stimulus is shifted towards the second stimulus. More generally, the perceived shifts or jumps of each stimulus toward one another in the CRE are termed sensory saltation (Geldard, 1975, 1982). Given the right conditions (see next section), in the basic two-tap variant with equal stimulus presentation time and intensity, the first stimulus will be shifted towards the position of the second stimulus. Originally, the second stimulus was not expected to shift at all, hence the terms “attractee” for the first stimulus, and “attractant” for the second stimulus (Geldard, 1975, 1982). However, newer findings show that the second stimulus can be mislocalized towards the first stimulus (Kilgard and Merzenich, 1995; Trojan et al., 2010). Typically, the shift of the second stimulus will be considerably smaller, if present at all (Trojan et al., 2010), but under specific experimental conditions it may become equally large as the shift of the first stimulus (Kilgard and Merzenich, 1995).
The CRE is only observed within a range of temporal intervals. These temporal intervals are typically reported as the interstimulus interval (ISI) or the stimulus onset asynchrony (SOA). The ISI is the time between the end of one stimulus and the beginning of the other. SOA is the time between the beginning of one stimulus and the beginning of the other stimulus. To avoid confusion we have referred to these temporal intervals as delays.
Stimuli given at long temporal delays are localized near veridical, but as the delay is reduced the perceived location of the taps at each contact point will begin to scatter, a point termed “exodus” by Geldard (1975, 1982). It is unclear where exodus occurs, as it was apparently observed at 280 ms in the original CRE but was subject to substantial individual variability (Geldard, 1982) whereas in the reduced versions of the CRE there is already substantial attractee displacement even at intervals of 1020 ms (Trojan et al., 2010). The shorter the delay between the stimuli, the stronger the saltation effect becomes, typically leading to large attractee displacements towards the attractant. If the delay in the original CRE is reduced all the way to ~20ms, “co-incidence” can be observed, in which the last stimulus at an attractee location is shifted to the next attractor (Wieland, 1960, Geldard 1982), but only for certain reporting methods (see Trojan et al., 2010).
The stimulus spacing can influence whether the CRE can be induced at all and if so the degree of saltation. Geldard (1982) determined the maximal distances over which saltation could be induced at several body sites. Generally, these distances were larger when the stimuli were presented along the body axis in lateral–distal direction rather than in other orientations. The absolute extent of the reported distances in that study—from 6 cm at the dorsal forearm to 8 cm at the posterior thigh—are in conflict with other studies demonstrating the CRE at larger distances. For the forearm, which has been the most studied site for the CRE, it has been induced over distances of up to 23 cm (Flach and Haggard, 2006).
In conflict with Geldard’s (1982) original observations, the CRE can be induced with stimulus patterns crossing the body mid-line, both at the forehead (Trojan et al., 2009) and at the abdomen (Trojan et al., 2010). Furthermore, there is some evidence that the CRE also works even if the stimulated patches of skin are anatomically distinct. If, for instance, the first stimulus is presented on one arm and the second stimulus on the other, saltation can be observed if the arms are held close together (Eimer et al., 2005). Even more impressively, if stimuli are presented on the left and right index finger tips, the effect can be “felt” on a stick held between them (Miyazaki et al., 2010).
In combination, these findings question the existence of a strict upper spatial limit for the CRE. Obviously, saltation is not only determined by the proximity of the stimuli on the 2D skin surface, but also by the proximity in 3D external space (see also Trojan et al., 2014; Warren et al., 2010). Whether 2D or 3D representations—or a combination of both—are employed in the spatial perception of a saltatory stimulus may depend on various factors, such as instructions and task demands, and possibly influences the spatial extent of the CRE.
The CRE can be induced at stimulus intensities ranging from barely detectable to painful (Trojan et al., 2006). However, tactile stimuli can be localized better the stronger they are (Steenbergen et al., 2014). Thus, weaker stimuli imply a larger spatial uncertainty, allow for larger mislocalisation, and accordingly result in greater saltation (Tong et al., 2016). Furthermore, intensity affects the saliency of individual stimuli and may influence attention, leading to similar effects as those reported by Kilgard & Merzenich (1995).
Studies have used varying methods for measuring the CRE. Some studies have used a simple detection method, asking whether or not a touch was perceived at a predefined position (e.g., Blankenburg et al., 2006). This yes-no method is unsuited to measuring the perceived displacement of the attractee and attractor locations in relation to their spatiotemporal configuration. Furthermore, yes-no methods have large individual variability as participants have different criterions for declaring they detected touch. Forced choice methods in which the subject can choose amongst several stimulus positions (e.g., Flach and Haggard, 2006) overcome this problem but still have limited sensitivity. More sensitive methods include the verbal estimation of location or participant-led adjustment of the attractee-attractant delay to achieve a predetermined amount of displacement (Geldard, 1975). Unfortunately these estimation and reproduction methods complicate matters due to their higher order cognitive requirements. Pointing is probably the most intuitive and straightforward way to report positions on the body surface. It is highly sensitive, and less likely to suffer from cognitive reporting biases (Trojan et al., 2010). Furthermore, it can provide parametric spatial measures not only of the perceived position of the saltatory stimulus, but of all stimuli involved in a pattern.
It is not surprising that studies using different reporting methods have come to conflicting conclusions. For instance, using just one arbitrary position for yes/no judgments can lead to massive under- or overestimation of the CRE, depending on where this position is located; and effects of the stimulation pattern on the attractant rather than the attractee can only be identified if the perceived position of the latter is actually assessed. Despite these methodological differences, most studies support—or at least do not contradict—the core aspects of the CRE: perceived spatial contraction with reduced temporal delay and a displacement of the attractee towards the attractant.
Saltation: multiple biases?
The compressive effects of the CRE are likely due to multiple biases. Interestingly a single touch stimulus, given at an intensity similar to that often used in the CRE, is itself subject to a small spatial bias (Trojan et al., 2010). When presented on the forearm weak stimuli are biased toward the middle of the forearm (Green, 1982; Steenbergen et al., 2014). This localization shift could represent a bias towards the immediately preceding stimulus or statistical properties of the stimulus distribution (Chalk et al., 2010; Steenbergen et al., 2014) or a general bias to the middle of the response space (Huttenlocher et al., 1991).
It also appears that a single touch is subject to temporal bias. The time between a touch and its conscious detection is limited by nerve conduction velocity. A touch on the ankle takes 50 ms longer than a touch on the forehead to reach the brain. If simultaneous touch is given to the ankle and forehead, the forehead touch is often judged first (Harrar and Harris, 2005) but not by as much as predicted for the longer conduction time from the ankle (Bergenheim et al., 1996). This bias is removed when the two touches are perceptually bound, such as when you touch your leg with your hand (Von Békésy, 1963). Thus a single touch is subject to a relatively small temporal bias, which is dependent on its distance from the brain.
The saltatory bias in the CRE can be thought of as two biases: a contraction and a position shift. The evidence for two biases is obvious when attention is directed to the location at which one of the stimuli will appear. Kilgard and Merzenich (1995) found that localization is shifted toward the attractee if attention if cued at that location (and vice versa), but the distance between the localized attractee and attractant is unchanged. Whereas when they reduced the temporal delay and held attention constant, a contraction was observed.
Models of sensory saltation
Numerous models have been proposed to account for the saltatory effects of the CRE. Willard Brigner (1988) put forward the space-time rotation model to explain the reduced rabbit pattern. His hypothesis was that spatial coordinates are rotated such that the stimuli are now closer together on the space axis. It is unclear how this transformation would occur and how it would explain the percept arising from more complex stimulus configurations. Similar models posit that a constant velocity is desired across multiple locations at the cost of adjusting space and time (Collyer, 1977; Jones and Huang, 1982), but these cannot explain the utterly reduced rabbit configuration. In attempt to account for some of these shortcomings Wiemer (2000) proposed a model in which the average time between two locations being stimulated is used as a proxy for the distance between them. Consequently skin locations that are frequently stimulated close together in time should come to be represented adjacently in the somatosensory cortex. While this model may perform well on average, it wrongly predicts that length expansion occurs for rabbit-like stimuli with long temporal delays.
Does the percept for each variant of the CRE rely on separate mechanisms, or can they be explained under a single model? An important consideration for the skin is that temporal resolution is much better than the spatial resolution. Daniel Goldreich hypothesized that the saltatory biases of the CRE result from the integration of an expectation for speed (Goldreich, 2007). This Bayesian observer model predicts that when we are uncertain about the spatial properties of a pattern (as in the CRE) we defer to a prior expectation for slow speeds of tactile motion. Thus consistent with the CRE, at short temporal delays a slow moving object (or spatiotemporal pattern) must only have moved a short distance. A similar low speed prior operates in vision (Stocker and Simoncelli, 2006; Weiss et al., 2002), where experimental manipulation of the low speed prior has been shown to influence perceived motion (Sotiropoulos et al., 2011). Stocker and Simoncelli (2006) proposed that if such shifts come from priors that these priors might be represented in area MT, which was recently shown to be involved in perceiving tactile motion (Amemiya et al., 2017). Therefore further tactile studies should consider area MT as a candidate location for a velocity prior. Further evidence for the Bayesian observer model is given by the observation that using a weaker stimulus results in greater saltation (Tong et al., 2016). Ernst and Banks (2002) showed that when integrating information from different sensory inputs that the weighting given to the input is related to the acuity of that input (i.e. inputs with lower variance are given more weighting). In the CRE situation, modelling suggests that a weak input is given less weight and the prior expectation for low speed more weight, resulting in greater saltation (Tong et al., 2016).
The Bayesian observer model also assumes that we have an expectation that sequential touch stimuli arriving nearby in space and time are in some way connected. That is the attractee influences the perceived attractor location, and the attractor influences the perceived attractee location. The former might be referred to as a prediction and the latter, where perceived location of one stimulus in influenced by stimuli presented after it, termed post-diction (Eagleman and Sejnowski, 2000). This assumption about connectivity is likely valid – as shown by the brain’s adjustment for neural latency mentioned above when the touches are in the same external space and that the two-point discrimination threshold is lower for sequentially presented stimuli.
Neural processing of spatiotemporal stimuli
Geldard and colleagues initially hypothesized that the CRE was caused by mechanical transduction of the stimuli by the skin. This hypothesis was put to rest in their initial paper when they showed that the CRE was intact when electro-cutaneous stimuli were used, succinctly summed up by the authors, “the ‘rabbit’ could not be electrocuted”. Geldard and colleagues (1985, 1982) then proposed that processing of the CRE stimuli occurs in the primary somatosensory cortex on the basis of their finding that the CRE does not cross the midline. The basis for this proposal is flawed as others have found that the CRE does cross the body midline, as measured by pointing responses (Trojan et al., 2010) suggesting that the CRE is not restricted to one hemisphere. The CRE is not simply restricted to cutaneous 2D space; it can cross the limbs, requiring access to proprioceptive and visual information (Eimer et al., 2005). It can also extend onto tools held in the hands (Miyazaki et al., 2010), cross the visual blind spot (Lockhead et al., 1980), and switch between different sensory modalities (Asai and Kanayama, 2012).
We also know that touch location is not simply processed in S1. Although there is an orderly matching from axons in the spinal cord to S1, the map in S1 is distorted compared the periphery. Our perception of touch location is mostly veridical so there must be cross talk between S1 input and higher order representations. Furthermore spatiotemporal patterns are not just processed in S1, with a study showing clear evidence for SII processing (Zhu et al., 2007). The final touch location is likely coded in external reference frame co-ordinates, perhaps centered on the head (Batista et al., 1999). This set of co-ordinates requires the integration of skin-based and external reference frames, which no doubt requires higher order processing (for models see Badde and Heed, 2016).
In humans the only study we know of to investigate the neural mechanisms of the CRE was motivated by the finding, now known to be incorrect, that the CRE does not cross the body midline. The study provided inconclusive evidence for increased activity at the location in S1 of the illusory stimulus (Blankenburg et al., 2006). However, this was problematic as the stimulus patterns were likely not experientially similar as they were measured using an insensitive detection method. For example, Cholewiak and Collins (2000) presented a linear pattern and a saltatory pattern and found that on only 63% of trials were perceived as identical. The Blankenburg study also found similar increases in higher order areas such as secondary somatosensory cortex, which is known to receive inputs from both hemispheres. Interestingly, in a visual motion illusion, the representation of position only became distorted at higher levels of the cortex (Kanai and Verstraten, 2006). In touch, the findings are inconclusive, but suggest a role for more than one higher order area of the brain mediating the rabbit effect.
Saltation in other modalities
Saltation is not restricted to touch, as it is observed within and between other sensory modalities. Saltatory effects are observed for cutaneous heat and pain stimuli (Trojan et al., 2006), auditory stimuli (Bremer et al., 1977; Shore et al., 1998), and in vision (Lockhead et al., 1980). The effects of a CRE stimulus configuration within a given sensory modality are not purely locational, for instance visual saltation of two differently colored stimuli can result in a blending of the colors (Geldard, 1976). Further they are not only unimodal, for instance the CRE can hop along a stick held between the left and right hand (Miyazaki et al., 2010). Similarly a visual flash that is congruent with the CRE strengthens the effect, and an incongruent one attenuates it (Yao et al., 2009; Asai and Kanayama, 2012). Hence the CRE, or at least CRE-like effects reflect the general principles of spatiotemporal processing.
Comparison with other spatiotemporal illusions
The CRE has many perceptual and mechanistic similarities to other spatiotemporal configurations. In the Tau effect the two distances between three equally spaced stimuli depend upon their relative temporal intervals. Such that the stimulus pair with the longer temporal interval is perceived as further apart than the stimulus pair with the shorter temporal interval (Helson and King, 1931). In the Kappa effect, the temporal intervals are held constant and the spatial intervals varied such that the perceived temporal interval between sequential stimulus locations depends upon their relative spatial distance (Cohen et al., 1953). Critically, the Tau and Kappa effects differ from the CRE, as they cannot be reduced down to two-tap patterns.
Often the CRE is confused with apparent motion, which can arise from the same spatiotemporal configuration. The percept of one moving stimulus can emerge at short temporal delays, termed apparent motion (Kirman, 1974; Sherrick and Rogers, 1966). In contrast, the CRE is distinguished by its discrete perception at a well-defined position/s. At certain delays an observer may switch between the percept of apparent motion and that of the CRE (Sherrick, 1968). The apparent motion percept can be forced if a continuous motion context is given on either side of the CRE (Nguyen et al., 2016). It is interesting to consider that although apparent motion is always perceived to arise from one object, this does not have to be the case for the CRE. If Gestalt principles apply—which does not have to be the case—the simplest perceptual solution is that the CRE stimulus arises from one object hopping in a relatively smooth motion (Shore et al., 1998).
If we look back to the original CRE it is difficult to predict the percept that should arise. The original CRE plays out over longer spatial and temporal intervals than the reduced versions. Due to its complexity, the percept may be subject to mechanisms that stabilize space and time in local and global contexts.
Another outstanding mystery of the CRE is that under natural conditions a shift towards the attractant is observed. If the effect is attention dependent it is unclear why attention should be naturally directed to the attractant, as this is observed in the utterly reduced rabbit in which no anticipatory mechanism could be used to predict the direction of the second stimulus relative to the first. Furthermore it is observed in the reduced rabbit in which a reference stimulus is given at the attractee location a second before the CRE is given – existing models predict that attention should be cued to this location. This observation is not constrained to discrete stimuli as it is observed for continuous motion or when continuous motion occurs either side of a spatial gap. We may learn more about this phenomenon by further investigating the biases as contractions and shifts. As these biases may be subtle the use of a robust and comparable methodology for reporting localization, such as pointing, will be critical to unveiling their mechanisms. Additional experimental verification of the low-speed prior assumed by Bayesian models of the CRE may prove informative. Other properties of the lifetime statistics of touch to the skin might show that priors for motion on the skin have non-uniform velocity profiles.
To uncover the neural mechanisms of the CRE a well thought out study is necessary to directly compare the activity resulting from a displaced saltatory stimulus compared to an undisplaced stimulus. Looking beyond the CRE it is clear there is more to learn about the neural processing of spatiotemporal touch stimuli. Existing evidence points to higher order areas of the brain. Pinpointing these areas, what properties they process, and how they work together are questions for future research. A better understanding of the limitations of touch processing will guide the development of emerging technologies that rely on touch such as human-machine interfaces, exoskeletons, and sensory substitution/addition devices.
In summary, the Cutaneous Rabbit Effect shows that spatiotemporal tactile perception is subject to substantial position bias. The CRE only occurs under a prescribed set of conditions, requiring weak touch, and only working over a range of spatial and temporal intervals, which are interdependent. The CRE demonstrates that the perceived position of a tactile stimulus is dependent on stimuli presented before or after it and/or at different positions. Although there are many variants of the CRE, only the Bayesian inference model seems to provide a unifying model of the observed position biases. Further work is required to determine where the neural activity that reflects this model takes place, and if the environment statistics of touch conform to low speeds. Future studies might also seek to explain more complex spatiotemporal patterns or to provide a more complete explanation of the spatial biases of the CRE.
- Amemiya, T., Beck, B., Walsh, V., Gomi, H., Haggard, P. (2017). Visual area V5/hMT+ contributes to perception of tactile motion direction: a TMS study. Sci. Rep. 7.
- Asai, T., Kanayama, N. (2012). “Cutaneous rabbit” hops toward a light: unimodal and cross-modal causality on the skin.. Front. Percept. Sci. 3: 427.
- Badde, S., Heed, T. (2016). Towards explaining spatial touch perception: Weighted integration of multiple location codes.. Cogn. Neuropsychol. 33: 26-47.
- Batista, A.P., Buneo, C.A., Snyder, L.H., Andersen, R.A. (1991). Reach plans in eye-centered coordinates.. Science 285: 257–260.
- Bergenheim, M., Johansson, H., Granlund, B., Pederson, J. (1996). Experimental evidence for a synchronization of sensory information to conscious experience.. Sci. Conscious. First Tucson Discuss. Debates MIT Press Camb.: 303-310.
- Blankenburg, F., Ruff, C.C., Deichmann, R., Rees, G., Driver, J. (2006). The Cutaneous Rabbit Illusion Affects Human Primary Sensory Cortex Somatotopically.. PLOS Biol. 4: e69.
- Bremer, C.D., Pittenger, J.B., Warren, R., Jenkins, J.J. (1977). An illusion of auditory saltation similar to the cutaneous “rabbit.”. Am. J. Psychol. 90: 645–654.
- Brigner, W.L. (1988). Saltation as a rotation of space-time axes.. Percept. Mot. Skills 66: 637–638.
- Chalk, M., Seitz, A.R., Seriès, P. (2010). Rapidly learned stimulus expectations alter perception of motion.. J. Vis. 10: 2.
- Cholewiak, R.W., Collins, A.A. (2000). The generation of vibrotactile patterns on a linear array: Influences of body site, time, and presentation mode.. Atten. Percept. Psychophys. 62: 1220–1235.
- Cohen, J., Hansel, C., Sylvester, J. (1953). A new phenomenon in time judgment.. Nature 172: 901.
- Collyer, C. (1977). Discrimination of spatial and temporal intervals defined by three light flashes: Effects of spacing on temporal judgments and of timing on spatial judgments.. Atten. Percept. Psychophys. 21: 357–364.
- Eagleman, D.M., Sejnowski, T.J. (2000). Motion integration and postdiction in visual awareness.. Science 287: 2036–2038.
- Eimer, M., Forster, B., Vibell, J. (2005). Cutaneous saltation within and across arms: a new measure of the saltation illusion in somatosensation.. Percept. Psychophys. 67: 458–468.
- Ernst, M.O., Banks, M.S. (2002). Humans integrate visual and haptic information in a statistically optimal fashion.. Nature 415: 429-433.
- Flach, R., Haggard, P. (2006). The cutaneous rabbit revisited.. J. Exp. Psychol. Hum. Percept. Perform. 32: 717–732.
- Geldard, F.A. (1985). The mutability of time and space on the skin.. J. Acoust. Soc. Am. 77: 233–237.
- Geldard, F.A. (1982). Saltation in somesthesis.. Psychol. Bull. 92: 136.
- Geldard, F.A. (1976). The saltatory effect in vision.. Sens. Processes 1: 77–86.
- Geldard, F.A.. Sensory saltation: metastability in the perceptual world.. Lawrence Erlbaum Associates, New York..
- Geldard, F.A., Sherrick, C.E. (1972). The cutaneous “rabbit”: a perceptual illusion.. Science 178: 178–179.
- Goldreich, D. (2007). A Bayesian perceptual model replicates the cutaneous rabbit and other tactile spatiotemporal illusions.. PLoS ONE 2: e333.
- Green, B.G. (1982). The perception of distance and location for dual tactile pressures.. Percept. Psychophys. 31: 315–323.
- Harrar, V., Harris, L.R. (2005). Simultaneity constancy: detecting events with touch and vision.. Exp. Brain Res. 166: 465–473.
- Helson, H., King, S. (1931). The tau effect: An example of psychological relativity.. J. Exp. Psychol. 14(3): 202–217.
- Huttenlocher, J., Hedges, L.V., Duncan, S. (1991). Categories and particulars: Prototype effects in estimating spatial location.. Psychol. Rev. 98: 352.
- Jones, B., Huang, Y.L. (1982). Space-time dependencies in psychophysical judgment of extent and duration: Algebraic models of the tau and kappa effects.. Psychol. Bull. 91: 128.
- Kanai, R., Verstraten, F.A. (2006). Visual transients reveal the veridical position of a moving object.. Perception 35: 453–460.
- Kilgard, M.P., Merzenich, M.M. (1995). Anticipated stimuli across skin.. Nature 373: 663.
- Kirman, J.H. (1974). Tactile apparent movement: The effects of interstimulus onset interval and stimulus duration.. Percept. Psychophys. 15: 1-6.
- Lockhead, G.R., Johnson, R.C., Gold, F.M. (1980). Saltation through the blind spot.. Percept. Psychophys. 27: 545–549.
- Miyazaki, M., Hirashima, M., Nozaki, D. (2010). The “cutaneous rabbit” hopping out of the body.. J. Neurosci. 30: 1856–1860.
- Nguyen, E.H.L., Taylor, J.L., Brooks, J., Seizova-Cajic, T. (2016). Velocity of motion across the skin influences perception of tactile location.. J. Neurophysiol. 115: 674.
- Sherrick, C.E. (1968). Bilateral apparent haptic movement.. Percept. Psychophys. 4: 159–160.
- Sherrick, C.E., Rogers, R. (1966). Apparent haptic movement.. Percept. Psychophys. 1: 175–180.
- Shore, D.I., Hall, S.E., Klein, R.M. (1998). Auditory saltation: a new measure for an old illusion.. J. Acoust. Soc. Am. 103: 3730–3733.
- Sotiropoulos, G., Seitz, A.R., Seriès, P. (2011). Changing expectations about speed alters perceived motion direction.. Curr. Biol. 21: R883–R884.
- Steenbergen, P., Buitenweg, J.R., Trojan, J., Veltink, P.H. (2014). Tactile localization depends on stimulus intensity.. Exp. Brain Res. 232: 597–607.
- Stocker, A.A., Simoncelli, E.P. (2006). Noise characteristics and prior expectations in human visual speed perception.. Nat. Neurosci. 9: 578–585.
- Tong, J., Ngo, V., Goldreich, D. (2016). Tactile length contraction as Bayesian inference.. J. Neurophysiol. 116: 369.
- Trojan, J., Getzmann, S., Moller, J., Kleinbohl, D., Holzl, R. (2009). Tactile-auditory saltation: spatiotemporal integration across sensory modalities.. Neurosci. Lett. 460: 156–160.
- Trojan, J., Heil, M., Maihöfner, C., Hölzl, R., Kleinböhl, D., Flor, H., Benrath, J. (2014). Spatiotemporal integration of tactile patterns along and across fingers.. Neuropsychologia 53: 12–24.
- Trojan, J., Stolle, A.M., Kleinbohl, D., Morch, C.D., Arendt-Nielsen, L., Holzl, R. (2006). The saltation illusion demonstrates integrative processing of spatiotemporal information in thermoceptive and nociceptive networks.. Exp. Brain Res. 170: 88–96.
- Trojan, J., Stolle, A.M., Mršić Carl, A., Kleinböhl, D., Tan, H.Z., Hölzl, R. (2010). Spatiotemporal integration in somatosensory perception: effects of sensory saltation on pointing at perceived positions on the body surface.. Front. Psychol. 1: 206.
- Von Békésy, G. (1963). Interaction of paired sensory stimuli and conduction in peripheral nerves.. J. Appl. Physiol. 18: 1276–1284.
- Warren, J.P., Santello, M., Helms Tillery, S.I. (2010). Electrotactile stimuli delivered across fingertips inducing the Cutaneous Rabbit Effect.. Exp. Brain Res. 206: 419–426.
- Weiss, Y., Simoncelli, E.P., Adelson, E.H. (2002). Motion illusions as optimal percepts.. Nat. Neurosci. 5: 598–604.
- Wieland, B.A. (1960). The Interaction of Space and Time in Cutaneous Perception.. Am. J. Psychol. 73: 248–255.
- Wiemer, J., Spengler, F., Joublin, F., Stagge, P., Wacquant, S. (2000). Learning cortical topography from spatiotemporal stimuli.. Biol. Cybern. 82: 173–187.
- Yao, R., Simons, D., Ro, T. (2009). Keep your eye on the rabbit: Cross-modal influences on the cutaneous rabbit illusion.. J. Vis. 9: 705.
- Zhu, Z., Disbrow, E.A., Zumer, J.M., McGonigle, D.J., Nagarajan, S.S. (2007). Spatiotemporal integration of tactile information in human somatosensory cortex.. BMC Neurosci. 8: 21.
- Gallace, A., 2014. In touch with the future : the sense of touch from cognitive neuroscience to virtual reality C. Spence, ed., Oxford : Oxford University Press.
- Grunwald, M (Ed.) (2008). Human Haptic Perception: Basics and Applications. Springer Science & Business Media.