letters to nature height using software available from Sontek . From each time series we calculated mean near-bed velocity independent of ow direction . Mean near-bed velocity was compared between treatments using a non-parametric Mann Whitney U-test because variances could not be transformed to satisfy parametric assumptions . 26 . Hart , D. D . The adaptive signi cance of territoriality in lter-feeding larval black ies -LRB- Diptera : Simuliidae -RRB- . Oikos 46 , 88 92 -LRB- 1986 -RRB- . 27 . Englund , G. Asymmetric resource competition in a lter-feeding stream insect -LRB- Hydropsyche siltalai : Trichoptera -RRB- . Freshwat . Biol . 26 , 425 432 -LRB- 1991 -RRB- . 28 . Okamura , B. Microhabitat variation and patterns of colony growth and feeding in a marine bryozoan . Ecology 73 , 1502 1513 -LRB- 1992 -RRB- . 29 . Vogel , S. Life in Moving Fluids -LRB- Princeton Univ. . Press , Princeton , 1994 -RRB- . 30 . Finnigan , J. Turbulence in plant canopies . Annu . Rev. Fluid Mech . 32 , 519 571 -LRB- 2000 -RRB- . Resource consumption After measuring near-bed ow , 278 mg of SPM stained with Rose Bengal dye was released as a single pulse into each stream19 . Larvae were allowed to feed for 15 min -LRB- a duration less than gut passage times -RRB- before they were removed from their nets and frozen . We dissected larval guts later and measured the diameter and band length of stained SPM in foreguts using a dissecting microscope and ocular micrometer . Because foreguts are essentially cylindrical , the consumption of SPM by each larva was calculated as mm3 SPM by p band length in foregut -LRB- 1/2 foregut diameter -RRB- 2 . Per capita consumption was compared between treatments using t-tests . Total resource consumption -LRB- the summed consumption of SPM by all larvae inhabiting a stream -RRB- was compared between treatments using a non-parametric Mann Whitney U-test because variances could not be transformed to satisfy parametric assumptions . We used a paired t-test to compare observed resource consumption in mixed assemblages with the total expected SPM consumption2 . Acknowledgements We thank D. Doak , D. Hart , M. Loreau , P. Morin , S. Naeem , K. Sebens , D. Tilman , J. Thomson and T. Welnitz for comments ; and S. Brooks for advice on hydrodynamic measurements . This work was supported by grants from the National Science Foundation to M.A.P. and to B.J.C. Competing interests statement The authors declare that they have no competing nancial interests . Correspondence and requests for materials should be addressed to B.J.C. -LRB- e-mail : bc84@umail.umd.edu -RRB- . Bed roughness At the end of the experiment we recorded the downstream location of every caddis y net and measured their maximum heights and widths . We calculated the average maximum height and density of the roughness elements , as well as their aggregation and topographical complexity . Aggregation measures the spacing between roughness elements as the mean euclidian distance between neighbouring nets . Topographical complexity measures the spatial uniformity or non-uniformity of roughness elements as the standard deviation of the parabolic area -LRB- in mm2 -RRB- of catchnets . An s.d. of 0 indicates a uniform streambed -LRB- no topographical complexity -RRB- , whereas a higher s.d. indicates greater streambed complexity . We compared all four aspects of bed roughness between treatments using t-tests . Received 8 October ; accepted 26 November 2001 . 1 . Hector , A. et al. . Plant diversity and productivity experiments in European grasslands . Science 286 , 1123 1127 -LRB- 1999 -RRB- . 2 . Loreau , M. & Hector , A. Partitioning selection and complementarity in biodiversity experiments . Nature 412 , 72 76 -LRB- 2001 -RRB- . 3 . Mulder , C. , Uliassi , D. & Doak , D. Physical stress and diversity productivity relationships : The role of positive interactions . Proc . Natl Acad . Sci . USA 98 , 6704 6708 -LRB- 2001 -RRB- . 4 . Tilman , D. et al. . Diversity and productivity in a long-term grassland experiment . Science 294 , 843 845 -LRB- 2001 -RRB- . 5 . Jones , C. G. , Lawton , J. H. & Shachack , M. Positive and negative effects of organisms as physical ecosystem engineers . Ecology 78 , 1946 1957 -LRB- 1997 -RRB- . 6 . Luttge , U. Physiological Ecology of Tropical Plants -LRB- Springer , Berlin , 1997 -RRB- . 7 . Naeem , S. , Thompson , L. J. , Lawler , S. P. , Lawton , J. H. & Wood n , R. M. Declining biodiversity can alter the performance of ecosystems . Nature 368 , 734 737 -LRB- 1994 -RRB- . 8 . Cardinale , B. J. , Nelson , K. & Palmer , M. A. Linking species diversity to the functioning of ecosystems : on the importance of environmental context . Oikos 91 , 175 183 -LRB- 2000 -RRB- . 9 . Chapin , F. S. et al. . Consequences of changing biodiversity . Nature 405 , 234 242 -LRB- 2000 -RRB- . 10 . Tilman , D. , Lehman , D. & Thompson , K. Plant diversity and ecosystem productivity : theoretical considerations . Proc . Natl Acad . Sci . USA 94 , 1857 1861 -LRB- 1997 -RRB- . 11 . Hooper , D. & Vitousek , P . The effects of plant composition and diversity on ecosystem processes . Science 277 , 1302 1305 -LRB- 1997 -RRB- . 12 . Huston , M. Hidden treatments in ecological experiments : re-evaluating the ecosystem function of biodiversity . Oecologia 110 , 449 460 -LRB- 1997 -RRB- . 13 . Wardle , D. A. Is `` sampling effect '' a problem for experiments investigating biodiversity ecosystem function relationships ? Oikos 87 , 403 410 -LRB- 1999 -RRB- . 14 . Fridley , J. D . The in uence of species diversity on ecosystem productivity : how , where , and why ? Oikos 93 , 514 526 -LRB- 2001 -RRB- . 15 . Tilman , D. et al. . The in uence of functional diversity and composition on ecosystem processes . Science 277 , 1300 1302 -LRB- 1997 -RRB- . 16 . Chapin , S. et al. . Ecosystem consequences of changing biodiversity . BioScience 48 , 45 52 -LRB- 1998 -RRB- . 17 . Palmer , M. A. et al. . Biodiversity and ecosystem function in freshwater sediments . Ambio 26 , 571 577 -LRB- 1997 -RRB- . 18 . Nowell , A. R. M. & Jumars , P. Flow environments of aquatic benthos . Annu . Rev. Ecol . Syst . 15 , 303 328 -LRB- 1984 -RRB- . 19 . Cardinale , B. J. & Palmer , M. A. Disturbance moderates biodiversity ecosystem function relationships : evidence from caddis y assemblages in stream mesocosms . Ecology -LRB- in the press -RRB- . 20 . Loudon , C. & Alstad , D. N. Theoretical mechanisms of particle capture : Predictions for hydropsychid distributional ecology . Am . Nat . 135 , 360 381 -LRB- 1990 -RRB- . 21 . Eckman , J. E. , Nowell , A. R. M. & Jumars , P. J. Sediment destabilization by animal tubes . J. Mar. . Res . 39 , 361 374 -LRB- 1981 -RRB- . 22 . Johnson , A. Flow around phoronids : Consequences of a neighbor to suspension feeders . Limnol . Oceanogr . 35 , 1395 1401 -LRB- 1990 -RRB- . 23 . Huettel , M. & Gust , G. Impact of bioroughness on interfacial solute exchange in permeable sediments . Mar. . Ecol . Prog . Ser . 89 , 253 267 -LRB- 1992 -RRB- . 24 . Butman , C. A. , Frechette , M. , Geyer , W. R. & Starczak , V. R. Flume experiments on food supply to the blue mussel Mytilus edulis L. as a function of boundary-layer ow . Limnol . Oceanogr . 39 , 1755 1768 -LRB- 1994 -RRB- . 25 . Sebens , K. P. , Witting , J. & Helmuth , B. Effects of water ow and branch spacing on particle capture by the reef coral Madracis mirabilis -LRB- Duchassaing and Michelotti -RRB- . J. Exp . Mar. . Biol . Ecol . 211 , 1 28 -LRB- 1997 -RRB- . ... . Humans integrate visual and haptic information in a statistically optimal fashion Marc O. Ernst * & Martin S. Banks Vision Science Program/School of Optometry , University of California , Berkeley 94720-2020 , USA ... . When a person looks at an object while exploring it with their hand , vision and touch both provide information for estimating the properties of the object . Vision frequently dominates the integrated visual haptic percept , for example when judging size , shape or position1 3 , but in some circumstances the percept is clearly affected by haptics4 7 . Here we propose that a general principle , which minimizes variance in the nal estimate , determines the degree to which vision or haptics dominates . This principle is realized by using maximum-likelihood estimation8 15 to combine the inputs . To investigate cue combination quantitatively , we rst measured the variances associated with visual and haptic estimation of height . We then used these measurements to construct a maximum-likelihood integrator . This model behaved very similarly to humans in a visual haptic task . Thus , the nervous system seems to combine visual and haptic information in a fashion that is similar to a maximum-likelihood integrator . Visual dominance occurs when the variance associated with visual estimation is lower than that associated with haptic estimation . The estimate of an environmental property by a sensory system can be represented by Si f i S 1 where S is the physical property being estimated and f is the operation by which the nervous system does the estimation . The subscripts refer to the modality -LRB- i could also refer to different cues within a modality -RRB- . Each estimate , Si , is corrupted by noise . If the noises are independent and gaussian with variance j 2 , and the i bayesian prior is uniform , then the maximum-likelihood estimate * Present address : Max Planck Institute for Biological Cybernetics , Tubingen 72076 , Germany . NATURE | VOL 415 | 24 JANUARY 2002 | www.nature.com 2002 Macmillan Magazines Ltd 429 letters to nature -LRB- MLE -RRB- of the environmental property is given by 1 = j2 i S wi Si with wi i 1 = j2 j ^ ^ j 2 Thus , the MLE rule states that the optimal means of estimation -LRB- in the sense of producing the lowest-variance estimate -RRB- is to add the sensor estimates weighted by their normalized reciprocal variances8 15 . If the MLE rule is used to combine visual and haptic estimates , SV and SH , the variance of the nal -LRB- visual haptic -RRB- estimate , S , is j2 j2 j2 2 V H 2 3 VH jV jH Thus , the nal estimate has lower variance than either the visual or the haptic estimator . Implementation of MLE integration is shown for two hypothetical cases in Fig. 1 . We examined visual haptic integration quantitatively to determine whether human performance is optimal . Observers looked at and/or felt a raised ridge -LRB- Fig. 2 -RRB- and judged its height -LRB- vertical extent -RRB- . To work out the predictions of the MLE rule , we rst determined the variances of the visual and haptic height estimates -LRB- within-modality -RRB- by conducting discrimination experiments . In the haptic-alone experiment , observers indicated which of two sequentially presented ridges was taller from haptic information alone ; in the visual-alone experiment , they did the same from visual information alone . There were four conditions in the visual experiment that differed in the amount of noise in the stimulus -LRB- see Methods -RRB- . By adding noise we made the visually speci ed height less reliable . Visual-alone and haptic-alone discrimination data are shown in Fig. 3a . The proportion of trials in which the observer indicated that the comparison stimulus -LRB- variable height -RRB- appeared taller than the standard stimulus -LRB- xed height of 55 mm -RRB- is plotted as a function of the height of the comparison stimulus . The dashed red line and symbols represent the haptic discrimination data , and the solid blue curves with open symbols represent the visual data for the four levels of noise . These psychometric functions were well t by cumulative gaussian functions . The discrimination threshold is de ned as the difference between the point of subjective equality -LRB- PSE -RRB- and the height of the comparison stimulus when it is judged taller than the p standard stimulus 84 % of the time . The 84 % point corresponds to 2 times the standard deviation of the underlying estimator . The haptic discrimination threshold was roughly 0.085 times the average ridge height -LRB- which was 55 mm -RRB- . As the noise increased from 0 to 200 % , the visual discrimination thresholds increased from 0.04 to 0.2 times the average height . Thus , when the visual noise was 0 % , the visual discrimination threshold was roughly half the haptic threshold ; when the visual noise was 200 % , the visual threshold was more than double the haptic threshold . In the visual haptic experiment , observers simultaneously looked at and felt two raised ridges that were presented sequentially . In one presentation the visually and haptically speci ed heights were equal -LRB- comparison stimulus -RRB- ; in the other presentation they differed -LRB- standard stimulus -RRB- . The difference -LRB- D -RRB- in the speci ed heights was 6 6 , 6 3 or 0 mm -LRB- the average of SH and SV was 55 mm -RRB- . For each D in the standard stimulus -LRB- randomly presented -RRB- , the height of the comparison stimulus was varied randomly from trial to trial -LRB- 47 63 mm -RRB- . On each trial , the observer indicated which stimulus seemed taller . Figure 3b shows the proportion of trials in which the comparison stimulus was chosen as taller as a function of the height of the comparison stimulus . From these psychometric functions , we estimated the PSE the comparison height appearing equal to the standard height and the just-discriminable change in height -LRB- threshold -RRB- . Using the within-modality data , we can predict what an observer using MLE will do when presented visual and haptic information 2 2 H / V = 1 2 2 H / V = 4 Probability Probability densities Combined Haptic Visual VH H V ^ SH 0.5 wV * 0.5 wH * Psychometric function ^ SV Probability densities Combined Visual Haptic VH V VH H ^ SH 0.8 wV * ^ SV 0.2 wH * Psychometric function Estimated height Proportion ` taller ' Proportion ` taller ' 1.00 0.84 PSE 0.50 T VH 1.00 0.84 PSE 0.50 T VH 0 SH S0 = 5.5 cm SV 0 SH S0 = 5.5 cm SV Physical height Figure 1 Maximum-likelihood estimation integration : two hypothetical situations . Visually and haptically speci ed heights differ by D. Dashed gaussians in the top panels represent probability densities of the -LRB- unbiased -RRB- estimated height from visual and haptic assessment , and solid gaussians represent probability densities for the combined estimate . On the left , the visual and haptic variances are equal -LRB- j2 = j2 1 -RRB- and both their H V weights are 0.5 -LRB- equation -LRB- 2 -RRB- -RRB- . The mean of the combined probability density is therefore equal to the mean of the visual and haptic densities and the variance is reduced by half -LRB- equation -LRB- 3 -RRB- -RRB- . If the observer bases judgements of relative height on the combined 430 probability density , the psychometric function would be a cumulative gaussian -LRB- bottom left -RRB- with a point of subjective equality -LRB- PSE -RRB- equal to the average of the visual and haptic heights of the standard stimulus . On the right , the haptic variance is four times the visual variance : j2 = j2 4 . By equation -LRB- 2 -RRB- , the visual weight -LRB- wV -RRB- is 0.8 and the haptic weight H V -LRB- wH -RRB- is 0.2 . Thus , the combined probability density is shifted towards the visual estimate and its variance is 0.8 times the visual variance -LRB- equation -LRB- 3 -RRB- -RRB- . Accordingly , the psychometric function should be shifted so that the PSE is closer to the visual height of the standard stimulus . NATURE | VOL 415 | 24 JANUARY 2002 | www.nature.com 2002 Macmillan Magazines Ltd letters to nature simultaneously , and we compare these predictions to the performance in the visual haptic experiment . First , we describe the analysis of the PSE data and predictions for the weights . From equation -LRB- 2 -RRB- and the relationship between threshold and estimator variance : wV j2 T2 H H 4 2 wH jV T 2 V where TH and TV are the haptic and visual thresholds -LRB- 84 % points in Fig. 3a -RRB- . Incorporating the normalization assumption -LRB- wV wH 1 -RRB- , the predicted weights for optimal integration are wV T2 H T T2 H 2 V a CRT Stereo glasses and wH T2 V T T2 H 2 V 5 The predicted visual weights are represented by the curve and shaded surround in Fig. 3c . The predicted weights vary signi cantly with the amount of visual noise in the stimulus : the visual weights are higher when the noise level is low , and lower when the noise level is high . Assuming that the visual and haptic estimators are on average unbiased -LRB- SV SV and SH SH -RRB- , the weights can be derived experimentally : wV PSE 2 SH = SV 2 SH 6 where PSE is the height of the comparison stimulus that matched the apparent height of the standard stimulus . The visually and haptically speci ed heights in the standard stimulus , SV and SH , are indicated on the right ordinate . Figure 3c shows that as the noise level was increased the visual weight decreased , and the PSE shifted from SV towards SH . Because the noise level varied randomly from trial to trial , the weights must have been set within the 1-s stimulus presentation . Below , we suggest a mechanism for such dynamic weight adjustment . In summary , the predicted and observed PSEs are similar , suggesting that humans do combine visual and haptic information in a fashion similar to MLE integration . According to the MLE rule , the combined estimates should have lower variance , and therefore lower discrimination thresholds , than either the visual or haptic estimate alone -LRB- equation -LRB- 3 -RRB- -RRB- . To derive predictions for the visual haptic discrimination thresholds , we rewrite equation -LRB- 3 -RRB- : T2 T2 1 1 1 T2 2 V H 2 , 2 2 2 7 VH T VH T V T H TV TH The predicted and observed thresholds are shown in Fig. 3d . The open symbols represent the visual-alone thresholds and the dashed line represents the haptic-alone threshold . The shaded area represents the predicted visual haptic thresholds ; they are always lower than the visual-alone and haptic-alone thresholds at the corresponding noise level . The lled purple symbols represent the observed visual haptic discrimination thresholds ; as noise level increases , the just-noticeable difference in height becomes greater . Most notably , the predicted and observed visual haptic discrimination thresholds are similar . As with the PSE data , this indicates that human observers may combine visual and haptic information in a manner similar to MLE integration . In summary , we found that height judgements were remarkably similar to those predicted by the MLE integrator . Thus , the nervous system seems to combine visual and haptic information in a fashion similar to the MLE rule : visual and haptic estimates are weighted according to their reciprocal variances -LRB- equation -LRB- 2 -RRB- -RRB- . Naturally , it is important to determine whether this rule characterizes the estimation of other stimulus properties such as shape , depth , localization , roughness or compliance . The relative contributions of vision and haptics to perceiving such object properties have been studied previously . For example , subjects have grasped a square while looking at it through a distorting lens that made it appear rectangular1 . The shape of the uni ed percept was determined almost completely by vision , so the phenomenon was called ` visual capture ' . Numerous studies have NATURE | VOL 415 | 24 JANUARY 2002 | www.nature.com Opaque mirror Forcefeedback devices h idt W Visual and haptic scene Noise : 3 cm equals 100 % 3-c ep md th s tep ht eig al h Visu ht eig ic h apt H b Right eye 's image Left eye 's image Figure 2 Apparatus and stimuli . a , Observers viewed the re ection of the visual stimulus , presented on a cathode ray tube -LRB- CRT -RRB- binocularly in a mirror . CrystalEyes -LRB- StereoGraphics -RRB- liquid-crystal shutter glasses were used to present binocular disparity . The surfaces of the stimuli were perpendicular to the line of sight . A head and chin rest limited head movements . The right hand was beneath the mirror and could not be seen . The haptic stimulus was presented with two PHANToM force-feedback devices , one each for the index nger and thumb . b , Stereograms representative of visual stimuli , which should be viewed by cross-fusing . Top row , stereogram has no noise and the horizontal bar is raised above the background . Bottom row , stereogram of bar and background contains noise , with random displacements of dots parallel to the line of sight . 431 2002 Macmillan Magazines Ltd With noise Without noise letters to nature replicated visual capture in shape and size perception3 ,16,17 , depth perception18 and localization2 ,19 21 . But visual capture does not occur in the perception of surface roughness6 ,22 ; instead , perceived roughness is affected nearly equally by haptics and vision . Does a dynamic cue-combination rule , such as the one described here , determine the degree to which vision or haptics dominates ? The statistically optimal means of combining visual and haptic information the MLE rule predicts that visual capture should occur whenever the visual estimate of a property has much less variance than that of the haptic estimate . Haptic capture should be observed when the reverse occurs . We observed behaviour like visual capture when the visual stimulus was noise-free , and behaviour similar to haptic capture when the visual stimulus was quite noisy -LRB- Fig. 3c -RRB- . In visual haptic tasks , the MLE integrator described here always uses information from both sensory systems , so the combined percept will always re ect both sources of information . Different behaviour may be observed when the discrepancy between two information sources is large . With large discrepancies between information sources , the nervous system may exhibit robust behaviour10 in which a discrepant source is discounted9 ,23 . In robust estimation , the weights associated with different information sources are determined by more than the variances of the sensory estimators ; they are also determined by the discrepancy between their estimates . In our experiments , the differences between the visually and haptically speci ed stimuli were never greater than 11 % , and the visual haptic data always exhibited an in uence of both sensory systems . If the differences had been larger , we might a Proportion of trials perceived as ` taller ' 1.00 Haptic 0.75 Visual 0 % 67 % 133 % 200 % Noise level have observed discounting of one sense . It would be interesting to know whether such vetoing occurs when observers become aware of the con ict between visual and haptic inputs . If the nervous system implements MLE integration , the weights must be proportional to the reciprocal variances of the probability densities associated with the visual and haptic estimates of the environmental property in question -LRB- equation -LRB- 2 -RRB- and Fig. 1 -RRB- . Of course , the variances change from one object property to the next -LRB- such as size , shape or roughness -RRB- and from one situation to another -LRB- for example , visual variance increases as the lighting is degraded -RRB- . Does the nervous system need to calculate or learn the variances associated with the visual and haptic estimators for each property and situation to implement MLE integration ? Although explicit calculation or learning may occur24 , there are plausible schemes in which explicit calculation of variances or weights is unnecessary . Consider , for example , a population of visual and haptic neurons , each sensitive to a range of heights . Each neuron has a preferred height but also responds to other heights -LRB- that is , each neuron has a tuning function -RRB- . If the visual input speci es the height clearly -LRB- that is , high contrast , noise-free , and so on -RRB- , then the visual neurons preferring that height respond vigorously and those preferring other heights respond less , and the distribution of response across the population of visual neurons has a well de ned peak . Assume that the distribution across the population of haptic neurons has a less well de ned peak . Multiplication of these two distributions -LRB- pointby-point multiplication where the two populations are in registration according to the stimulus property being estimated -RRB- 25 yields a b Proportion of trials perceived as ` taller ' 1.00 Visual haptic discrimination -LRB- normalized across -RRB- Noise level Within-modality discrimination Visual haptic 0 % 67 % 133 % 0.75 200 % 0.50 0.50 0.25 Standard 0 50 55 60 Comparison height -LRB- mm -RRB- Weights -LRB- PSEs -RRB- 1.0 0 Visual haptic Predicted Empirical ` Visual capture ' 0.25 n = 4 0 45 55 SH SV Normalized comparison height -LRB- mm -RRB- Discrimination thresholds 65 c SV d 0.24 0.20 Threshold 0.16 0.12 0.08 0.04 0.8 0.2 Haptic weight Visual weight 0.6 0.4 0.4 0.6 0.2 0.8 0 1.0 Haptic -LRB- empirical -RRB- Visual -LRB- empirical -RRB- Visual haptic -LRB- predicted -RRB- Visual haptic -LRB- empirical -RRB- PSE SH ` Haptic capture ' 0 67 133 Noise level -LRB- % -RRB- 200 0 0 67 133 Noise level -LRB- % -RRB- 200 Figure 3 Predictions and experimental data . a , Within-modality discrimination . Proportion of trials in which a comparison was perceived as taller than the standard stimulus is plotted against the height of the comparison stimulus . Data were averaged for observers . Height of the standard stimulus was 55 mm . Haptic discrimination data are represented by red crosses and the dashed curve -LRB- best - tting cumulative gaussian -RRB- ; visual discrimination data are represented by blue curves , which correspond to four noise levels . b , Visual haptic discrimination . The average height of visual haptic standard stimulus was 55 mm ; the height difference , D , varied from -6 to +6 mm . To plot the data on the same coordinates , the psychometric functions for each D were shifted laterally by w VD/2 -LRB- w V is obtained from the regression of PSE against D -RRB- . Purple curves represent the different visual noise levels . c , Weights and PSEs . Abscissa represents the noise level , left 432 ordinate represents visual weight -LRB- w V ; haptic weight is 1 - w V -RRB- and right ordinate represents the PSEs relative to S V and S H. Purple symbols represent observed visual weights obtained from regression analysis of PSEs -LRB- equation 6 -RRB- across D. Shaded area represents predicted weights expected from within-modality discrimination -LRB- a ; equation -LRB- 5 -RRB- -RRB- ; its height represents predicted errors given the standard errors of the within-modality discrimination . d , Combined and within-modality discrimination thresholds . Justnoticeable differences in height are plotted against noise level . Thresholds are taken from psychometric functions in a and b. Dashed red line represents haptic-alone threshold ; open blue symbols represent visual-alone thresholds ; lled purple symbols represent combined visual haptic thresholds . Shaded area represents predicted visual haptic thresholds -LRB- equation -LRB- 7 -RRB- -RRB- . NATURE | VOL 415 | 24 JANUARY 2002 | www.nature.com 2002 Macmillan Magazines Ltd letters to nature peak response closer to the visual than the haptic peak , as with MLE integration . If degrading the visual input causes the response distribution of the visual neurons to spread , then multiplication of the visual and haptic distributions yields a peak closer to the haptic peak , again as in MLE integration . Thus , the estimator variances -LRB- and therefore the weights -RRB- do not have to be calculated explicitly : the behaviour of an MLE integrator might be achieved through interactions among populations of visual and haptic neurons . M 6 . Lederman , S. J. & Abbott , S. G. Texture perception : Studies of intersensory organization using a discrepancy paradigm , and visual versus tactual psychophysics . J. Exp . Psychol . Hum . Percept . Perform . 7 , 902 915 -LRB- 1981 -RRB- . 7 . 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Methods Stimuli The stimulus was a horizontal bar raised 30 mm above a plane ; the bar and plane were perpendicular to the line of sight -LRB- Fig. 2a -RRB- . The width of the bar was 150 mm ; its height varied but the average was S0 = 55 mm . Observers viewed the bar binocularly and/or grasped it with the index nger and thumb in order to estimate its height -LRB- Fig. 2a -RRB- . Its vertical position was varied randomly from trial to trial . The haptic stimulus was generated using two PHANToM -LRB- SensAble Technologies -RRB- force-feedback devices -LRB- Fig. 2a -RRB- , one each for the index nger and thumb . Finger and thumb movements had all six degrees of freedom in the 20-cm3 workspace . The threedimensional positions of the tips of the nger and thumb were monitored , and appropriate forces were applied when the tips reached the positions of the simulated haptic objects . PHANToMs compellingly simulate haptic properties such as the size , shape and stiffness of the bar . The apparatus was calibrated to align the visual and haptic stimuli spatially . The visual stimulus was a random-dot stereogram simulating the background plane and bar -LRB- Fig. 2 -RRB- . The dots subtended 8 arcmin at the 50-cm viewing distance . Dot density was roughly 9 dots per degree2 . New dots were displayed with each presentation . The positions of the nger and thumb -LRB- tracked by the PHANToMs -RRB- were indicated by small threedimensional markers ; the markers were visible until the bar was touched . Noise was added to the visual display to vary its reliability . The noise was a random displacement of the dot depths in the stereogram -LRB- direction parallel to line of sight -RRB- . The displacements were drawn from a random uniform distribution whose range was 0 , 67 , 133 or 200 % of the 3 cm depth step between the bar and plane . The displacement of the dots is shown in Fig. 2 . No noise was added to the haptic display . We wanted the presentation times for the visual and haptic stimuli to be identical . In the vision-alone discrimination experiment , the standard and comparison stimuli were displayed for 1 s each . In the haptic-alone discrimination experiment , the haptic stimulus began when the thumb and nger both contacted the bar and ended after 1 s . In the visual haptic trials , the visually speci ed bar did not appear until the bar was touched by both ngers simultaneously and the visual and haptic stimuli were extinguished after 1 s. Acknowledgements We thank M. Landy for comments on the manuscript ; and H. Ernst , X. Moncada , C. Alderson and S. Kashiwada for participating as observers . This research was supported by research grants from Air Force Of ce of Scienti c Research and the National Institutes of Health , and by an equipment grant from Silicon Graphics . Procedure Within-modality discrimination was measured in a two-interval , forced-choice scheme . Each trial consisted of the sequential -LRB- visual or haptic -RRB- presentation of two bars . In the standard interval , the bar was always 55 mm tall and in the comparison interval , it was shorter or taller than 55 mm . The standard and comparison stimuli were randomly assigned to the rst or second interval . The observer indicated the interval containing the apparently taller stimulus . The comparison height was varied according to the method of constant stimuli . We plotted psychometric functions , that is the proportion of trials in which the comparison was perceived as taller than the standard against the comparison height . From these functions , we could determine PSEs and discrimination thresholds . Half of the vision-alone and haptic-alone discrimination experiments were conducted -LRB- in random order -RRB- before the visual haptic experiment and the other half were conducted after . In the visual haptic experiment , observers were again presented two stimuli sequentially : the standard stimulus -LRB- visually and haptically speci ed heights differed by D -RRB- and the comparison stimulus -LRB- visually and haptically speci ed heights were the same -RRB- . The average height of the standard stimulus was always 55 mm and the visual haptic difference -LRB- D -RRB- ranged from -6 to +6 mm . The height of the comparison varied . The observer indicated the interval containing the apparently taller stimulus . Trials with different con icts were presented in random order to prevent visuomotor adaptation . No feedback was given in any of the experiments . Four observers -LRB- aged 22 to 33 -RRB- , naive to the experimental purpose , participated . They were right handed and had normal or corrected-to-normal vision . The observers were questioned at the end : none of them had noticed the con icts between the visually and haptically speci ed heights . Received 25 July ; accepted 15 November 2001 . 1 . Rock , I. & Victor , J. Vision and touch : An experimentally created con ict between the two senses . Science 143 , 594 596 -LRB- 1964 -RRB- . 2 . Hay , J. C. , Pick , H. L. Jr & Ikeda , K. Visual capture produced by prism spectacles . Psychonomic Sci . 2 , 215 216 -LRB- 1965 -RRB- . 3 . Warren , D. H. & Rossano , M. J. in The Psychology of Touch -LRB- eds Heller , M. A. & Schiff , W. -RRB- 119 137 -LRB- Erlbaum , Hillsdale , New Jersey , 1991 -RRB- . 4 . Power , R. P . The dominance of touch by vision : Sometimes incomplete . Perception 9 , 457 466 -LRB- 1980 -RRB- . 5 . Welch , R. B. & Warren , D. H. Immediate perceptual response to intersensory discrepancy . Psychol . Bull . 88 , 638 667 -LRB- 1980 -RRB- . Competing interests statement The authors declare that they have no competing nancial interests . Correspondence and requests for materials should be addressed to M.O.E. -LRB- e-mail : marc.ernst@tuebingen.mpg.de -RRB- . ... . Effects of grouping in contextual modulation Michael H. Herzog * & Manfred Fahle * * Human Neurobiology , University of Bremen , Argonnenstrasse 3 , 28211 Bremen , Germany City University , Department of Optometry and Visual Science , Tait Building , Northampton Square , London EC1V 0HB , UK ... . Perception of a visual target and the responses of cortical neurons can be strongly in uenced by a context surrounding the target1 27 . This observation relates to the fundamental issue of how cortical neurons code objects of the external world . In high-contrast regimes , embedding a target in an iso-oriented context reduces neural responses and deteriorates performance in psychophysical experiments . Performance from orthogonal surrounds is better than that from iso-oriented ones1 17 . This contextual interference is often postulated to be caused by long - or short-range interac433 NATURE | VOL 415 | 24 JANUARY 2002 | www.nature.com 2002 Macmillan Magazines Ltd

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O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

haptic
optimal
bayesian
cue integration
integration
vision