Longrangefractaldynamicinvisualsearchampbeyond长距离的视觉搜索和分形动力学超越课件.pptx

1、 Ralf Plag-Schtzenstrasse Karlsruhe-Germanyhttp:/www.fractal-dome.de/e2dg1.shtmlScale-free-Rethinking what we study&measurePower laws!BehaviorBehavior#Typical scale=Central tendencyNewman,M.(2005).Power laws,Pareto distributions and Zipfs laws.Physics Letters,2.Deterministic rules?Simple set of neur

2、onal interaction rules(e.g.,SOC,Volterra.)?Long-range dynamic?Memory?Are there correlations across sequence of fixations?What guides eye-movements during visual search?Find:What does visual search teach us?Perceptual processes!Efficiency&Accuracy Mechanisms Automatic vs.Voluntary Distributed vs.Focu

3、sed Attention Inattention,Pre-&Post-attention Early vs.late vision Search strategy Parallel,Serial,random or?Look for the red item+LLLLLLLLLLLL300400500#of itemsRT(msec)510150 ms/itemFeature searchFast(300ms)Parallel(0-10ms/item)Distributed attentionEarly visionFeatures.Find the odd itemDiscriminate

4、 by.Color xxxxxxx Size xxxxxxx Orientation -l-Movement xxxx-Depthx Conjunction SearchFbination of features 2 orientations(particular arrangement)Find:L among Ts TTTLTTTTTTTTLTTTTTTTTTTTTTTTTTL300500700#of itemsRT(msec)5101540 ms/item0 ms/itemFeatureConjunctionConjunction searchSlowerSequentialFocuse

5、d attention neededLate visionThe change in RT and/or accuracy with set size is a measure of the efficiency of search.In highly efficient searches,attention is deployed directly to the target location and,thus,the number of distractors does not influence RT.In inefficient search through items that ca

6、n be identified without fixation,each additional distractor typically adds 20-40 ms to the time required to find a present target and 40-80 ms to the time required to determine that a target is not present(Wolfe,1998).More recent visual search theoryDepth effects on visual search 1989-1997 shading t

7、exture gradientisoluminant gradientsaerial perspectiveheight-in-planeMy contribution to our understanding of early vision&the feature/conjunction distinctionARVO 95What guides search?Environmental informationLotsInternal cognitive processAttention.MemoryNeuronal interactions-Deterministic ProcessSel

8、f-Organized Criticality(SOC)?Horowitz,T.S.&Wolfe,J.M.(1998).Visual Search has no memory.Nature,357,575-577.Finding:Random repositioning of stimuli does not affect search RTs No memory?Do we keep track of where we look?Is there memory in search?Memory in visual search?Memory for locations in search(K

9、ristjansso,2000)Identity of objects accumulates over time(Treisman&Gelade,1980)Implicit memory(lots of context effects)Olivia&Wolfe,2004)Random repositioning of stimuli does not affect search RTs(Horowitz&Wolfe,1998)Inattentional amnesia in search(Wolfe,1999)(Wolfe,2003;Wolfe et al.,2000,2002)descri

10、bed repeated search tasks in which familiarity with a search display produced little or no improvement in search efficiencyEvidence forEvidence against We are able to keep track of where we look!Inhibition of return(Klein,1982)Failure to replicate inhibition of return(Wolfe&Pokorny,1990)Horowitz,T.S

11、.&Wolfe,J.M.(1998).Visual Search has no memory.Nature,357,575-577.Key Press RTs vs.Eye MovementsFinding:Random repositioning of stimuli does not affect search RTs Non-systematic eye-movementsEngle,1977;Ellis&Stark,1988;Scinto&Pillalamarri,1986;Krendel&Wodinsky,1960;Groner&Groner,1982Aks,D.J.Zelinsky

12、 G.&Sprott J.C.(2002).Memory Across Eye-Movements:1/f Dynamic in Visual Search.Nonlinear Dynamics,Psychology and Life Sciences,6(1),1-15.Gregory Zelinsky SUNY-StonybrookJulien C.Sprott UW-MadisonEye-movement studyCollaboratorsOverviewQUESTIONS.What guides complicated eye movements?Random or non-rand

13、om process?Is there memory across fixations?Might neural interactions drive search?METHOD OF TESTING.Challenging visual search taskKEY ANALYSES Heavy-tail distributions?Power law relation?Coloring of noise-Memory across eye-movements Fourier analysisVisual Search TaskTTTTTTTFind the upright“T”TTTTTT

14、TTTTTTTTTTTTTTTTTTTTTTMethod.Each trial contained 81 Ts.400 trials lasting 2.5 hours.1 second central fixation Eight 20-minute sessions separated by 5-minute rest Generation V dual purkinje-image(DPI)tracker Map trajectory of eyes:Duration&x,y coordinates for each fixation.-Differences between fixat

15、ions xn xn+1&yn yn+1Distance=(x2+y2)1/2 Direction=Arctan(y/x).Analyses Probability Distributions Power spectra(FFT)Descriptive&Correlational Statistics Additional tests.Results 24 fixations per trial(on average)7.6 seconds(SD=6.9 sec)per trial(316 ms/item).Mean fixation duration=212 ms(SD=89 ms)10,2

16、15 fixations across complete search experiment.Conventional search statsFocusing on the dynamicWhats the central tendency?Series of Fixation Differences(yn+1-yn)Scatter plot of 10,215 eye fixations for the entire visual search experiment.Eye FixationsDelay Plot of Fixationsyn-vs-y n+1Across 8 sessio

17、ns we see scaling:Fixation frequency decreased from 1888 to 657Fixation duration increased from 206 to 217 ms.Changes in fixation position xn xn+1 decreased yn yn+1 increased No typical scale!Scaling from Context sensitivity-Scale-free processPower laws!Rethinking what we study&measureHeavy-tail dis

18、tributionsnPower-laws,Pareto&80/20 lawsnSmall events are common;large ones are rare!xn-vs-x n+1Heavy-tail distributionsnSmall events are common;large ones are rare!yn-vs-y n+1Network-DistributionBarabasi,A.&Bonabeau,E.(2003).Scale-Free Networks.Scientific American,288,60-69.http:/www.nd.edu/networks

19、/gallery.htmEdelman&Tononi,2000Spectral analysis Fast-Fourier Transform (FFT)Power vs.Frequency Regression slope=power exponentf a af-2=1/f 2Brown noiseNoisy time seriesWhitePinkBrownWhite NoisePink NoiseBrown Noise1/f 0 noise-flat spectrum=no correlation across data pointsShort&Long range=0 1/f noi

20、se-shallow slope=subtle long range correlation1/f 2 noise-steep slope=Predictable long-range,undulating correlation Short range=0(successive events uncorrelated)Power law indicates Fractal properties:Scale-free(means w/measuring resolution)Self-similar(statistically)Critical+flexible(1/f)Memory Stee

21、pness of the slope(on a log-log scale)reflects.Correlation across data points White-no memory Pink-subtle,long-range Brown-uncorrelated in shortest-range+Predictable long-rangePower Spectra on raw fixationsaPower Spectra of first differences across fixations a=-.6 Distance across eye fixations(x2+y2

22、)1/2a=-.47a=-0.3 a=-1.8Additional fractal measuresnAutocorrelationnRelative Dispersion(SD/M)nIterated Functions Systems(IFS)nRescaled range R/S(Hurst exponent)-running sum of deviations from mean/SD evaluate persistence&anti-persistenceIterated Function Systems-IFS Test-(Peak&Frame,1994;Stewart,1989

23、).Fixation Series1234Start123412341234123412341234PinkNoiseBrown NoiseWhite Noise1/f 1/f 1/f Brown(ish)noiseClustering along diagonals reveals short-term,highly correlated consecutive data pointsRaw FixationsFixation differences Pink(ish)noiseTriangular microstructure associated w/long-term,loosely

24、correlated consecutive data pointsClustering indicates correlated fixations.Direction of fixations show anti-correlated movements a indicated by absence of main diagonals.IFS Test:Fixation directionIFS tests yields patterns consistent w/FFT results Summary of results:Sequence of Absolute eye positio

25、ns-1/f brown noise Short-term memory.Differences-across-fixations-1/f pink noise Longer-term memory.Long-range fractals?Interaction dominant dynamicsSOC(phase transition&critical phenomena)Bak,PVanOrden,G,Holden,J&Turvey,M.(2003).Self-organization of cognitive performance.Journal of Experimental Psy

26、chology:General,132(3),331-350.Thornton,T.&Gilden,D.L.(in press).Provenance of correlations in psychological data.Psychonomic Bulletin&Review.Lattka-VolterraShort range ARMAWagenmakers,E.,Farrel,S.&Ratcliff,R.(2005).Human cognition&a pile of sand.A discussion on serial correlation&self-organized cri

27、ticality.Journal of Experimental Psychology:General,134(1),108-116.Modified random walksPercolation(forest-fire)models(Big controversy!)Source of 1/f dynamic?More sources of 1/f noise.See Newman,M.(2005).Power laws,Pareto distributions and Zipfs laws.Physics Letters,2.nCombining exponentialsnInverse

28、s of quantitlesnYule processnHighly optimized tolerance modelsnCoherent noise mechanismnRandom multiplicative mechanismnFragmentationModelHebb,1969;Rummelhardt&McClelland,1985 Grossberg,19xx;Neuronal interactions-implicit guidanceCan eye movements be described by a simple set ofneuronal interaction

29、rules(e.g.,SOC)to produce 1/f behavior?Increasing Neural Activation-04SOC Network(Adapted from Bak,Tang,&Wiesenfeld,1987)04SOC Network(Adapted from Bak,Tang,&Wiesenfeld,1987)Increasing Neural Activation-Stimulate 1 neuronZ(x,y)=initially stimulated site As individual neurons are activated beyond a t

30、hreshold(of 3),activity(4)is dispersed to surrounding cells.Threshold rule:For Z(x,y)Zcr=3 Activity in the original site is depleted to zero.Z(x,y)-Z(x,y)-4Surrounding activity increases by 1Z(x,y)-Z(x,y)+104Neural SOC Neural SOC w/eye movements trailsEye movements are pulled to the site(s)of greate

31、st activation Complex&effective search For Z(x,y)Zcr Z(x,y)-Z(x,y)-4 Z(x+1,y)-Z(x+1,y)+1 Z(x,y+1)-Z(x,y+1)+1Simple set of SOC rules.can produce:RESULTS Raw fixations-(1/f2 brown noise)Fixation differences-(1/f pink noise)MODEL?.Self-organized criticality(SOC;Bak,Tang,&Wiesenfeld,1987)vs.Lattka-Volte

32、rra,ARMA etc Mainzer,K.(1997).Thinking in complexity:The complex dynamics of matter,mind&mankind.Berlin:Springer.Pg.128Palmer,S.(1999).Vision Science:Photons to phenomenology.Boston:MIT.FEFIPSLPNSCRASCONCLUSIONS Long-range dynamic across eye-movements!Neural interactions-1/f relative eye-movements.S

33、elf-organizing&critical system-effective searchhttp:/psychology.uww.edu/Aks/papers/AZS01.pptAks,D.J.Zelinsky G.&Sprott J.C.(2002).Memory Across Eye-Movements:1/f Dynamic in Visual Search.Nonlinear Dynamics,Psychology and Life Sciences,6(1).Bluebird contributed by www.Sierra foothill.orgReferencesBak

34、,P.(1996).How nature works:the science of self-organized criticality.New York:Springer-Verlag.Bak,P.,&Tang,C.(1989).Earthquakes as a self-organized critical phenomenon.Journal of Geophysics Research-Solar.Earth Planet,94,15635-15637.Bak,P.,Tang,C.,&Wiesenfeld,K.(1987).Self-organized criticality:An e

35、xplanation of 1/f noise.Physical Review Letters,59,381-384.Bak,P.,Tang,C.,&Wiesenfeld,K.(1988).Self-organized criticality.Physical Review A,38,364-374.Ellis,S.R.,&Stark,L.(1986).Statistical dependency in visual scanning.Human Factors,28(4),421-438.Gilden,D.L.(1996).Fluctuations in the time required

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37、vements.In G.dYdewalle&J.V.Van Rensbergen(Eds.),Perception and Cognition.Irwin D.E.,(1996).Integration and accumulation of information across saccadic eye movements.In Inui,T.,&McLelland,J.L.(Eds.,Attention and performance XVI:Information integration in perception and communication(pp.125-155).Londo

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47、mic Bulletin&Review 1,202-238.Iterated Function Systems-IFS Test-(Peak&Frame,1994;Stewart,1989).Fixation Series1234Start123412341234123412341234123412341234123412341234123412341234123412341234123412341234123412341234PinkNoiseBrown NoiseWhite Noise1/f 1/f 1/f Brown(ish)noiseClustering along diagonals

48、 reveals short-term,highly correlated consecutive data pointsRaw FixationsFixation differences Pink(ish)noiseTriangular microstructure associated w/long-term,loosely correlated consecutive data pointsClustering indicates correlated fixations.Direction of fixations show anti-correlated movements a indicated by absence of main diagonals.IFS Test:Fixation directionAnti-correlated SOC neuronal activity w/o eye movement trails