598 nature neuroscience • volume 5 no 6 • june 2002articlesThe human ability to analyze visual motion in general scenes farexceeds the capabilities of the most sophisticated computer visionalgorithms. Yet psychophysical experiments show that humans alsomake some puzzling mistakes, misjudging speed or direction ofvery simple stimuli. In this paper, we propose that such mistakes ofhuman motion perception represent the best solution of a ratio-nal system designed to operate in the presence of uncertainty.In both biological and artificial vision systems, motion analy-sis begins with local measurements such as the output of direc-tion-selective cells in primary visual cortex1, or of spatial andtemporal derivative operators in artificial systems2,3. These arethen integrated to generate larger, more global motion descrip-tions. The integration process is essential because the initial localmotion measurements are ambiguous. For example, in the vicin-ity of a contour, only the motion component perpendicular tothe contour can be determined (a phenomenon referred to as the‘aperture problem’)2,4–7. Such an integration stage seems to beconsistent with much of the psychophysical8–11and physiologi-cal8,12–14data.Despite the vast amount of psychophysical data publishedover the past two decades, the nature of the integration schemeunderlying human motion perception remains unclear. This istrue even for the simple and widely studied ‘plaid’ stimulus, inwhich two superimposed oriented gratings translate (move with-out changing shape, size or orientation) in the image plane(Fig. 1a). Due to the aperture problem, each grating’s motion isconsistent with an infinite number of possible translational veloc-ities lying on a constraint line in the space of all velocities(Fig. 1b). When viewing a single drifting grating in isolation,subjects typically perceive it as translating in a direction normalto its contours (Fig. 1b). When two gratings are presented simul-taneously, subjects often perceive them as a coherent patterntranslating with a single motion5,7.How is this coherent pattern motion estimated? Most expla-nations are based on one of three rules7: intersection of con-straints (IOC), vector average (VA), or feature tracking (FT). TheIOC solution is the unique translation vector consistent with theMotion illusions as optimal perceptsYair Weiss1, Eero P. Simoncelli2and Edward H. Adelson31School of Computer Science and Engineering, Hebrew University of Jerusalem, Givat Ram Campus, Jerusalem 91904, Israel2Howard Hughes Medical Institute, Center for Neural Science and Courant Institute of Mathematical Sciences, New York University, 4 Washington Place, New York, New York 10003, USA3Brain and Cognitive Sciences Department, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139, USACorrespondence should be addressed to Y.W. ([email protected])Published online: 20 May 2002, DOI: 10.1038/nn858The pattern of local image velocities on the retina encodes important environmental information.Although humans are generally able to extract this information, they can easily be deceived into see-ing incorrect velocities. We show that these ‘illusions’ arise naturally in a system that attempts toestimate local image velocity. We formulated a model of visual motion perception using standardestimation theory, under the assumptions that (i) there is noise in the initial measurements and (ii)slower motions are more likely to occur than faster ones. We found that specific instantiation of sucha velocity estimator can account for a wide variety of psychophysical phenomena.information of both gratings. Graphically, this corresponds tothe point in velocity space that lies at the intersection of bothconstraint lines (Fig. 1b, circle). The VA solution is the averageof the two normal velocities. Graphically, this corresponds to thepoint in velocity space that lies halfway between the two normalvelocities (Fig. 1b, square). An FT solution corresponds to thevelocity of some feature of the plaid intensity pattern (for exam-ple, the locations of maximum luminance at the grating inter-sections)15,16. For plaids, the FT and IOC solutions bothcorrespond to the veridical (true) pattern motion.Which of the three rules best describes human perception? Theanswer is not clear: depending on the stimulus, the perceived pat-tern motion can be nearly veridical (consistent with IOC or FT) orcloser to the VA solution. The relevant stimulus features includerelative grating orientation and speed17–19, contrast20, presenta-tion time17and retinal location17.Similar effects have been reported with stimuli that appearquite different from plaids16,21. For a moving rhombus (Fig. 2),as for a plaid pattern, the motion of each opposing pair of sides isconsistent with a constraint line in the space of velocities. Asshown in the velocity space diagrams (Fig. 2c and f), IOC or FTpredicts horizontal motion, whereas VA predicts diagonal motion.Perceptually, however, the rhombus appears to move horizon-tally at high contrast and diagonally at low contrast. To furthercomplicate the situation, the percept depends on the shape. Ifthe rhombus is fattened (Fig. 2d), it appears to move horizon-tally at both contrasts. To view these moving stimuli, seehttp://www.cs.huji.ac.il/~yweiss/Rhombus.One might reason that the visual system uses VA for a thin,low-contrast rhombus, and IOC/FT for a thin, high-contrastrhombus and for a fat rhombus. Although a model based on thisad hoc combination of rules certainly fits the data, it is clearlynot a parsimonious explanation. Furthermore, each of the ide-alized rules is limited to stimuli containing straight structuresat only two orientations, and does not offer a method for com-puting the normal velocities of those structures. One would pre-fer a single, coherent model that could predict the perceived© 2002 Nature Publishing Group http://neurosci.nature.comarticlesnature neuroscience • volume 5 no 6 • june 2002 599velocity of any arbitrary spatiotemporal stimulus that appearsto be translating. We have developed such a model based on asimple formulation of the problem of velocity estimation andon a few reasonable assumptions.In Helmholtz’s view, our percepts are our best guess as to whatis in the world, given both sensory data and prior experience22.To make this definition more quantitative, one must specify (i)what is ‘best’ about a best guess,
View Full Document
Unlocking...