Perception & Psychophysics 2003, 65 (3), 429-457 The dynamical foundations of motion pattern formation: Stability, selective adaptation, and perceptual continuity HOWARD S. HOCK Florida Atlantic University, Boca Raton, Florida GREGOR SCHÖNER Ruhr-Universität Bochum, Bochum, Germany and MARTIN GIESE Max Planck Institute for Biological Cybernetics, Tübingen, Germany A dynamical model is used to show that global motion pattern formation for several different ap- parent motion stimuli can be embodied in the stable distribution of activationover a population of con- currently activated, directionally selective motion detectors. The model, which is based on motion de- tectors being interactive, noisy, and self-stabilizing, accounts for such phenomena as bistability, spontaneous switching, hysteresis, and selective adaptation. Simulations show that dynamical solu- tions to the motion correspondence problem for a bistable stimulus (two qualitativelydifferent patterns are formed) apply as well to the solution for a monostable stimulus (only one pattern is formed) and highlight the role of interactions among sequentially stimulated detectors in establishing the state de- pendence and, thereby, the temporal persistence of percepts. In this article, an intuitivelyaccessible dynamical model motion correspondenceproblem for a bistablestimulus (for of motion pattern formation is proposed that accounts in a which two qualitativelydifferent patterns are formed) ap- unified manner for bistability,spontaneousswitching, hys- plies as well to the solution for a monostable stimulus (for teresis, and the effects of adaptation. The model is based which only one pattern is formed), and new predictions on substantialevidence that motion detectors in the visual emerge regarding solutionsto the correspondenceproblem. system are interactive (they mutually influence each oth- Our theoretical objective, therefore, is to unify tradi- er’s activation), that the activation levels of neurons fluc- tional approaches, which have emphasized what is per- tuate randomly (Softky & Koch, 1993), and most signifi- ceived when a motion stimulus is presented (i.e., the solu- cantly, that mechanisms intrinsic to individual detectors tion to the motion correspondence problem; see, e.g., stabilize their activation.On this basis, it is shown, for sev- Ullman, 1979), and dynamical approaches, which have eral different apparent motion stimuli, that perceived emphasizedthe process of perceptualchange(e.g.,Ditzinger global motion patterns can be embodied in the stable dis- & Haken, 1995; Kawamoto & Anderson, 1985; Koechlin, tribution of activation over a population of concurrently Anton, & Burnod, 1999; Schöner & Hock, 1995). Al- activated, directionally selective motion detectors; higher thoughmost of the same conceptsare inherent in other dy- order pattern detectors are not required to account for namical models (e.g., Chey, Grossberg, & Mingolla,1997; global pattern formation for these stimuli. The dynamical Grossberg & Mingolla, 1985; Grossberg & Rudd, 1989; model shows that interactions between currently stimu- Koechlin et al., 1999; Williams, Phillips, & Sekuler, 1986; lated detectors and detectors that will be stimulated in the Wilson, Ferrera, & Yo,1992), the proposed model stands immediate future are crucial for establishingthe temporal apart for the following reasons. (1) It aims for theoretical persistence of a perceived pattern (i.e., its temporal stabil- parsimony and generalizability; the dynamical represen- ity). It is demonstrated that the dynamical solution to the tation is derived from just a few very simple principles that apply irrespective of the particulars of the neurophysio- logical substrate (in contrast, e.g., with neurophysiologi- Grant supportfrom the Deutsche Volkswagenstiftungis gratefully ac- cally specific mechanisms inherent in the dynamicalmod- knowledged. We also thank David Nichols for his help with the simula- tions. Correspondence concerning this article should be addressed to els of such investigators as Grossberg, Mingolla, and H. S. Hock, Department of Psychology, Florida Atlantic University, colleaguesor Koechlinet al.). (2) The functionof activation- Boca Raton, FL 33431 (e-mail: [email protected]). stabilizing mechanisms is made explicit. (3) Interactions 429 Copyright 2003 Psychonomic Society, Inc. 430 HOCK, SCHÖNER, AND GIESE between simultaneously and sequentially stimulated de- are possible (Attneave, 1974; Kolers, 1972).A “solution,” tectors are distinguished with respect to their functional which entails establishingwhich of the alternative motion significance for pattern formation and pattern stability. paths is perceived, is required for both monostable and (4) The dynamical representations are constrained by a bistable motion stimuli. For example, both horizontal and wide range of dynamical data (measurements of sponta- diagonalmotionsare possiblefor the translationalmotion neousswitching,hysteresis,and adaptation).(5) The frame- stimulusillustratedin Figure 1A, but the solutionto the mo- work is generalizableto motion pattern formation in other tion correspondence problem always results in the percep- paradigms. tion of horizontal motion (Kolers, 1972); the translational stimulus is monostable. In contrast, both horizontal and IS STABILIZATION NECESSARY? vertical motions are possible for the motion quartet illus- EVIDENCE FROM BISTABLE STIMULI trated in Figure 1B, and there are two solutionsto the mo- tion correspondence problem—one resulting in the per- Natural, everyday percepts are very stable. It rarely hap- ception of horizontal motion, the other in the perception pens that two qualitatively different percepts are formed of vertical motion;the motion quartetstimulusis bistable. for the same stimulus (bistability), and the experience of The implications of bistability are examined in this spontaneous switching between alternative percepts is study, using the motion quartet as an exemplary stimulus. likewise rare. Because everyday experiencesof monostabil- As is illustratedin Figure 1B, the motion quartet is formed ity are so pervasive, perceptual stability (and the potential by simultaneously presenting two elements located in di- for it to be lost) is not always recognized as an important agonallyoppositecorners of an imaginary rectangle, then problem for the perceptual psychologist. Historically, simultaneouslypresentingtwo elements in the other diag- however, stability was once a central issue. William James onally oppositecorners, then the first pair again, and so on (1890) famously recognized the problem of stable per- (Chaudhuri & Glaser, 1991; Hock, Kelso, & Schöner, cepts emerging from the “blooming, buzzing confusion’’ 1993; Hoeth, 1968; Kruse, Stadler, & Wehner, 1986; Ra- of sensory input, and Wolfgang Köhler (1920/1938) the- machandran & Anstis, 1985; P. von Schiller, 1933). The orized that perceptual experience was isomorphic to the elements are perceived to move either horizontallyor ver- stable, equilibrium states of electrical fields formed in the tically, but the two directions are never perceived at the brain. In both of the above, it was assumed that stabilityis same time, even though motion detectors selective for established by brain mechanisms in response to stimulus both horizontal and vertical motion are stimulated at the input. This view, however, was effectively challenged by same time. Hock et al. (1993) varied the aspect ratio of the James Gibson (1966), who attributed the stability of real- quartet, the vertical dividedby the horizontal distance be- world percepts to the tuning of our visual system to un- tween element positions,and showed that (1) perceptionis ambiguous, invariant properties of stimulation that di- bistable for aspect ratios not too different from 1.0— rectly specify the source of the stimulation, the objects in either the horizontal or the vertical motion pattern is per- the world and their spatial layout. From this perspective, ceived for the same stimulus—and (2) perception sponta- there is no “blooming, buzzing confusion’’ and no iso- neously switches between the two patterns, the switching morphism with respect to internal brain states. Percepts rate being highest for aspect ratios near 1.0. formed for natural stimuli are stable because they are uniquely specified by information in the stimulus, not be- Adaptation and Switching cause of intrinsic neural stabilizing mechanisms. In the past, perceptual switching for bistable stimuli has Although Gibson (1966) has had great impact on cur- been attributed to the adaptation,or neural fatigue, of the rent thinking, bistable stimuli for which two qualitatively perceived pattern and, at the same time, recovery from the different patterns can be formed provide an important effects of prior adaptation of previously perceived mo- constraint on theories of perception. This is because it is tions (Köhler & Wallach, 1944; Spitz & Lipman, 1962). very unlikely that stabilizing mechanisms have evolved On this basis, the pattern perceived through the course of just for the perceptionof bistable stimuli and are irrelevant these adaptation-induced changes is the one with the to pattern formation for monostablestimuli. Our expecta- greater strength. This kind of account of perceptualswitch- tion is that understanding the perception of bistable stim- ing does not require the introduction of a stabilization uli will provide insights into pattern formation when per- mechanism, but it is inconsistent with recent evidence ception is monostable.