Modelling stereokinetic phenomena by a minimum relative motion assumption: the tilted disk, the ellipsoid and the tilted bar

The stereokinetic phenomena of the tilted disk and of the ellipsoid are visual illusions of depth elicited by a flat figure with elliptic contour rotating at uniform speed in the frontal plane of an observer. Strictly related to the appearance of the ellipsoid is the stereokinetic phenomenon of the tilted bar, elicited by a line segment of constant length rotating at uniform speed in the frontal plane. We present a mathematical model of these phenomena, based on an assumption of minimization by the Visual System of the differences between the lengths of the velocity vectors of the stimulus (minimum relative motion assumption): the “rigidity hypothesis” is able to explain the appearance of the tilted disk but not the appearance of the ellipsoid and of the tilted bar. The theoretical results obtained by our modelling are in good agreement with the experimental observations.

[1]  Scott O. Murray,et al.  Processing Shape, Motion and Three-dimensional Shape-from-motion in the Human Cortex , 2003 .

[2]  S. Ullman,et al.  The interpretation of visual motion , 1977 .

[3]  Dejan Todorovic,et al.  Analysis of two- and three-dimensional rigid and nonrigid motions in the stereokinetic effect , 1993 .

[4]  J E Cutting,et al.  Perception and information. , 1987, Annual review of psychology.

[5]  Mario Zanforlin,et al.  Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption , 2004, Biological Cybernetics.

[6]  H. F. J. M. Buffart,et al.  Formal theories of visual perception , 1978 .

[7]  M. Zanforlin.  The height of a stereokinetic cone: A quantitative determination of a 3-D effect from 2-D moving patterns without a “rigidity assumption” , 1988, Psychological research.

[8]  R. B. Mefferd.  Perception of Depth in Rotating Objects: 7. Influence of Attributes of Depth on Stereokinetic Percepts , 1968 .

[9]  J. Farrell,et al.  Visual transformations underlying apparent movement , 1983, Perception & psychophysics.

[10]  A. Cowey,et al.  Blindness to form from motion despite intact static form perception and motion detection , 2000, Neuropsychologia.

[11]  R. Shepard.  Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming. , 1984, Psychological review.

[12]  James E Cutting,et al.  An Invariant for Wheel-Generated Motions and the Logic of its Determination , 1980, Perception.

[13]  R. B. Mefferd,et al.  Perception of Depth in Rotating Objects: 4. Fluctuating Stereokinetic Perceptual Variants , 1968, Perceptual and motor skills.

[14]  D. Gilden,et al.  The effect of configural orientation on perceived trajectory in apparent motion , 1988, Perception & psychophysics.

[15]  J. Cutting,et al.  The minimum principle and the perception of absolute, common, and relative motions , 1982, Cognitive Psychology.

[16]  G Johansson,et al.  Vector analysis in visual perception of rolling motion , 1974, Psychologische Forschung.

[17]  O. Reiser,et al.  Principles Of Gestalt Psychology , 1936 .

[18]  Peter Ulric Tse,et al.  The duration of 3-D form analysis in transformational apparent motion , 2002, Perception & psychophysics.

[19]  G J Andersen,et al.  A Counterexample to the Rigidity Assumption in the Visual Perception of Structure from Motion , 1984, Perception.

[20]  S Ullman,et al.  Rigidity and Misperceived Motion , 1984, Perception.

[21]  R. Shepard.  Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming. , 1984, Psychological review.

[22]  G. Vallortigara,et al.  Depth effect from a rotating line of constant length , 1988, Perception & psychophysics.

[23]  D. Foster.  Visual apparent motion and the calculus of variations , 1978 .

[24]  Mario Zanforlin,et al.  Analytic determination of the depth effect in stereokinetic phenomena without a rigidity assumption , 2004, Biological Cybernetics.

[25]  S. Gunnar O. Johansson,et al.  Configurations in event perception : an experimental study , 1951 .

[26]  P Bressan,et al.  Perceptual Alternations in Stereokinesis , 1988, Perception.

[27]  Carsten Nicolas Boehler,et al.  Binding 3-D Object Perception in the Human Visual Cortex , 2008, Journal of Cognitive Neuroscience.

[28]  V. Bruce,et al.  Visual Perception: Physiology, Psychology and Ecology , 1985 .

[29]  K. Duncker,et al.  Über induzierte Bewegung , 1929 .

[30]  S Ullman,et al.  Maximizing Rigidity: The Incremental Recovery of 3-D Structure from Rigid and Nonrigid Motion , 1984, Perception.

[31]  P. Bressan,et al.  Multiple 3-D Interpretations in a Classic Stereokinetic Effect , 1986, Perception.