Abstract
When a circular disk with an eccentric dot is set in slow rotary motion a compelling impression of a three-dimensional cone is observed. Similarly a line segment of constant length, a bar, rotating on the frontal plane appears slanted in depth. The two stereokinetic phenomena cannot be explained on the basis of Ullman's method of extracting depth from 2-D moving stimuli i.e. the rigidity assumption. A new analytic model is here presented based on the hypothesis that the visual system minimizes the relative velocity differences among all the points of the moving pattern. Two different methods of calculating the depth displacement are described: the velocity field method and the trajectories method. Both lead to the same results. A comparison of the theoretical results with the experimental ones supports the validity of the model.
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References
Beghi L, Vicario G, Zanforlin M (1983) The perceptual centre of visual configurations. Accademia Patavina di Scienze, Lettere ed Arti 95:133–148
Bennet BM, Hoffman DD (1985) The computation of structure from fixed-axis motion: nonrigid structures. Biol Cybern 51:295–300
Braunstein ML, Anderson GJ (1984) A counterexample to the rigidity assumption in the visual perception of structure from motion. Perception 13:213–217
Cutting JE (1987) Perception and information. Ann Rev Psychol 38:61–90
Duncker K (1929) Ueber induzierte Bewegung. Ein Beitrag zur Theorie optischer wahrgenommener Bewegung. Psychol Forsch 12:159–180
Fischer GT (1956) Factors affecting estimation of depth with variation of the stereokinetic effect. Am J Psychol 69:252–257
Johansson G (1974) Vector analysis in visual perception of rolling motion: a quantitative approach. Psychol Forsch 36:311–319
Longuet-Higgins HC (1986) Visual motion ambiguity. Vision Res 26:181–183
Mefferd RB Jr (1968) Perception of depth in rotating objects: 7. Influence of attributes of depth on stereokinetic percepts. Percept Motor Skills 27:1179–1193
Metelli F (1940) Ricerche sperimentali sulla percezione del movimento. Riv Psicol 36:319–370
Metelli F (1964) Repos apparent et phenomenes de “totalisation cyclique” dans la perception visuelle. J Pyschol Norm Pathol 51:1–38
Musatti CL (1924) Sui fenomeni stereocinetici. Arch Ital Psicol 3:105–120
Musatti CL (1955) La stereocinesi e il problema delia struttura dello spazio visibile. Riv Psicol 49:3–57
Nakayama K (1980) Biological image motion processing: a review. Vision Res 25:625–660
Reichardt W, Egelhaaf M (1988) Movement detectors provide sufficient information for local computation of 2-D velocity field. Naturwissenschaften 75:313–315
Renwall P (1929) Zur Theorie des. stereokinetischen Phenomenes. Ann Univ Aboensis, Ser. B, Tom. X:13–75
Robinson JO, Piggins JD, Wilson JA (1985) Shape, height and angular movement in stereokinesis. Perception 14:677–683
Rubin E (1927) Visuell wahrgenommene wirkliche Bewegungen. Z Physiol 103:284–392
Todd JT (1985) Perception of structure from motion: is projective correspondence of moving elements a necessary condition? J Exp Psychol Hum Percept Perf 11:689–710
Ullman S (1979) The interpretation of visual motion. MIT Press, Cambridge, Mass
Ullman S (1984a) Maximizing rigidity. The incremental recovery of 3-D structure from rigid and non-rigid motion. Perception 13:255–274
Ullman S (1984b) Rigidity and misperceived motion. Perception 13:218–219
Wallach H, Weiss A, Adams PA (1956) Circles and derived figures in rotation. Am J Psychol 69:48–59
Zanforlin M (1988a) The height of a stereokinetic cone: a quantitative determination of a 3-D effect from a 2-D moving pattern without a “rigidity assumption”. Psychol Res 50:162–172
Zanforlin M (1988b) Stereokinetic phenomena as good Gestalts. The minimum principle applied to circles and ellipses in rotation: a quantitative analysis and a theoretical discussion. Gestalt Theory 10:187–214
Zanforlin M (1989) Gestalt theory and perception of a three-dimensional world of objects through motion. In: Gestalt Psychology: its origin, foundations and influence, International Workshop, Firenze (in press)
Zanforlin M, Vallortigara G (1988) Depth effect from a rotating line of constant length. Percept Psychophys 44:493–499
Zanforlin M, Vallortigara G (1990) The magic wand: a new stereokinetic anomalous surface. Perception 19:447–457
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Beghi, L., Xausa, E. & Zanforlin, M. Analytic determination of the depth effect in stereokinetic phenomena without a rigidity assumption. Biol. Cybern. 65, 425–432 (1991). https://doi.org/10.1007/BF00204655
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DOI: https://doi.org/10.1007/BF00204655