Abstract
In this paper we study a spiral illusion generated by fractal islands. Furthermore, by a neuro-scientific consideration we present a new class of geometrical illusions. In order to analyse these illusions, we propose a new mathematical method.
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Arai H.: A nonlinear model of visual information processing based on discrete maximal overlap wavelet. Interdiscip. Inf. Sci. 11, 177–190 (2005)
Arai H.: Wavelets. Kyoritsu Publ. Co., Tokyo (2010) (in Japanese)
Arai H., Arai S.: Common factor of a certain kind of tilt illusions clarified by a wavelet, VISION. J. Vis. Soc. Japan 17, 259–265 (2005) (in Japanese)
Arai H., Arai S.: Finite discrete, shift-invariant, directional filterbanks for visual information processing, I: Construction. Interdiscip. Inf. Sci. 13, 255–273 (2007)
Arai H., Arai S.: 2D tight framelets with orientation selectivity suggested by vision science. Invited paper. JSIAM Lett. 1, 9–12 (2009)
Cohen A., Daubechies I., Feauveau J.-C.: Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 45, 485–560 (1992)
Coifman R.R., Donoho D.L.: Translation invariant de-noising. Lect. Notes Stat. 103, 125–150 (1995)
Daubechies I., Han B., Ron A., Shen Z.: Framelets: MRA-based construction of wavelet frames. Appl. Comput. Harmon. Anal. 14, 1–46 (2003)
Fraser J.: A new visual illusion of direction. Br. J. Psychol. 2, 307–320 (1908)
Gallant J.L., Braun J., Van Essen D.C.: Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex. Science 259, 100–103 (1993)
Gallant J.L., Conner C.E., Rakshit S., Lewis J.W., Van Essen D.C.: Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey. J. Neurophysiol. 76, 2718–2739 (1996)
Gregory R.L., Heard P.: Border locking and the Cafe Wall illusion. Perception 8, 365–380 (1979)
Kitaoka A.: Tilt illusions after Oyama (1960): a review. Jpn. Psychol. Res. 49, 7–19 (2007)
Kitaoka A.: Geometrical illusions. In: Goto, T., Tanaka, H. (eds) Handbook of the Science of Illusion., pp. 56–77. University of Tokyo Press, Tokyo (2005) (in Japanese)
Kitaoka A., Pinna B., Brelstaff G.: New variants of the spiral illusion. Perception 30, 637–646 (2001)
Lauwerier H.A.: Fractals: Endlessly Repeated Geometrical Figures. Princeton University Press, Princeton (1991)
Morgan M.J., Moulden B.: The Münsterberg figure and twisted cords. Vis. Res. 26, 1793–1800 (1986)
Nason G.P., Silverman B.W.: The stationary wavelet transform and some statistical applications. Lect. Notes Stat. 103, 281–299 (1995)
Percival D.B., Walden A.T.: Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge (2000)
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H. Arai was supported partly by Precursory Research for Embryonic Science and Technology, Japan Science and Technology Agency, and by Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science.
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Arai, H., Arai, S. Framelet analysis of some geometrical illusions. Japan J. Indust. Appl. Math. 27, 23–46 (2010). https://doi.org/10.1007/s13160-010-0009-6
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DOI: https://doi.org/10.1007/s13160-010-0009-6