Five types of anomalous perceptions created by the same mirror-reflection process

  • Kokichi Sugihara Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Keywords: Picture, 3D interpretation, Depth perception, Left-right reversal illusion, Height reversal illusion, Lying-standing illusion, Somersault illusion, Replacement illusion


The real world and its mirror image are plane symmetric to each other with respect to a mirror surface, but mirror images are often perceived differently due to optical illusions. This paper shows that there are at least five types of different illusory perceptions of mirror images of pictures, although they arise from the same optical process. In all five illusions, we place a 2D picture of a 3D object horizontally, and see its image reflected by a vertical mirror. In some cases, the left and the right are reversed (left-right reversal illusion), sometimes horizontal planes change their heights (height reversal illusion), sometimes a lying object rises up (lying-standing illusion), sometimes the object turns upside down as if having done a somersault (somersault illusion), and sometimes the object is replaced by a rather different object (replacement illusion). This paper examines why these illusions occur from geometrical and psychological points of view.


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Gibson, J. J. (1950). The perception of the visual world. Cambridge, MA: The Riverside Press.

Gregory, R. L. (1970). The intelligent eye. London: Weidenfeld & Nicolson.

Hoffman, D. D. (1998). Visual intelligence: How we create what we see. New York, NY Brockman Inc.

Necker, L. A. (1832). Observations on some remarkable phenomena seen in Switzerland; and an optical phenomenon which occurs on viewing of a crystal or geometrical solid. Philosophical Magazine, 3rd series, 1, 329–337. Retrieved from

Perkins, D. N. (1972). Visual discrimination between rectangular and nonrectangular parallelepipeds. Perceptual Psychology, 12, 293–331. Retrieved from

Perkins, D. N. (1973). Compensating for distortion in viewing picture obliquely. Perceptual Psychology, 14, 13–18. Retrieved from

Richards, W., & Miller, J. F., Jr. (1971). The corridor illusion. Perception & Psychophysics, 9, 421–423. Retrieved from

Robinson, J. O. (1998). The psychology of visual illusion. Mineola, NY: Dover Publications.

Shepard, R. N. (1990). Mind sights: Original visual illusions, ambiguities, and other anomalies with a commentary of the play of mind in perception and art. New York, NY: W. H. Freeman and Company.

Sugihara, K. (2015a). Ambiguous cylinders: A new class of impossible objects. Computer Aided Drafting, Design and Manufacturing, 25, 19–25.

Sugihara, K. (2015b). Height reversal generated by rotation around a vertical axis. Journal of Mathematical Psychology, 68–69, 7–12. doi: 10.1016/

Sugihara, K. (2016a). Anomalous mirror symmetry generated by optical illusion. Symmetry, 8, 21, doi: 10.3390/sym8040021

Sugihara, K. (2016b). A new type of impossible objects that become partly invisible in a mirror. Japan Journal of Industrial and Applied Mathematics, 33, 525–535. doi: 10.1007/s13160-016-0233-9

Sugihara, K. (2018). Topology-disturbing objects: A new class of 3d optical illusion. Journal of Mathematics and the Arts, 12, 1–17. doi: 10.1080/17513472.2017.1368133

Sugihara, K. (2020a). Ambiguous tiling. Computer Aided Geometric Design, 79, 101851. doi: 10.1016/j.cagd.2020.101851

Sugihara, K. (2020b). Family tree of impossible objects created by optical illusion. Bridges 2020 Conference Proceedings (pp. 329–336). Retrieved from

Sugihara, K. (2020c). 3D Schröder Staircase, First prize of the best illusion of the year contest 2020. Retrieved from

Sugihara, K. (2021). Rising object illusion, top ten finalist of the best illusion of the year contest 2021. Retrieved from

Sugihara, K. (2022). Rising object illusion. Journal of Mathematics and the Arts, 16(3), 232–243. doi: 10.1080/17513472.2022.2045047

Sugihara, K., & Pinna, B. (2022). Rectangularity is stronger than symmetry in interpreting 2D pictures as 3D objects. Frontiers in Human Neuroscience, 16, 849159. doi: 10.3389/fnhum.2022.849159
How to Cite
Sugihara K. (2023). Five types of anomalous perceptions created by the same mirror-reflection process. Journal of Illusion, 4.
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