Anomalous Mirror Symmetry Generated by Optical Illusion

Sugihara, Kōkichi

doi:10.3390/sym8040021

Cited by 14 publications

(12 citation statements)

References 10 publications

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“…Recently, a systematic method was proposed to create objects called ambiguous cylinders [5], where an object changes its appearance drastically in its mirror reflection; for example, a circle changes to a square or a flower changes to a butterfly. The same concept was also applied to other variations of anomalous behaviors of mirror reflections, such as the disappearance of parts of objects [6], the disturbance of topology [7], height reversal [8] and right-left reversal [9]. Similar design algorithms were also studied for wire frame art.…”

Section: Introductionmentioning

confidence: 99%

Reflexively-Fused Cylinders

Sugihara¹,

Moriguchi²

2018

Symmetry

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Abstract:The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented.

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Section: Introductionmentioning

confidence: 99%

Reflexively-Fused Cylinders

Sugihara¹,

Moriguchi²

2018

Symmetry

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“…The behavior seems impossible because the right-facing arrow turns toward the left in the mirror. This object is an example of the ambiguous cylinders ( Sugihara, 2015 , 2016 ), which have two quite different appearances and it is difficult to believe that they come from the same object. When we rotate this object around a vertical axis, the appearance changes as shown by a sequence of snap shots at the bottom.…”

Section: Discussionmentioning

confidence: 99%

Rectangularity Is Stronger Than Symmetry in Interpreting 2D Pictures as 3D Objects

Sugihara

Pinna

2022

Front. Hum. Neurosci.

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It is known that the human brain has a strong preference for rectangularity in interpreting pictures as 3D shapes. Symmetry is also considered to be a factor that the human vision system places high priority on when perceiving 3D objects. Thus, a question is raised: which is more basic, the rectangularity preference or the symmetry preference? To answer this question, we carried out experiments using pictures that have at least two interpretations as 3D objects, one of which was rectangular but not symmetric, and the other of which was symmetric but not rectangular. We found that the preference for rectangularity is stronger than that for symmetry. This observation will help us to understand various 3D optical illusions, including the room-size illusion and the ambiguous object illusion.

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“…A model-based invariant of 3D centro-symmetry under a 2D perspective projection is only a common intersection of line segments that connect corresponding pairs of points. This can be proven by showing that a 3D centro-symmetrical interpretation can always be constructed from a 2D image that satisfies this constraint (see also [25,[32][33][34] for analogous theorems of 3D mirror and rotational symmetry). A common intersection in a 2D image is a projection of the symmetry point of the constructed 3D centro-symmetrical interpretation and its symmetry line segments are projected to the line segments that connect the corresponding pairs of points in a 2D image.…”

Section: A 2d Perspective Projection Of 3d Centro-symmetrymentioning

confidence: 99%

Influence of 3D Centro-Symmetry on a 2D Retinal Image

Sawada

2020

Symmetry

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An object is 3D centro-symmetrical if the object can be segmented into two halves and the relationship between them can be represented by a combination of reflection about a plane and a rotation through 180° about an axis that is normal to the plane. A 2D orthographic image of the 3D centro-symmetrical object is always 2D rotation-symmetrical. Note that the human visual system is known to be sensitive to 2D rotational symmetry. This human sensitivity to 2D rotational symmetry might also be used to detect 3D centro-symmetry. If it is, can this detection of 3D centro-symmetry be helpful for the perception of 3D? In this study, the geometrical properties of 3D centro-symmetry and its 2D orthographic and perspective projections were examined to find out whether 3D centro-symmetry plays any role in the perception of 3D. I found that, from a theoretical point-of-view, it is unlikely that 3D centro-symmetry can be used by the human visual system to organize a 2D image of an object in a way that makes it possible to recover the 3D shape of an object from its 2D image.

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Anomalous Mirror Symmetry Generated by Optical Illusion

Cited by 14 publications

References 10 publications

Reflexively-Fused Cylinders

Reflexively-Fused Cylinders

Rectangularity Is Stronger Than Symmetry in Interpreting 2D Pictures as 3D Objects

Influence of 3D Centro-Symmetry on a 2D Retinal Image

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