Influence of 3D Centro-Symmetry on a 2D Retinal Image
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-symmetri...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1863 |
| _version_ | 1797548062508318720 |
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| author | Tadamasa Sawada |
| author_facet | Tadamasa Sawada |
| author_sort | Tadamasa Sawada |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:54:03Z |
| format | Article |
| id | doaj.art-9507b7f0f455485b803eccaa03b40bb2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:54:03Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9507b7f0f455485b803eccaa03b40bb22023-11-20T20:47:01ZengMDPI AGSymmetry2073-89942020-11-011211186310.3390/sym12111863Influence of 3D Centro-Symmetry on a 2D Retinal ImageTadamasa Sawada0School of Psychology, National Research University Higher School of Economics, 101000 Moscow, RussiaAn 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.https://www.mdpi.com/2073-8994/12/11/1863centro-symmetryrotational symmetryinvariantvisual perception3D symmetry3D recovery |
| spellingShingle | Tadamasa Sawada Influence of 3D Centro-Symmetry on a 2D Retinal Image Symmetry centro-symmetry rotational symmetry invariant visual perception 3D symmetry 3D recovery |
| title | Influence of 3D Centro-Symmetry on a 2D Retinal Image |
| title_full | Influence of 3D Centro-Symmetry on a 2D Retinal Image |
| title_fullStr | Influence of 3D Centro-Symmetry on a 2D Retinal Image |
| title_full_unstemmed | Influence of 3D Centro-Symmetry on a 2D Retinal Image |
| title_short | Influence of 3D Centro-Symmetry on a 2D Retinal Image |
| title_sort | influence of 3d centro symmetry on a 2d retinal image |
| topic | centro-symmetry rotational symmetry invariant visual perception 3D symmetry 3D recovery |
| url | https://www.mdpi.com/2073-8994/12/11/1863 |
| work_keys_str_mv | AT tadamasasawada influenceof3dcentrosymmetryona2dretinalimage |