Symmetry Definitions and Perception of Symmetry . Computer Vision Seminar – Symmetry Presented by: Dado Ofir Haifa university. Symmetry - OutLine. Definitions. Motivation. Type of symmetry. Symmetry groups. Perception of Symmetry. Summary. Symmetry. Definitions:
Computer Vision Seminar – Symmetry
" 1.(Beauty resulting from) right proportion between the parts of the body or any whole, balance, harmony, keeping. 2. Such structure as allows of an objects being divided by a point or a line or plane or radiating lines or planes into two or more parts exactly similar in size and shape and in position relative to the dividing point, ect. repetition of exactly similar parts facing each other or a centre,...."
The letter A has reflection symmetry similar to the butterfly.
This is a D12. Patterns like these often appear in stained glass windows. This group contains 12 reflections and a rotation of order 12
This is a D3 group. It contains three reflections and a rotation of order 3. It sort of looks like a hubcap, doesn't it? Some people call these wheel patterns.
This is a D1 group. All dihedral groups contain a reflection.
This is an example of C3. It is somewhat more interesting than C1. There is a rotation of order three.
This is C1. No reflections and no rotations other than the trivial rotation
This is an example of C12
This type has only a translation.
This type has a translation and a vertical mirror.
This type has a translation and a rotation.
This type has a translation and a horizontal mirror.
This type has a translation and a reflection.
This type has two vertical mirrors and a glide reflection.
This last type has two vertical mirrors and a horizontal mirror. There are also rotations in this group.
Platonic solids are perfectly regular solids with the following conditions: all sides are equal and all angles are the same and all faces are identical. In each corner of such a solid the same number of surfaces collide. Only five Platonic solids exist: tetrahedron , hexahedron, octahedron, dodecahedron and icosahedron
“Psychologically speaking, symmetry is not relatively superficial characteristic of pattern and object like, say, color but that it is an essential characteristic which affects profoundly both their immediate perception and their memorability”
(Corballis,1963; Corballis and Beale, 1976, 1983)
In order to process it as possible, the visual apparatus resorts to legerdemain and since no vertical symmetry in the plane of the figure is observable it resorts to an alternative interpretation and creates a 3D figure which is symmetrical
Duplicate the right side
Duplicate the left side
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