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Symmetry

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...

Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

Symmetry Elements in a Crystal

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Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

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Properties of Fourier series II

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Related Experiment Video

Updated: Jun 24, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Symmetry, probability, and recognition in face space.

Lawrence Sirovich¹, Marsha Meytlis

¹Laboratory of Applied Mathematics, Mount Sinai School of Medicine, 1 Gustave L. Levy Place, New York, NY 10029, USA. lawrence.sirovich@mssm.edu

Proceedings of the National Academy of Sciences of the United States of America

|April 15, 2009

Summary

This summary is machine-generated.

Human face recognition relies on midline symmetry, with evidence suggesting a lower dimensional face space than previously thought. This research developed a novel algorithm achieving nearly 100% accuracy in facial coding and recognition.

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Area of Science:

Neuroscience
Cognitive Science
Computer Vision

Background:

Facial symmetry is crucial for human face coding and recognition.
This aligns with primate cortex organization and human psychophysical studies.
Previous estimates of face recognition space dimensions may be overestimated.

Purpose of the Study:

To investigate the role of midline symmetry in facial recognition.
To determine the dimensional space required for human face recognition.
To develop a highly accurate facial recognition algorithm.

Main Methods:

Analysis of facial midline symmetry in human faces.
Development of a probability distribution model for face space.
Construction and testing of a novel facial recognition algorithm.

Main Results:

Midline symmetry is a key factor in facial coding and recognition.
The dimensional space for human face recognition is significantly lower than previously estimated.
A probability distribution model generated realistic synthetic faces.
The developed recognition algorithm achieved nearly 100% accuracy.

Conclusions:

Facial midline symmetry is fundamental to efficient facial recognition.
A reduced dimensional face space model accurately represents human facial perception.
The novel algorithm offers a highly effective solution for facial recognition tasks.