Types of Symmetry

Symmeter can measure the level of both bi-lateral and radial symmetry in an image. The term bi-lateral symmetry refers to side-to-side symmetry, as if a mirror line was placed on the image, typically (but not necessarily) in a top to bottom fashion. Bi-lateral symmetry is a comparison of the left and right halves of the area of the image.

Radial symmetry is a measure of the image as if it were divided into a series of pie-shaped segments and each segment were compared to its opposite segment.

Area of Interest

When measuring the symmetry of an image, you first must specify an Area of Interest. This is a shape that defines the area that you'd like to measure. Symmeter offers several types of Areas of Interest, including square, rectangle, circle, ellipse, and polygon. Each type can be applied, sized, and rotated on an image so the area that you wish to measure, and only that area, is evaluated.

Pixel Comparison

Once an Area of Interest has been defined, Symmeter calculates the value, or level of symmetry by comparing each pixel with its corresponding pixel on the other side of the "mirror." The number of similar pixels are counted and shown as a weighted percentage of the total pixels within the image.

As in the first example below, an Area of Interest that is all of a single color (such as all white), will have a Symmeter coefficient value of 1. An area that is vertically split half white and half black will have a Symmeter value of close to zero, since no pixels are the same on either side of the bisecting line. The third illustration below will yield a Symmeter value of approximately 1, since pixels on each side of the centerline are identical.

In the fourth example above, the diagonal color change will generate a Symmeter coefficient value of very close to .50, since almost exactly half the pixels will match their corresponding pixel on the other side of the centerline.

Are these values exact? Yes, the calculation is exact, but you may see some variance in the values, based on pixel compression introduced into the image. JPEG images, as an example use pixel value manipulation to create highly compressed image sizes. If you run a test on an image that is all of a single color and don't get a coefficient value that is 1, it is most likely because of very slight variances in the pixel color values in the image due to compression algorithms like this.

A Little More About Radial Symmetry

Radial symmetry measure is a bit more complicated than bi-lateral symmetry. In effect, when measuring radial symmetry, the image is divided into a number of segments, sort of like equally sized pie slices in a pie chart. Each pie segment is then compared to its opposite in order to determine its Symmeter value. Make sense?