Structural Similarity (SSIM) Index is an image quality metric. SSIM index is computed for the image with respect to the reference image. The reference image is usually needs to be of perfect quality. This quantitative measure considers three parameters namely luminance, contrast and structural information between the two images to computed the SSIM value.

When to Use

  • SSIM can be used in television industry to determine the quality of video streamed from the satellites.
  • SSIM can be used as a benchmark to check the performance of other image progressing algorithms, like image compression.

Concepts

The human visual system is adapted to extract structural information. The SSIM algorithm separates out the similarity measurements into three different components:

  • Luminance
  • Contrast
  • Structural

The luminance between the two signals is determined by the mean intensity of the signals. The contrast is determined by the standard deviation. And the structural is determined by the correlation of the two signals.

L x , y = 2 μ x μ y + C 1 / 2 μ x 2 + μ y 2 + C 1
C x , y = 2 σ x σ y + C 2 / 2 σ x 2 + σ y 2 + C 2
S x , y = σ x y + C 3 / σ x σ y + C 3

where

  • μx is the mean over a window in Image X,

  • μy is the mean over a window in Image Y,

  • σx is standard deviation (square root of variance) over a window in Image X,

  • σx is standard deviation (square root of variance) over a window in Image Y,

  • σxy is co-variance over a window between Image X and Image Y,

  • x and y refer to a local window in the Image X and Y respectively,

  • C1, C2 and C3 are constants.

SSIM (x,y) is a multiplication of these three components.

If C3 is set to C2/2, then over a particular window:

S S I M x , y = 2 μ x μ y + C 1 * 2 σ x y + C 2 / μ x 2 + μ y 2 + C 1 * σ x 2 + σ y 2 + C 2

The Mean-SSIM is the average over all such local windows. The window is moved across the image one pixel at a time.

Normal SSIM

In normal SSIM, a circular symmetric Gaussian weighting function is used calculate the mean values. Choose Normal SSIM when the image has low contrast or does not contain clear structural information; for example, when the image is a texture sample.

Fast SSIM

Fast SSIM uses a faster approach to calculate the variance and mean values, which are time-consuming in normal SSIM. The gradient images are calculated using the Roberts gradient templates to represent variance. Mean values are calculated by averaging pixels in the local window. Fast SSIM is best suited for images which have clear structural information, such as strong edges. Because it is based on gradient images, Fast SSIM may not be sufficient if the image has low contrast or poor structural information.