SSIM

SSIM, or Structural Similarity Index Measure, is a method for assessing the similarity between two images or video frames. It aims to model perceived changes in structural information, as well as luminance and contrast, to provide a metric that better correlates with human visual quality than traditional error measures such as mean squared error or peak signal-to-noise ratio. SSIM was introduced in 2004 by Wang, Bovik, Sheikh, and Simoncelli and has since become widely used in image and video processing tasks, including compression, denoising, and restoration.

The standard SSIM computation compares two images, x and y, using local windows that slide across the image. For each window, three components are computed: luminance, contrast, and structure. Let μx and μy be the mean intensities, σx and σy the standard deviations, and σxy the cross-covariance. The three comparison functions are:

l(x,y) = (2 μx μy + C1) / (μx^2 + μy^2 + C1),

c(x,y) = (2 σx σy + C2) / (σx^2 + σy^2 + C2),

s(x,y) = (σxy + C3) / (σx σy + C3).

The SSIM index for a window is the product l(x,y) · c(x,y) · s(x,y). An SSIM map is formed by sweeping the window across the image, and the overall SSIM index is typically the mean of that map. Constants C1, C2 (and C3) stabilize the divisions.

Variants and extensions include Multi-Scale SSIM (MS-SSIM), color SSIM, and fast approximations. SSIM is widely used as an objective quality metric for codecs and restoration methods, but it requires a reference image and can be sensitive to alignment, scale, and cropping. It does not always align perfectly with perceptual judgments across all content.