The Structural SIMilarity Index

The Structural SIMilarity Index

2022-11-10 Paper Reading Note

1. Over all Purpose

The luminance information computation method is: However, based on our prior knowledge

The structures of the objects in the scene are independent of the illumination.

Then we can define the structural information in an image as those attributes that represent the structure of objects in the scene. (Since luminance and contrast can vary across a scene, we can use the local luminance and contrast.)

2. System Diagram

SSIM

Fig. 1 Diagram of the structural similarity (SSIM) measurement system.

The system separates the task of similarity measurement into three comparisons: luminance, contrast and structure.

3. Details

Three Important conditions

1. Symmetry: ;
2. Boundedness: ;
3. Unique maximum: if and only if ;

Luminance Measurement

Luminace Comparison

where the constance is included to avoid instability when is very close to zero. where is the dynamic range of the pixel values, and is a small constant.

Contrast Measurement

Remove the intensity from the signal. So in discrete form, the resulting signal corresponds to the projection of vector onto the hyperplane defined by Use the standard deviation as an estimate of the contrast (unbiased estimate)

Contrast Comparison

Structure Comparison

SSIM

Where , and are parameters used to adjust the relative importance of the three components.