Czenakowski Distance

The Czenakowski distance (sometimes shortened as CZD) is a per-pixel quality metric that estimates quality or similarity by measuring differences between pixels. Because it compares vectors with strictly non-negative elements, it is often used to compare colored images, as color values cannot be negative. This different approach has a better correlation with subjective quality assessment than PSNR.

Definition

Androutsos et al. give the Czenakowski coefficient as follows:

$d_z(i,j) = 1 - \frac$

Where a pixel $x_i$ is being compared to a pixel $x_j$ on the ''k''-th band of color – usually one for each of red, green and blue.

For a pixel matrix of size $M \times N$, the Czenakowski coefficient can be used in an arithmetic mean spanning all pixels to calculate the Czenakowski distance as follows:

$\frac\sum^_\sum^_\begin1 - \frac\end$

Where $A_k(i,j)$ is the ''(i, j)''-th pixel of the ''k''-th band of a color image and, similarly, $B_k(i,j)$ is the pixel that it is being compared to.

Uses

In the context of image forensics – for example, detecting if an image has been manipulated –, Rocha et al. report the Czenakowski distance is a popular choice for Color Filter Array (CFA) identification.

References

Computer graphics
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