Czenakowski distance explained

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-

	p
2\sum
	k=1

min(x_ik, x_jk)

	p
\sum
	k=1

(x_ik+x_jk)

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 x N

, the Czenakowski coefficient can be used in an arithmetic mean spanning all pixels to calculate the Czenakowski distance as follows:

	1
	MN

	M-1
\sum
	i=0

	N-1
\sum
	j=0

\begin{pmatrix}1-

	3
2\sum
	k=1

min(A_k(i,j), B_k(i,j))

	3
\sum
	k=1

(A_k(i,j)+B_k(i,j))

\end{pmatrix}

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.