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.[citation needed]
Definition
Androutsos et al. give the Czenakowski coefficient as follows:[1]
[math]\displaystyle{ d_z(i,j) = 1 - \frac{ 2\sum^{p}_{k=1} \text{min}(x_{ik},\ x_{jk})}{ \sum^{p}_{k=1}( x_{ik} + x_{jk} ) } }[/math]
Where a pixel [math]\displaystyle{ x_i }[/math] is being compared to a pixel [math]\displaystyle{ x_j }[/math] on the k-th band of color – usually one for each of red, green and blue.
For a pixel matrix of size [math]\displaystyle{ M \times N }[/math], the Czenakowski coefficient can be used in an arithmetic mean spanning all pixels to calculate the Czenakowski distance as follows:[2][3]
[math]\displaystyle{ \frac{1}{MN}\sum^{M-1}_{i=0}\sum^{N-1}_{j=0}\begin{pmatrix}1 - \frac{ 2\sum^{3}_{k=1} \text{min}(A_k(i,j),\ B_k(i,j))}{ \sum^{3}_{k=1}( A_k(i,j) + B_k(i, j) ) }\end{pmatrix} }[/math]
Where [math]\displaystyle{ A_k(i,j) }[/math] is the (i, j)-th pixel of the k-th band of a color image and, similarly, [math]\displaystyle{ B_k(i,j) }[/math] 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.[2]
References
- ↑ Androutsos, D.; Plataniotiss, K.N.; Venetsanopoulos, A.N. (1998). "Distance measures for color image retrieval". Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269). 2. pp. 770–774. doi:10.1109/ICIP.1998.723652. ISBN 0-8186-8821-1. https://ieeexplore.ieee.org/document/723652.
- ↑ 2.0 2.1 Rocha, Anderson; Scheirer, Walter; Boult, Terrance; Goldenstein, Siome (October 2011). "Vision of the unseen". ACM Computing Surveys 43 (4): 1–42. doi:10.1145/1978802.1978805. ISSN 0360-0300. https://doi.org/10.1145/1978802.1978805.
- ↑ Advances in Computer Vision and Information Technology. New Delhi, India: I.K. International Pvt. Ltd.. 2007. p. 91. ISBN 978-81-89866-74-7. https://books.google.com/books?id=pNKxKYHL2RYC&pg=PA91.
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