17 February 2010 A perceptual similarity measure based on smoothing filters and the normalized compression distance
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Abstract
We present an empirical study of properties of the remarkable Normalized Compression Distance (NCD), a mathematical formulation by M. Li et al. that quantifies similarity between two binary strings as the additional amount of algorithmic information required to transform the description of one to the other. In particular, we are interested in the NCD values between an image and its modified versions by common image processing techniques. Experimental data obtained indicate that the NCD is symmetric and transitive, and that it can be used as a reasonable perceptual measure of similarity, but only in the spatial domain. Further, the NCD clusters the common image processing techniques into three groups in a manner consistent with the human perception of similarity. We also introduce two independent modifications to the NCD and study their properties. The first modification calls for applying a median filter and then thresholding to the input images before the NCD is computed, which results in a more uniform distribution of the NCD values. The second modification modifies the NCD formula to reflect the running time as well as the size of the shortest program that transforms one input string to the other. Obtained data show that using this modified NCD, it is possible to classify subtle changes (e.g., watermarking) to a font character image as similar to the original and drastic changes (e.g., rotation by 90 degrees) as different.
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Nicholas Tran, Nicholas Tran, } "A perceptual similarity measure based on smoothing filters and the normalized compression distance", Proc. SPIE 7527, Human Vision and Electronic Imaging XV, 75270M (17 February 2010); doi: 10.1117/12.845400; https://doi.org/10.1117/12.845400
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