Effect of Image Linearization on Normalized Compression Distance

Abstract

Abstract. Normalized Information Distance, based on Kolmogorov complexity, is an emerging metric for image similarity. It is approximated by the Normalized Compression Distance (NCD) which generates the relative distance between two strings by using standard compression algorithms to compare linear strings of information. This relative distance quantifies the degree of similarity between the two objects. NCD has been shown to measure similarity effectively on information which is already a string: genomic string comparisons have created accurate phylogeny trees and NCD has also been used to classify music. Currently, to find a similarity measure using NCD for images, the images must first be linearized into a string, and then compared. To understand how linearization of a 2D image affects the similarity measure, we perform four types of linearization on a subset of the Corel image database and compare each for a variety of image transformations. Our experiment shows that different linearization techniques produce statistically significant differences in NCD for identical spatial transformations.

Kernelized Supervised Dictionary Learning

“…However, this led to contradictory results in the literature: while it is shown in [92] that using JPEG2000 yields better results than string compressors on the classification of satellite images, [89] and [93] conclude that JPEG and JPEG2000 does not yield better results than string compressors on images. Also, Bardera et al conclude that string compressors perform better than an image compressor (using JPEG2000) in image registration [85].…”

“…Second, there is no single approach to convert 2D to 1D data as there are two degrees of freedom in this conversion: how to scan an image and how to take the pixels from two images whose similarities are to be computed [85]. The first degree of freedom leads to many different approaches of linearizing 2D data such as row by row, column by column, scan filling curves, global line sampling, zigzag linearization, Hilbert-Peano curve, and self-describing context-based pixel ordering (SCPO) [85,89]. The effect of linearization using four of the above linearization approaches was empirically investigated on the computation of NCD in [89].…”

“…The first degree of freedom leads to many different approaches of linearizing 2D data such as row by row, column by column, scan filling curves, global line sampling, zigzag linearization, Hilbert-Peano curve, and self-describing context-based pixel ordering (SCPO) [85,89]. The effect of linearization using four of the above linearization approaches was empirically investigated on the computation of NCD in [89]. They concluded that: "images may not be fully expressible as a string, at least using current compression algorithms" and also that their results "certainly indicate that the method of linearization does matter".…”

Maximizing Kolmogorov Complexity for accurate and robust bright field cell segmentation

“…Many methods of linearization were explored in [27] and column concatenation was found to be effective because spatially located regularities are picked up by compression. Bzip2 is applied to compute the compression size of each individual string and also each pairwise concatenated string (for N C D , Equation 2).…”

ADAMAS: Interweaving unicode and color to enhance CAPTCHA security

“…Mortensen et al [30] compare several types of linearization and find that despite producing different NCD values, none of them uniformly outperforms the others. We follow prior researchers in similar applications [29,31] and use a row-byrow scan of the image for linearization.…”