A layered version of the Block Decomposition Method [1, 2] ("Layered BDM"), serves as a descriptor of both weighted networks and grayscale or color images. This descriptor provides an estimate of Kolmogorov Complexity that's sensitive to morphological perturbation. To estimate the complexity of a grayscale texture, we quantize it and aggregate the estimated Kolmogorov complexity values of binary 4 x 4 squares, estimated through the Coding Theorem Method [3, 4].

// CTMs is a hashtable with binary 2D blocks as keys // their respective values being estimations of Kolmogorov complexity // obtained through the Coding Theorem Method function LayeredBDM (grayImage, CTMs, blockSize, blockOffset, q)	// the image is quantized in q digital levels	imag <- quantize(grayImage, q)	blocksList = {}	for i in 1:q // the quantized image is binarized through the q digital layers	binImag <- binarize(i, imag)	// and decomposed into n x n blocks, which are added to the blockList	blocksList.append(blockDecompose(binImag, blockSize, blockOffset))	// we count the appearance of all binary blocks through all layers	// and store the count of each into a hash table with the blocks as keys	// and the blockCount as values	blockHT(blocks:blockCount) <- countBlocks(blockList)	// The blocks' CTM values are retrieved from the CTMs hashtable, these and	// the Log2 of the cardinality of each are added to compute the BDM value	lBDM <- CTMs(keys(blockHT)) + Log2(values(blockHT))	return(lBDM) 

[1] Antonio Rueda-Toicen, "Morphological Image Analysis through Estimations of Kolmogorov Complexity" (in preparation)

[2] Hector Zenil, Santiago Hernández-Orozco, Narsis A.Kiani, Fernando Soler-Toscano, Antonio Rueda-Toicen, and Jesper Tegner "A Decomposition Method for Global Evaluation of Shannon Entropy and Local Estimations of Algorithmic Complexity", https://arxiv.org/abs/1609.00110

[3] Fernando Soler - Toscano, Hector Zenil, Jean-Paul Delahaye, and Nicolas Gauvrit (2014) "Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines." PLoS ONE 9 (5) : e96223.

If you use this code or algorithm for a publication, please cite the above references and the following:

Rueda-Toicen, Antonio, Image Analysis with Estimations of Kolmogorov Complexity, (2018), GitHub repository, https://github.com/andandandand/ImageAnalysisWithAlgorithmicInformation, DOI: /10.5281/zenodo.1291510

@misc{Rueda-Toicen2018, author = {Rueda-Toicen, Antonio}, title = {Image Analysis with Estimations of Kolmogorov Complexity}, year = {2018}, publisher = {GitHub}, howpublished = {https://github.com/andandandand/ImageAnalysisWithAlgorithmicInformation}, DOI = {/10.5281/zenodo.1291510} url = {https://doi.org/10.5281/zenodo.1291510} } 

• antonio "dot" rueda "." toicen "at" gmail 'dot' com
• antonio "dot" rueda "." toicen "at" algorithmicnaturelab 'dot' com

DOI: https://zenodo.org/record/1291511#.WyWwtKdKhRY