Image distortion analysis based on normalized perceptual information distance

The normalized information distance (NID) is an universal metric distance based on Kolmogorov complexity. However, NID is not computable in a Turing sense. The normalized compression distance (NCD) is a computable distance that approximates NID by using normal compressors. NCD is a parameter-free distance that compares two signals by their lengths after separate compression relative to the length of the signal resulting from their concatenation after compression. The use of NCD for image retrieval over large image databases is difficult due to the computational cost of compressing the query image concatenated with every image in the database. The use of dictionaries extracted by dictionary-based compressors, such as the LZW compression algorithm, has been proposed to overcome this problem. Here we propose a Content-Based Image Retrieval system based on such dictionaries for the mining of hyperspectral databases. We compare results using the Normalized Dictionary Distance (NDD) and the Fast Dictionary Distance (FDD) against the NCD over different datasets of hyperspectral images. Results validate the applicability of dictionaries for hyperspectral image

<p> Image similarity measurement is a common issue in a broad range of applications in image processing, recognition, classification and retrieval. Conventional image similarity measures are often limited to specific applications and cannot be applied in general scenarios. The theory of Kolmogorov complexity provides a universal framework for a generic similarity metric based on information distance between objects. Normalized Information Distance (NID) has been shown to be a valid and universal distance metric applicable in measurement of similarity of any two objects, and has been successfully applied to a wide range of applications in the past. The difficulty of NID lies in the non-computable nature of the Kolmogorov complexity, and thus approximation has to be applied in practice. Here we propose a perceptually-inspired Normalized Conditional Compression Distance (NCCD) measure by using the Divisive Normalization Transform (DNT) as a means to model the non-linear behavior of the Human Visual System (HVS) in reducing statistical dependencies of visual signals for efficient representation, and show that this perceptual extension of NID can be used in a wide range of image processing applications, including texture classification and face recognition. </p>

The data contained in the DNA atom for even basic unicellular life forms is huge and requires proficient capacity. Proficient capacity implies, expulsion of all excess from the information being put away. The Proposed Compression calculation “GENBIT Compress” is solely intended to dispense with all repetition from the DNA groupings of extensive genomes. We characterize a pressure separation, taking into account an ordinary compressor to show it is a permissible separation. Just as of late have researchers started to value the way that pressure proportions imply a lot of essential measurable data. In applying the methodology, we have utilized another DNA succession compressor “GENBIT Compress”. The NCD is universal in that it is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, is provably optimal in the sense that it minimises every computable normalized metric that satisfies a certain density requirement. However, the optimality comes at the price of using the non-computable notion of Kolmogorov complexity. We propose precise notions of similarity metric, normal compressor, and show that the NCD based on a normal compressor is a similarity metric that approximates optimality The normalized compression distance, an efficiently computable, and thus practically applicable form of the normalized information distance is used to calculate Distance Matrix The normalized compression distance, an effectively processable, and along these lines for all intents and purposes relevant type of the standardized data separation is utilized to figure Distance Matrix. In this paper this new separation framework is proposed to recreate Phylogenetic tree. Phylogeny are the fundamental device for speaking to the relationship among organic elements. Phylogenetic remaking techniques endeavor to locate the developmental history of given arrangement of species. This history is generally depicted by an edge weighted tree, where edges relate to various branches of advancement, and the heaviness of an edge compares to the measure of developmental change on that specific branch. We developed a phylogenetic tree with BChE DNA arrangements of warm blooded creatures giving new proposed separation grid by GENBIT compressor to NJ (Neighbor-Joining calculation) tree. The results in the present research confirm the existence of low compression ratios for natural DNA sequences with high repetitive DNA bases(A, C, G, T), the more repetitive bases, the less is their compression ratios. The ultimate goal is, of course, to learn the “genome organization” principles, and explain this organization using our knowledge about evolution.

ABSTRACTAs with conventional images corner detection is an important aspect of many computer vision problems involving catadioptric images. However, classical image processing algorithms are no longer appropriate for catadioptric images due to nonuniform resolution and distortions of catadioptric images. In this paper, we propose a novel approach to corner detection for catadioptric images based on triangle mesh. First, we transform catadioptric images to spherical images by combining an improved projection model for central catadioptric cameras with triangle mesh for a unit sphere. Spherical images yield a spatially uniform resolution domain for processing catadioptric images. Then, based on the topology of a triangle mesh, variations of light intensity with respect to directions for each image patch are measured to detect corners. The proposed algorithm addresses problems of catadioptric image processing caused by non-uniform resolution and distortions of these images. Experimental results showed that comparing to widely used methods, the triangle mesh-based corner detection algorithm can achieve higher repeatability rate relative to different imaging condition changes.

Information distance has become an important tool in a wide variety of applications. Various types of information distance have been made over the years. These information distance measures are different from entropy metric, as the former is based on Kolmogorov complexity and the latter on Shannon entropy. However, for any computable probability distributions, up to a constant, the expected value of Kolmogorov complexity equals the Shannon entropy. We study the similar relationship between entropy and information distance. We also study the relationship between entropy and the normalized versions of information distances.

1. UNIVERSALITYThe theory of Kolmogorov complexity is based on thediscovery, by Alan Turing in 1936, of the universal Turingmachine. After proposing the Turing machine as anexplanation of the notion of a computing machine, Turingfound that there exists one Turing machine which cansimulate any other Turing machine.Complexity, according to Kolmogorov, can be measuredby the length of the shortest program for a universal Turingmachine that correctly reproduces the observed data. It hasbeen shown that, although there are many universal Turingmachines(andthereforemanypossible ‘shortest’ programs),the corresponding complexities differ by at most an additiveconstant.The main thrust of the theory of Kolmogorov complexityis its ‘universality’; it strives to construct universal learningmethods based on universal coding methods. Thisapproach was originated by Solomonoff and made moreappealing to mathematicians by Kolmogorov. Typicallythese universal methods will be computable only in someweak sense. In applications, therefore, we can only hopeto approximate Kolmogorov complexity and related notions(such as randomnessdeficiency and algorithmic informationmentioned below). This special issue contains both materialon non-computable aspects of Kolmogorov complexity andmaterial on many fascinating applications based on differentways of approximating Kolmogorov complexity.2. BEGINNINGSAs we have already mentioned, the two main originators ofthe theory of Kolmogorovcomplexity were Ray Solomonoff(born 1926) and Andrei Nikolaevich Kolmogorov (1903–1987). The motivations behind their work were completelydifferent; Solomonoff was interested in inductive inferenceand artificial intelligence and Kolmogorov was interestedin the foundations of probability theory and, also, ofinformation theory. They arrived, nevertheless, at the samemathematical notion, which is now known as Kolmogorovcomplexity.In 1964 Solomonoff published his model of inductiveinference. He argued that any inference problem can bepresentedas a problemof extrapolatinga verylongsequenceof binary symbols; ‘given a very long sequence, representedby T, what is the probability that it will be followed by a

Spiral waves characterization: Implications for an automated cardiodynamic tissue characterization

In C-alike programs, the source code is separated into header files and source files. During the software evolution process, both these two kinds of files need to adapt to changing requirement and changing environment. This paper studies the coevolution of header files and source files of C-alike programs. Using normalized compression distance that is derived from Kolmogorov complexity, we measure the header file difference and source file difference between versions of an evolving software product. Header files distance and source files distance are compared to understand their difference in pace of evolution. Mantel tests are performed to investigate the correlation of header file evolution and source file evolution. The study is performed on the source code of Apache HTTP web server.

To Identify the Particular image from a huge dataset is key problem in Image Processing. To retrieve the exact image a block truncation coding based method is used. To derive feature descriptors Dot Diffusion Block Truncation Coding (DDBTC) is used. The image features derived from color quantizer as well as Bitmap image. Using color quantizer Color Histogram Features (CHF) is obtained and using Bitmap image Bit Pattern Feature (BPF) is obtained. The various distance measures are employed to match the sameness between images. Calculated results are better in term of Average Recall Rate (ARR) and Average Precision rate (APR).

We use an information-theoretic distortion measure called the Normalized Compression Distance (NCD), first proposed by M. Li et al., to determine whether two rectangular gray-scale images are visually distinguishable to a human observer. Image distinguishability is a fundamental constraint on operations carried out by all players in an image watermarking system. The NCD between two binary strings is defined in terms of compressed sizes of the two strings and of their concatenation; it is designed to be an effective approximation of the noncomputable but universal Kolmogorov distance between two strings. We compare the effectiveness of different types of compression algorithms? in predicting image distinguishability when they are used to compute the NCD between a sample of images and their watermarked counterparts. Our experiment shows that, as predicted by Li's theory, the NCD is largely independent of the underlying compression algorithm. However, in some cases the NCD fails as a predictor of image distinguishability, since it is designed to measure the more general notion of similarity. We propose and study a modified version of the NCD to model the latter, which requires that not only the change be small but also in some sense random with respect to the original image.

In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual information, and higher interaction information relate to each other. This is answered by Hu's theorem, which is widely known in the form of information diagrams: it relates shapes in a Venn diagram to information functions, thus establishing a bridge from set theory to information theory. In this work, we view random variables together with the joint operation as a monoid that acts by conditioning on information functions, and entropy as a function satisfying the chain rule of information. This abstract viewpoint allows to prove a generalization of Hu's theorem. It applies to Shannon and Tsallis entropy, (Tsallis) Kullback-Leibler Divergence, cross-entropy, Kolmogorov complexity, submodular information functions, and the generalization error in machine learning. Our result implies for Chaitin's Kolmogorov complexity that the interaction complexities of all degrees are in expectation close to Shannon interaction information. For well-behaved probability distributions on increasing sequence lengths, this shows that the per-bit expected interaction complexity and information asymptotically coincide, thus showing a strong bridge between algorithmic and classical information theory.Comment: 46 pages, 5 figures

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.

Currently, various techniques for measuring the proximity between two objects in the internet network are continuously being developed. The objects in question are in the form of concepts, e-mails, words, and so on. Normalized Web Distance (NWD) has proven to be a simple, yet powerful measure of the semantic linkages between the two concepts. NWD has several approaches according to the object being measured, such as Normalized Google Distance (NGD) and Normalized Compression Distance (NCD). NGD and NCD have a way of determining similarity and calculating the distance to find the similarity of two different measuring objects. This paper shows and provides information on the performance of the two NWD approaches, namely NGD and NCD to facilitate understanding of the use of NGD and NCD on various problems. Correct understanding can put the NGD and the NCD in the right case.

The neuronal functional connectivity is a complex and non-stationary phenomenon creating dynamic networks synchronization determining the brain states and needed to produce tasks. Here, as a measure that quantifies the synchronization between the neuronal electrical activity of two brain regions, we used the normalized compression distance (NCD), which is the length of the compressed file constituted by the concatenated two signals, normalized by the length of the two compressed files including each single signal. To test the NCD sensitivity to physiological properties, we used NCD to measure the cortico-muscular synchronization, a well-known mechanism to control movements, in 15 healthy volunteers during a weak handgrip. Independently of NCD compressor (Huffman or Lempel Ziv), we found out that the resulting measure is sensitive to the dominant-non dominant asymmetry when novelty management is required (p = 0.011; p = 0.007, respectively) and depends on the level of novelty when moving the non-dominant hand (p = 0.012; p = 0.024). Showing lower synchronization levels for less dexterous networks, NCD seems to be a measure able to enrich the estimate of functional two-node connectivity within the neuronal networks that control the body.

Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, ...). Crudely speaking, it enables us to better distinguish between mathematical possible (possible abnormal) and physically possible situations. We show that this formalization is not only in good accordance with theoretical physics, but it can also be applied to robust control: instead of requiring that the control work for all mathematically possible situations, we only require that the control works for all non-abnormal situations.