In this paper we present a new framework for the analysis of scene visibility and radiosity complexity. We introduce a number of complexity measures from information theory quantifying how difficult it is to compute with accuracy the visibility and radiosity in a scene. We define the continuous mutual information as a complexity measure of a scene, independent of whatever discretisation, and discrete mutual information as the complexity of a discretised scene. Mutual information can be understood as the degree of correlation or dependence between all the points or patches of a scene. Thus, low complexity corresponds to low correlation and vice versa. Experiments illustrating that the best mesh of a given scene among a number of alternatives corresponds to the one with the highest discrete mutual information, indicate the feasibility of the approach. Unlike continuous mutual information, which is very cheap to compute, the computation of discrete mutual information can however b...

We propose a new approach, based on information theory, to study the visibility of a scene. Thus, we will define the concepts of entropy and mutual information applied to 3D scene visibility. Mainly, we analize the concept of entropy (or randomness) of scene visibility and we examine the relationship between entropy of scene visibility and the expected value of the mean square error for all form factors. Next, these concepts are applied to diverse sample scenes and the accuracy of the values presented is analyzed. Key Words: Rendering, Radiosity, Monte Carlo, Information Theory, Entropy 1 Introduction In this paper, the visibility of a scene, which is directly related to form factors [1], is analyzed from the viewpoint of information theory. In many different fields, the concept of entropy has been studied at length and has been used as a starting point in order to study complexity [6, 10, 18, 19]. In our case, we study the entropy of scene visibility and leave the study of scene com...

Abstract—Encryption is used to securely transmit data in open networks. Each type of data has its own features, therefore different techniques should be used to protect confidential image data from unauthorized access. Most of the available encryption algorithms are mainly used for textual data and may not be suitable for multimedia data such as images. In this paper, we introduce a block-based transformation algorithm based on the combination of image transformation and a well known encryption and decryption algorithm called Blowfish. The original image was divided into blocks, which were rearranged into a transformed image using a transformation algorithm presented here, and then the transformed image was encrypted using the Blowfish algorithm. The results showed that the correlation between image elements was significantly decreased by using the proposed technique. The results also show that increasing the number of blocks by using smaller block sizes resulted in a lower correlation and higher entropy. Index Terms—Image correlation, Image encryption, Image entropy, Permutation.

In this report we define the continuous mutual information of scene visibility, independent of whatever discretisation, and we prove that it is the least upper bound of the discrete mutual information. Thus, continuous mutual information can be understood as the maximum information transfer in a scene. Keywords: rendering, radiosity, Monte Carlo, information theory, entropy, mutual information 1. Previous concepts 1.1. Radiosity and form factor The radiosity equation solves for the illumination in a diffuse environment. It can be written in the form B(x) = E(x) +R(x) Z S B(x 0 )V (x; x 0 ) cosqcosq 0 pr 2 dA 0 (1) where B(x) is the radiosity, E(x) is the emittance, R(x) is the reflectance, S is the set of surfaces that form the environment, x; x 0 are points on surfaces of the environment, dA 0 is an area differential at point x 0 , r is the distance between x and x 0 , V (x; x 0 ) is a visibility function equal to 1 if x and x 0 are mutually visible and ...

this dissertation. 1.1 Radiosity, Complexity, and Information Theory The three fundamental pillars of this thesis are radiosity, complexity, and information theory: One of the most important topics in computer graphics is the accurate computation of the global illumination in a closed virtual environment (scene), i.e. the intensities of light over all its surfaces. "The production of realistic images requires in particular a precise treatment of lighting e#ects that can be achieved by simulating the underlying physical phenomena of light emission, propagation, and reflection"[82]. This type of simulation is called global illumination and is represented by the rendering equation [43], which is a Fredholm integral equation of the second kind. However obtaining an exact representation of the illumination is an intractable problem. Many di#erent techniques are used to obtain an approximate quantification of it [12, 82, 33]

We present a novel information-theoretic approach for thresholdingbased segmentation that uses the excess entropy to measure the structural information of a 2D or 3D image and to locate the optimal thresholds. This approach is based on the conjecture that the optimal thresholding corresponds to the segmentation with maximum structure, i.e., maximum excess entropy. The contributions of this paper are severalfold. First, we introduce the excess entropy as a measure of the spatial structure of an image. Second, we present an adaptive thresholding method based on the maximization of excess entropy. Third, we propose the use of uniformly distributed random lines to overcome the main drawbacks of the excess entropy computation. To show the good performance of the proposed segmentation approach different experiments on synthetic and real brain models are carried out. 2 A. Bardera, I. Boada, M. Feixas and M. Sbert 1

Abstract. Typical analytical measures in graph theory like degree centrality, betweenness and closeness centralities are very common and have long history of their successful use. However, modeling of covert, terrorist or criminal networks through social graph dose not really provide the hierarchical structure of such networks because these networks are composed of leaders and followers. It is possible mathematically, for some graphs to estimate the probability that the removal of a certain number of nodes would split the networks into may be non functional network. In this research we investigate and analyze a social network using Bayes probability theory model to calculate entropy of each node present in the network to high light the important actors in the network. This is accomplished by observing the amount of entropy change computed by successively removing each node in the network.

Noname manuscript No. (will be inserted by the editor) Evolving coordinated group behaviours through maximization of mean mutual information

We studied complexity of the stock market by modeling ǫ-machine of Standard and Poor’s 500 index from February 1983 to April 2006 using causal-state splitting reconstruction algorithm. We found that the statistical complexity and the number of causal states of constructed ǫ-machines have decreased for twenty years and that the average memory length needed to predict the future optimally has become shorter. These results support that the randomness of market has increased and the information is delivered to the economic agents more rapidly in year 2006 than in year 1983 and hence immediately applied to the market prices.