Theory of fuzzy integrals and its applications

Computation of good viewpoints is important in several fields: computational geometry, visual servoing, robot motion, graph drawing, etc. In addition, selection of good views is rapidly becoming a key issue in computer graphics due to the new techniques of Image Based Rendering. Although there is no consensus about what a good view means in Computer Graphics, the quality of a viewpoint is intuitively related to how much information it gives us about a scene. In this paper we use the theoretical basis provided by Information Theory to define a new measure, viewpoint entropy, that allows us to compute good viewing positions automatically. We also show how it can be used to select a set of good views of a scene for scene understanding. Finally, we design an algorithm that uses this measure to explore automatically objects or scenes.

Viewpoint Selection using Viewpoint Entropy

All self-respecting nonlinear scientists know self-organization when they see it: except when we disagree. For this reason, if no other, it is important to put some mathematical spine into our floppy intuitive notion of self-organization. Only a few measures of self-organization have been proposed; none can be adopted in good intellectual conscience. 
To find a decent formalization of self-organization, we need to pin down what we mean by organization. The best answer is that the organization of a process is its causal architecture—its internal, possibly hidden, causal states and their interconnections. Computational mechanics is a method for inferring causal architecture—represented by a mathematical object called the e-machine—from observed behavior. The e-machine captures all patterns in the process which have any predictive power, so computational mechanics is also a method for pattern discovery. In this work, I develop computational mechanics for four increasingly sophisticated types of process—memoryless transducers, time series, transducers with memory, and cellular automata. In each case I prove the optimality and uniqueness of the e-machine's representation of the causal architecture, and give reliable algorithms for pattern discovery. 
The e-machine is the organization of the process, or at least of the part of it which is relevant to our measurements. It leads to a natural measure of the statistical complexity of processes, namely the amount of information needed to specify the state of the E-machine. Self-organization is a self-generated increase in statistical complexity. This fulfills various hunches which have been advanced in the literature, seems to accord with people's intuitions, and is both mathematically precise and operational.

/pdf/causal-architecture-complexity-and-self-organization-in-time-1057jo2eu4.pdf

Causal architecture, complexity and self-organization in time series and cellular automata

In this paper, a novel statistical model based on Benford's law for the probability distributions of the first digits of the
block-DCT and quantized JPEG coefficients is presented. A parametric logarithmic law, i.e., the generalized Benford's
law, is formulated. Furthermore, some potential applications of this model in image forensics are discussed in this paper,
which include the detection of JPEG compression for images in bitmap format, the estimation of JPEG compression Qfactor
for JPEG compressed bitmap image, and the detection of double compressed JPEG image. The results of our
extensive experiments demonstrate the effectiveness of the proposed statistical model.

A generalized Benford's law for JPEG coefficients and its applications in image forensics

Viewpoint selection is an emerging area in computer graphics with applications in fields such as scene exploration, image-based modeling, and volume visualization. In particular, best view selection algorithms are used to obtain the minimum number of views (or images) in order to understand or model an object or scene better. In this article, we present a unified framework for viewpoint selection and mesh saliency based on the definition of an information channel between a set of viewpoints (input) and the set of polygons of an object (output). The mutual information of this channel is shown to be a powerful tool to deal with viewpoint selection, viewpoint stability, object exploration and viewpoint-based saliency. In addition, viewpoint mutual information is extended using saliency as an importance factor, showing how perceptual criteria can be incorporated to our method. Although we use a sphere of viewpoints around an object, our framework is also valid for any set of viewpoints in a closed scene. A number of experiments demonstrate the robustness of our approach and the good behavior of the proposed measures.

A unified information-theoretic framework for viewpoint selection and mesh saliency

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 be quite demanding. We will develop cheap complexity measure estimates and derive practical algorithms from this framework in future work.

http://graphics.cs.kuleuven.be/publications/AITFFTAOSC/AITFFTAOSC_paper.pdf

An information theory framework for the analysis of scene complexity

Benford's Law (also known as the First Digit Law) is well known in statistics of natural phenomena. It states that, when dealing with quantities obtained from Nature, the frequency of appearance of each digit in the first significant place is logarithmic. This law has been observed over a broad range of statistical phenomena. In this paper, we will explore its application to image analysis. We will show how light intensities in natural images, under certain constraints, obey this law closely. We will also show how light intensities in synthetic images follow this law whenever they are generated using physically realistic methods, and fail otherwise. Finally, we will study how transformations on the images affect the adjustment to the Law and how the fitting to the law is related to the fitting of the distribution of the raw intensities of the image to a power law.

Benford's law for natural and synthetic images

Energy-saving light positioning using heuristic search

The aim of this paper is twofold. In one hand, we want to make evident the necessity that agents operating in multi-agent environments have for a social model that somehow allows them to determine the trust they can put in the assertions made by the other agents in the environment. In the other hand, we want to introduce a quite general mechanism, fuzzy filters, based on fuzzy systems theory, which allows us to satisfy that necessity. We will study a problem where individual taxi driver agents compete in order to obtain passengers to transport in exchange of money. We have implemented a simulation in which the behavior of each individual agent is given by a set of fuzzy systems. Agents use one of them to determine the next passenger to go for. The other fuzzy systems, the fuzzy filters, allows the modeling of the other agents from the point of view of the confidence their assertions deserve. Agents will make use of those fuzzy filters to decide whether they must compete or not against the other agents for a passenger. A quite simple evolutionary method allows us to see how individual agents can improve their performance by refining its internal models of the competitor agents.

/pdf/a-fuzzy-system-based-approach-to-social-modeling-in-multi-561u9b35pe.pdf

A fuzzy system based approach to social modeling in multi-agent systems

Finding an optimal discretization of a scene is an important but difficult problem in radiosity. The efficiency of hierarchical radiosity for instance, depends entirely on the subdivision criterion and strategy that is used. We study the problem of adaptive scene discretization from the point of view of information theory. In previous work, we have introduced the concept of mutual information, which represents the information transfer or correlation in a scene, as a complexity measure and presented some intuitive arguments and preliminary results concerning the relation between mutual information and scene discretization. In this paper, we present a more general treatment supporting and extending our previous findings to the level that the development of practical information theory-based tools for optimal scene discretization becomes feasible.

Esteve del Acebo

Papers

An information theory framework for the analysis of scene complexity

Benford's law for natural and synthetic images

Energy-saving light positioning using heuristic search

A fuzzy system based approach to social modeling in multi-agent systems

Information theory tools for scene discretization