Thinning Algorithm Using Hypergraph Based Morphological Operators

The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper briefly describes morphological operators using hypergraph and its applications for thinning algorithms. The morphological operators using hypergraph method is used to preventing errors and irregularities in skeleton, and is an important step recognizing line objects. The morphological operators using hypergraph such as dilation, erosion, opening, closing is a novel approach in image processing and it act as a filter remove the noise and errors in the images.Comment: Advance Computing Conference (IACC), 2015 IEEE International,Banglore Indi

Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians

The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG Bayesian networks, and there exists a commercial implementation of this algorithm. However, this algorithm can only be used for MoG BNs. Some limitations of such networks are as follows. All continuous chance variables must have conditional linear Gaussian distributions, and discrete chance nodes cannot have continuous parents. The methods described in this paper will enable us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This includes networks with continuous chance nodes with non-Gaussian distributions, networks with no restrictions on the topology of discrete and continuous variables, networks with conditionally deterministic variables that are a nonlinear function of their continuous parents, and networks with continuous chance variables whose variances are functions of their parents.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006

A New Pruning Method for Solving Decision Trees and Game Trees

The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we do not need a conditional probability for each edge emanating from a chance node. Instead, we require a joint probability for each path from the root node to a leaf node. We compare the pruning method to the traditional rollback method for decision trees and game trees. For problems that require Bayesian revision of probabilities, a scenario tree representation with the pruning method is more efficient than a decision tree representation with the rollback method. For game trees, the pruning method is more efficient than the rollback method.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Binary Join Trees

The main goal of this paper is to describe a data structure called binary join trees that are useful in computing multiple marginals efficiently using the Shenoy-Shafer architecture. We define binary join trees, describe their utility, and sketch a procedure for constructing them.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Valuation Networks and Conditional Independence

Valuation networks have been proposed as graphical representations of valuation-based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory, Spohn's epistemic belief theory, and Zadeh's possibility theory. In this paper, we show how valuation networks encode conditional independence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, directed acyclic graph models, directed balloon graph models, and recursive causal graph models.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Conditional Independence in Uncertainty Theories

This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and conditional independence in terms of factorization of the joint valuation. The definitions of independence and conditional independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992

A Fusion Algorithm for Solving Bayesian Decision Problems

This paper proposes a new method for solving Bayesian decision problems. The method consists of representing a Bayesian decision problem as a valuation-based system and applying a fusion algorithm for solving it. The fusion algorithm is a hybrid of local computational methods for computation of marginals of joint probability distributions and the local computational methods for discrete optimization problems.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991

Solving Hybrid Influence Diagrams with Deterministic Variables

We describe a framework and an algorithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continuous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy's fusion algorithm for discrete influence diagrams. We describe an extended Shenoy-Shafer architecture for propagation of discrete, continuous, and utility potentials in hybrid influence diagrams that include deterministic chance variables. The algorithm and framework are illustrated by solving two small examples.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

Valuation-Based Systems for Discrete Optimization

This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of values, and functions that map sample spaces of sets of variables to the set of values. The functions, called valuations, represent the factors of an objective function. Solving the optimization problem involves using two operations called combination and marginalization. Combination tells us how to combine the factors of the joint objective function. Marginalization is either maximization or minimization. Solving an optimization problem can be simply described as finding the marginal of the joint objective function for the empty set. We state some simple axioms that combination and marginalization need to satisfy to enable us to solve an optimization problem using local computation. For optimization problems, the solution method of valuation-based systems reduces to non-serial dynamic programming. Thus our solution method for VBS can be regarded as an abstract description of dynamic programming. And our axioms can be viewed as conditions that permit the use of dynamic programming.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990

Thermal noise induced stochastic resonance in self organizing Fe nanoparticle system

The natural world is replete with examples of multistable systems, known to respond to periodic modulations and produce a signal, which exhibits resonance with noise amplitude. This is a concept not demonstrated in pure materials, which involve a measured physical property. In a thermoremanent magnetization experiment with a common magnetic material, Fe, in the nanoparticulate form, we establish how magnetization in a system of dilute spins during dissipation of stored magnetic energy, breaks up into spontaneous oscillatory behavior. Starting at 175 K and aided by temperature (stochastic noise) the oscillation amplitude goes through a maximum, reminiscent of stochastic resonance. Our observation of thermal noise induced coherent resonance is due to intrinsic self-organizing magnetic dynamics of the Fe nanoperticle system without applying any external periodic force. These results yield new possibilities in design of magnetic materials and a platform to understand stochastic interference and phase synchronization in neural activity, as models for neural communication.Comment: 7 figure