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# Book Idea: Monte Carlo, Random Fields methods in Image Analysis

Published:

Last Edited: February 9, 2009, 10:39 pm

Title: Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability) (Hardcover)

Author: Gerhard Winkler

Description:

This second edition of G. Winkler's successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications.

Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required.

The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added. This second edition comes with a CD-ROM by F. Friedrich,containing a host of (live) illustrations for each chapter. In an interactive environment, readers can perform their own experiments to consolidate the subject.

Why?

Good ol' question why. What does image recognition have to do with lottery predictions you ask? first what does it have that is not in common!

For starters, image recognition is not about prediction, its about inference or classification of historical data.

A qualified image in nature, such an image of a tree can be categorized by finding repetitive features (such as leaves, trunk, tree apples etc) in lottery no such a repetitive features exists, no image recognition can be applied to lottery data as no repetitive matrix can be found (some will disagree on this point!)

However if an image is hard to categorize, it does not have distinctive features, image recognition becomes very hard (i.e computing some polygons by a deterministic algorithm and arriving with solutions to an equation in some n-space represented by some complex polynomial) and that's where stochastic methods such as Monte Carlo comes along, by a massive random sampling bombardment a target image is dissected and compared to some large database containing samples of vast number of possible shapes including complete shapes in a given classification (ie sequoia tree)

It can happen that image targeted for recognition fails even with Monte Carlo method. the failure (threshold of failure) is a function of incomplete sampling database and or function of computational time/space requirements needed to arrive with the solution (or approximation to the solution)

All images in theory should be recognizable providing that appropriate algorithm defining n-dimensional polygons exists or a an appropriate sampling exists in a database. The same is certain for a lottery game, a series of numbers can be in principle stored as some polynomial (coefficients ofwhich are ie winning lottery numbers) such a polynomial becomes an image/object in some n-dimensional space  (in a certain sense) or a database defined containing winning numbers (more common).

Can Monte Carlo be used in predictive sense?

Same way as image recognition methods can arrive with prediction about possible future state of an image (ie state of motion of a tree being perturbed by the wind) such a prediction would require ultra sophisticated algorithms but by Monte Carlo Stochastic methods motion of a tree can be extrapolated to the solutions that yet does not exist (future),  made possible by analyzing certain patterns that occured in the past, Monte Carlo can predict better than deterministic algorithm can especially in systems that are on the threshold of chaos.

Question than can Monte Carlo be used to predict lottery becomes a question of: is lottery a highly disordered system or is it a system that is in maximally disordred state (chaos) (in the case of latter Monte Carlo is of no value)

Reference:

http://www.amazon.com/Analysis-Random-Fields-Markov-Methods/dp/3540442138

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