lecture7 - VisualSimulation CAP6938 Dr.HassanForoosh...

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    Visual Simulation CAP 6938 Dr. Hassan Foroosh  Dept. of Computer Science UCF © Copyright Hassan Foroosh 2002
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    Modeling Texture What is texture? An image obeying some statistical properties Similar structures repeated over and over again Often has some degree of randomness
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    Stochastic Process  Terminology Random variable   nondeterministic value with a given probability distribution e.g. result of roll of dice discrete:  can take on a finite number of possible values continuous:  not discrete Probability density function (PDF) non-negative real valued function p(x) such that  called  probability distribution  when x is discrete sometimes  probability distribution  is used to refer to densities Discrete  stochastic process   sequence or array of random variables, statistically interrelated e.g. states of atoms in a crystal lattice Conditional probability P [ A|B,C ] means probability of A given B and C e.g. probability of snow today given snow yesterday and the day 
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    Statistical Inference Estimation Given measurements  z  =  (z 1 , z 2 , . .., z n ) Compute model parameters  x  =  (x 1 , x 2 , . .., x m ) Statistical estimation Given measurements  z  and uncertainty information Compute p( z ) – probability of every possible model Key Tool:   Bayes Law posterior (what’s the model?) prior (our knowledge about these parameters) likelihood (what measurement would we expect to see if we knew the model?) normalization
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  MAP Estimation Often we just want to maximize p(x|z) Can ignore p( z ), since it’s a constant (doesn’t depend  on  x ) Maximum a posteriori   (MAP)  estimate of  x  is What if no prior information? p(
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lecture7 - VisualSimulation CAP6938 Dr.HassanForoosh...

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