# 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
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
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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