8/13/2019 Gaussian Multivariate Distribution -Part 1

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8/13/2019 Gaussian Multivariate Distribution -Part 1

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8/13/2019 Gaussian Multivariate Distribution -Part 1

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Multi Variate Gaussian Distribution

The probability computation is simply writing out the formula

8/13/2019 Gaussian Multivariate Distribution -Part 1

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Multi Variate Gaussian Distribution

The covariance matrix is postive semidefinate and symmteric

The Cholesky decomposition of a symmetric, positive definite

matrix decom- poses A into a product of a lower triangular

matrix L and its transpose.

Thus the product

thus we can only compute

and take its tranpose

Thus we can perform the Cholskey factorization of the covari-

ance matrix to find

Then we take the inverse of

0.1.1 Code

The code can be found at git repository

in files ImgML/gaussian.hpp and ImgML.gaussian.cpp

files.

https://github.com/pi19404/OpenVisionhttps://github.com/pi19404/OpenVision