Difference between revisions of "Autocovariance Coefficients"

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Autocovariance is a measure of the degree to which the outcome of the function f (T + t) at coordinates (T+ t) depends upon the outcome of f(T) at coordinates t. It provides a description of the texture or a nature of the noise structure

Background

In statistics, given a real stochastic process f(t), the auto-covariance is simply the covariance of the signal against a time-shifted version of itself. If each state of the series has a mean:

<math> E=[f(T)]=\mu_T </math>

Notes

An auto-covariance function, which falls rapidly as a function of t, indicates that the resultant noise is in actual fact independent except at short separated distances, providing an appearance of 'sharp' noise.

An auto-covariance function, which falls off slowly and smoothly as a function of t, indicates that the noise is highly correlated. At a given point, a positive value of the auto-covariance means that the noise tends to be of the same sign, while a negative value indicates that the noise tends to be of the opposite sign.

In short, the amplitude of the auto-covariance at zero displacement provides a measure of the noise magnitude, while the shape the auto-covariance can be used to describe the nature of noise.

Image types

Color and black and white 3D and 4D images.