Shape description by image moments is a popular topic in image processing. Standard geometric moments are based on a non-orthogonal basis, which has introduced some problems for image reconstruction. Orthogonal moments such as Zernike and Legendre Moments which use orthogonal polynomials have been introduced to overcome this problem. These however are based on continuous polynomials, and are not really suited to digital images processing which is inherently rooted in a discrete domain. Hence, a new type of discrete orthogonal moments, based on Tchebichef polynomials has emerged.

Many spatially distributed data exhibit anisotropic spatial variation, especially when the data are distributed over a large area. The Semivariogram, or commonly (and inaccurately) just variogram is a measure of spatial correlation. It simply plots the semivariance (which is half the variance) of two points separated by a vector h against the magnitude of h. Easy right? Well there is a little bit more to it...

The method of least squares, or even simply maximum likelihood is one of the more powerful tools available to a statistician. It is powerful because its simplicity means it can be used in a variety of regression problems.

Regression simply means line fitting, and lines are just a graphical way to represent a model, which is the mathematical way to describe the relationship between an independent variable and one or more dependent variables. There is a lot of text on linear straight line fitting, so I’m not going to go into too much detail. I will however briefly discuss the principle behind least squares.

In order to analyse the frequency components of a curve using Fourier we must first represent it mathematically. As we are working with images, a discrete spatial domain, then we have to deal with discretisation.