Axis Arrays

To define the pixel coordinate system in §, we specified the location of each pixel by giving its centre position and width on each axis. Thus, for a given dimension, the pixel centre position C was derived from the corresponding pixel index $i$ according to the formula:

$C(i)=i-\frac{1}{2}$

and its width W was given by:

$W(i)=1$

An NDF's axis coordinate system extends this idea by allowing each of these centre and width functions to be determined by values stored in a 1-dimensional array. These axis arrays then act as ``look-up tables'' which convert pixel indices into pixel centre coordinates and width values on each axis:

This allows a wide range of possible coordinate systems to be accommodated. A third axis variance array is also provided as a look-up table to convert pixel indices into variance estimates, which can be used to represent any possible statistical uncertainty in a pixel's centre position.