Hitherto, an NDF has been considered simply as an N-dimensional array of pixels, addressed by a set of pixel indices. Since they are integer quantities, these indices cannot represent a continuous coordinate system, although the information stored in an NDF will almost always require that positions within it be describable to sub-pixel accuracy. For example, a calculation to determine the centroid position of a star in a 2-dimensional image will inevitably give rise to a non-integer result, for which a continuous (x,y) coordinate system will be required.
There are a number of ways in which a continuous coordinate system can be defined for a regular array of pixels. In the absence of other information, the NDF convention is to use a pixel coordinate system in which a pixel with indices (i,j) has its centre at the position:
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and is taken to be one unit in extent in each dimension. Pixel (1,1) would therefore be centred at the position (0.5,0.5) and would have its ``lower'' and ``upper'' corners located at positions (0.0,0.0) and (1.0,1.0) respectively, as follows:
This makes it possible to refer to fractional pixel positions--in this case within a 2-dimensional array, although the principle can obviously be extended to other numbers of dimensions.