Subpixel Coordinate Definition

An image is an array of numbers in 1, 2, or more dimensions. Each sample is called a "pixel", which is derived from the phrase "picture element". Although pixels are distinct, whole samples of the image, useful measurements must be made to sub pixel precision. In other words, a centroid position would be quoted as coordinate (204.553,198.234). The question naturally arises as to exactly where this point occurs within the integral pixel position. In other words, how far across pixel 204 is column 204.553? is it actually inside the pixel you see at position 204? Is that 204 pixels from the edge of the image? The answers to these questions are addressed by the FITS standard and FITS conventions. Mira adopts the FITS protocols for measuring sub pixel positions in all image formats. This is shown in the figure and is described below in greater details.

Definition

The exact center of a pixel is defined to be exactly at its coordinate label position. In other words, coordinate (1.0,1.0) occurs at the exact center of pixel (1,1).

A pixel is considered to be a sample of the image which extends from 0.5 pixels below to 0.5 pixels above its position on the image array. Therefore, pixel (1,1) samples the image over the square from column 0.5 to column 1.5 and row 0.5 to row 1.5. This means that, at the sub pixel level, an image of 1000 columns runs from the extreme limits at column 0.5 to column 1000.5 in pixel 1 and pixel 1000, respectively.

One potentially odd result of this sub pixel coordinate definition is that the pixel "crosses over" at the middle of the pixel. In other words, suppose you have magnified a displayed image and are viewing a pixel at column 42. When you roam the mouse pointer over column 42, you will see the coordinate display change in the following way: column 41.563, ..., 41.938, 42.063, ..., etc. The jump from 41.xxx to 42.xxx occurs as the pointer crosses the center of the pixel. At first, this may seem odd but it does make sense if you think of a pixel as being a sample of the image that extends for + and - 0.5 pixels from the center of the sample. Therefore, in this example, column 42 extends from coordinate 41.5 to coordinate 42.5.