GNU Astronomy Utilities


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6.4.3 Resampling

A digital image is composed of discrete ‘picture elements’ or ‘pixels’. When a real image is created from a camera or detector, each pixel’s area is used to store the number of photo-electrons that were created when incident photons collided with that pixel’s surface area. This process is called the ‘sampling’ of a continuous or analog data into digital data. When we change the pixel grid of an image or warp it as we defined in Warping basics, we have to ‘guess’ the flux value of each pixel on the new grid based on the old grid, or re-sample it. Because of the ‘guessing’, any form of warping on the data is going to degrade the image and mix the original pixel values with each other. So if an analysis can be done on an un-warped data image, it is best to leave the image untouched and pursue the analysis. However as discussed in Warp this is not possible most of the times, so we have to accept the problem and re-sample the image.

In most applications of image processing, it is sufficient to consider each pixel to be a point and not an area. This assumption can significantly speed up the processing of an image and also the simplicity of the code. It is a fine assumption when the signal to noise ratio of the objects are very large. The question will then be one of interpolation because you have multiple points distributed over the output image and you want to find the values at the pixel centers. To increase the accuracy, you might also sample more than one point from within a pixel giving you more points for a more accurate interpolation in the output grid.

However, interpolation has several problems. The first one is that it will depend on the type of function you want to assume for the interpolation. For example you can choose a bi-linear or bi-cubic (the ‘bi’s are for the 2 dimensional nature of the data) interpolation method. For the latter there are various ways to set the constants82. Such functional interpolation functions can fail seriously on the edges of an image. They will also need normalization so that the flux of the objects before and after the warpings are comparable. The most basic problem with such techniques is that they are based on a point while a detector pixel is an area. They add a level of subjectivity to the data (make more assumptions through the functions than the data can handle). For most applications this is fine, but in scientific applications where detection of the faintest possible galaxies or fainter parts of bright galaxies is our aim, we cannot afford this loss. Because of these reasons Warp will not use such interpolation techniques.

Warp will do interpolation based on “pixel mixing”83 or “area resampling”. This is also what the Hubble Space Telescope pipeline calls “Drizzling”84. This technique requires no functions, it is thus non-parametric. It is also the closest we can get (make least assumptions) to what actually happens on the detector pixels. The basic idea is that you reverse-transform each output pixel to find which pixels of the input image it covers and what fraction of the area of the input pixels are covered. To find the output pixel value, you simply sum the value of each input pixel weighted by the overlap fraction (between 0 to 1) of the output pixel and that input pixel. Through this process, pixels are treated as an area not as a point (which is how detectors create the image), also the brightness (see Flux Brightness and magnitude) of an object will be left completely unchanged.

If there are very high spatial-frequency signals in the image (for example fringes) which vary on a scale smaller than your output image pixel size, pixel mixing can cause ailiasing85. So if the input image has fringes, they have to be calculated and removed separately (which would naturally be done in any astronomical application). Because of the PSF no astronomical target has a sharp change in the signal so this issue is less important for astronomical applications, see Point Spread Function.


Footnotes

(82)

see http://entropymine.com/imageworsener/bicubic/ for a nice introduction.

(83)

For a graphic demonstration see http://entropymine.com/imageworsener/pixelmixing/.

(84)

http://en.wikipedia.org/wiki/Drizzle_(image_processing)

(85)

http://en.wikipedia.org/wiki/Aliasing


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