Bicubic downsampling and quality

Started Mar 20, 2000 | Discussions thread
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Furrukh Khan
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Bicubic downsampling and quality
Mar 20, 2000

Here is a precisely posed question regarding down sampling and quality, and my opinion about it. I have outlined the steps in my logic which have lead me to this conclusion. I look forward to hear other peoples opinions. Please let us keep the posts in this thread focused to precisely the question outlined below.

Let us assume we have two CCDs. To keep this discussion simple, let us use ordinary CCDs, not super CCDs. One is 1000 by 1000. The other is exactly like the first except that it has four times the area and contains 2000 by 2000 pixels. Each sensor on the smaller CCD is identical to each sensor on the larger CCD. The size of each sensor, and the density of packing is the same on both the CCDs. We use these CCds to take perfect images of exactly the same scene.

The question is: If I take the perfect image from the bigger 2000 by 2000 CCD and down sample it to 1000 by 1000 (using bicubic), will this look better, sharper, detailed, than the perfect image taken directly by the smaller 1000 by 1000 CCD? (we are not discussing noise here, the down sampled image will have less noise because of averaging effects). I argue that the down sampled image will be better. Here are my arguments:

In the first case, i.e. down sampling form the larger image, an intelligent bicubic algorithm is used to fit the information of the thrown away pixels to quadratic curves, to assign a value to the pixel that is kept. In the second case, i.e. the case of the perfect image obtained from the 1000 by 1000 CCD, each pixel is getting four times more image information from the scene (both the CCDs are receiving the same image, so four times more of a scene chunk falls on each pixel of the smaller CCD, as compared with the larger CCD), and this information is automatically and physically averaged out in a very crude way by the photons hitting the sensor area. This result is very similar to down sampling the 2000 by 2000 CCD image by using a crude nearest neighbor averaging algorithm. So the bicubic 1000 by 1000 down sampled image from the 2000 by 2000 CCD is sharper and better than the perfect image taken by the 1000 by 1000 CCD.

If we had used a crude nearest neighbor averaging method on the 2000 by 2000 perfect image, then we would get a result like the perfect 1000 by 1000 image from the 1000 by 1000 CCD.

So my conclusion is that the down sampled image from the bigger 2000 by 2000 CCD, will look better than the perfect image taken by using the 1000 by 1000 CCD, since it has made use of the information in a more intelligent way, which gives sharper results. The 1000 by 1000 CCD image is only perfect among images taken by using the 1000 by 1000 CCD. It is not perfect, when compared with the bicubic down sampled images from the 2000 by 2000 CCD.

I look forward to hearing comments from other people.

Cheers!

Furrukh

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