The pixels you discard contain valuable information.
The sampling theorem (Nyquist) tells us that the highest spatial frequency you can reproduce is at half the sample frequency. Basically this means that the highest spatial frequency you can have in an image is when alternate pixels are light-dark-light-dark- etc (imagine a vertical grating of alternate black and white lines). If you make the sample points further apart then the maximum spatial frequency you can store in the image has to be lower.
To downsample correctly you have to first remove frequencies above the Nyquist frequency and then you can sub-sample. If you do not remove those high spatial frequencies you get the inevitable aliasing (moire effects and jaggies - wheels going backwards in the movies). The very act of removing those spatial frequencies above Nyquist must reduce the information in your image.
This is related to the reason why many cameras have anti-aliasing filters or optical low-pass filters. For a given sample rate on the image chip (pixel spacing) there is a corresponding maximum spatial frequency that can be projected through the lens onto the imager. Anti-aliasing filters cut out the higher spatial frequencies to prevent the jaggies etc. (a particular problem at wide apertures).
Of course, if you are going to render your image at a smaller size then the loss of higher spatial frequencies will be less noticeable.
Tim
On 4 May 2004, at 12:02 am, Dale Hoffman wrote:
Snap logic tells me that downsampling an image should not degrade that image in any way, but is that the real story? Get theoretical if necessary and help me put this to rest.
DaleH
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