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In case of digital images, what is the relationship between sampling and number of pixels? For upsampling, the number of pixels increass, and for down sampling, the number of pixels decrease??

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    $\begingroup$ you got very similar questions to Man and @engr. Maybe check out their latest questions&answers! Generally, I think you know Man, and the questions you ask are of a very fundamental nature, so I'm guessing you two are taking the same classes, so here's what I tell my students when they show up for office consultation hours: It's excellent that you ask questions! Don't stop. However, it's often very useful to try and discuss a question with someone who's "on the same level" first, $\endgroup$ – Marcus Müller May 7 at 8:07
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    $\begingroup$ because that allows you and the other to "play" with the question, look at it from different sides, because they have the same background as you. If that's an option with you and @Man, do take the chance! Asking experts is still the right thing to do, but it can lead to overwhelming answers if you haven't tried to consider a problem given all the perspectives that you were specifically taught by your course / material, and a fellow student is just an excellent tool to do that. Again, if you can't discuss things with someone else, or rather directly ask here, DO THAT, please. $\endgroup$ – Marcus Müller May 7 at 8:10
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Yes. With upsampling, the number of pixels increase. But it is not just an arbitrary addition of pixels. Generally, the idea is to end up with a higher resolution version of the original image. So certain algorithms may need to be used to interpolate, etc.

With downsampling, on the other hand, the number of pixels decrease, and it would end up with a lower resolution version of the original image.

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Yes, that's correct. It's a natural extension of one dimensional up and down Sampling. However, one can define lattices (arbitary shapes) for sampling images, so one could downsample more in a particular axis than the other. Essentially instead of a sampling period, we have a sampling grid. There are benefits of using different freqeuency grids. Of course all of this holds without aliasing only when the sampling theorem holds. Otherwise you get aliasing.

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