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Can you capture/record a video playing on the screen using a recording software(or your custom code) such that every pixel is recorded and there is no loss of information ?

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Of course, but it won’t give you the original video, it will basically be like taking lots of screenshots in a row with PrtScr. Moreover, saving them uncompressed would make the video grow very big, very fast. You’ll need to compress it with something, but most video codecs are lossy. There do exist some codecs that are lossless (TechSmith includes such a codec with their screen-casting programs), but not surprisingly, they produce relatively large files and will usually need to be re-encoded with a lossy codec to bring them down to a useful size. –  Synetech Aug 26 '13 at 1:51

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You can, but it isn't recommended (depends on use), mainly because to store that amount of information requires significant disk space to be available, since to store a lot of information quickly enough means that no or little image processing must be made (with this I include compression) to save as much of the CPU processing power as possible.

For example, assume you're recording a 1024x768 screen at 30 fps and at 24-bit resolution. So, each pixel will take 3 bytes. On one second, doing the math, you will need to have a minimum of 70778880 bytes, or 67.5 MB of space to store all that. At 32-bit, you will need 90 MB.

Fraps, for instance, I believe it does that, although It uses a special codec for the purpose. In fact, most screencasters might, by the reasons pointed out in the first paragraph, record losslessly or near, since it isn't easy to trade-off compression for efficiency.

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So, if I record a high quality video at it's native resolution and play back both the recorded and original videos, there should be no discernible difference between the two? i.e every pixel is captured and reproduced exactly the same way –  Rnet Aug 26 '13 at 21:59
    
It would depend on the codec used, but as I said, most screencasters use a lossless or near lossless codec (as @Synetech pointed out, TechSmith does this, as Fraps or Hypercam). There shoudn't be a difference if the codec is lossless (i.e. there is a pixel-wise match between input and output). But you now asked a question - discernibility. The reason most codecs used (on regular video files) are lossy is because we allow some loss in quality in order to have a much lower filesize. However, this is impractical to do while you're recording the video (due to the reasons pointed before). –  Doktoro Reichard Aug 26 '13 at 23:13

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