Now I think you're getting somewhere, thanks for the code and stuff, really appreciate your effort to help me.
In better words, can we apply a "noise reduction" to the mouse movements without compromising the sensitivity or its ability to look in any direction? I forgot to mention that this is only for the view vector, not the position, because while the camera stand still, you can still look around, and that's what I want to de-noise.
For example, use a 2D paint program and try to draw a line on it, or even a circle (using the pencil tool, not the line tool), now you see how noisy the line is right? Well, that's what I want to de-noise.
The problem with presenting it as noise can be seen from your analogy - if you knew what you want to draw beforehand(circle) you could "remove noise" - however when it comes to random and non-fixed user input you cannot decide which is noise and which is not without affecting the whole thing some way or another - basically you do not know what the user wants to do in the future - you can try to extrapolate based on samples from his previous actions/behaviour but that's a real double-edged sword(you can totally impede the user input with this).
The easiest way IMO is the thing I suggested - eliminate any "twitch movement" under a certain threshold. You can specifically choose the threshold so it will suit your aims, even more you can make the threshold (previously I used the twitch_cap identifier for it) "dynamic" - it can take in some additional data(more samples, x versus y mouse movement, predicted mouse location at time T) to define this threshold better for the given situation. Anyways I think that all of these "solutions" will impede the user to some extent - moreover I really don't get why you'd want to add such a "crutch" for the user - he's got a mouse he should be able to control. A simple analogy - try playing a FPS like Tribes:Ascend - the best way to hit something with a projectile weapon (an aimbot would need a 4th degree equation to find the hit mark and it will still be inaccurate) is lowering your mouse sensitivity to around 10(by doing this you mostly remove any random twitching of the hand) and having control of your hand of course If you add any "crutches" as rotation corrections and mouse input corrections you'll probably just impede users. Still I am not sure what your goal is exactly - as I mentioned a video will be really helpful so people can get what you want( if you don't want to post a video of your project just post a video of some game or whatever that has your desired effect) or you can try to make a thorough explanation. What are your goals exactly - fps shooter/panoramic view/ "camera recording" etc. - because this:
Is there a solution to make a camera move more smooth, like the real professional video camera that are on a gyro to prevent sudden sharp movements?
isn't much help.
For now you can try implementing the mouse movement/angle threshold I talked about - by playing with the sensitivity and twitch_cap values you should be able to get something good.
P.S. More info would be highly appreciated - I can't solve a problem if I don't have enough data on it