I did a really simple proof that 2-3 megapixels is sufficient back in another forum here a few years back.
Basically I took two photos of a bird feeder in my back yard. It is intricate and has a delicate mesh.
One photo was taken by an entry-level dSLR at 3 megapixels. The other was taken by my current smartphone at the time that boasted 8 megapixels.
When looking at the detail at native 1:1 resolution, it was clear that way more detail was present on the 3 megapixel dSLR shot than the 8mp phone shot.
Some of you might be saying, "Well duh, a dSLR obviously takes better photos than a cell phone camera." To which I say, "Duh, that's not the point." The point is that if you have high quality optics and a high quality sensor, and a good implementation of these components, you will capture good detail even if you are "restricted" in pixels.
Blu-ray at 1080p, absent of high jpeg lossy compression (which Early explained in a few posts before this one), looks really, really good and sharp. I was floored when I saw it for the first time in a Sony store circa 2008. And what's the megapixels for a given frame of 1080p? It's 1920x1080=2.073 megapixel. Just 2mp.
Any perceived image quality problems in the HTC One camera can't be blamed from their megapixel downsizing. It's something else that's still not quite up to snuff.
I used to shoot exclusively at 3mp with my dSLR until more recently when I upgraded to a pro dSLR and the minimum setting was 6mp. So now I shoot at 6mp. I have no need to shoot at the full 21mp because I won't need to be printing billboard-sized photos.
The good thing about science is that it's true whether or not you believe in it. -Neil deGrasse Tyson
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