Pixels = resolution = quality is not always true, since other factors impact quality (low light, bright light, lens quality, etc.).
However, pixels determine potential quality. In this note, we explain why you will make much clearer and better decisions recognizing this.
Demonstrating This With Images
Here's a relatively high quality, high 'resolution' image:
It's 161 pixels wide across a small area of 1 - 2 feet, delivering a high ~100 PPF.
Now contrast this with this low quality, low resolution image:
This is 5 pixels wide and a total of 35 pixels covering the same exact area as the image above (enlarged so you can see it). This is clearly low quality.
Why? The pixels are being forced to cover areas wider than the details desired. You can see it the blockiness of the image. Those blocks are the limits of the pixel.
The image calls out 3 of the 35 pixels but you can make out pretty much all the individual pixels.
Now let's increase the pixels / resolution for this image.
A lot more details are being revealed now, as the number of pixels increases from 35 total to 140 and each pixel now can cover a smaller area.
Let's compare the two images to see key details in the image improve:
In the former image, the eyes were bigger than the pixels and therefore could not be captured. However, in the latter one, with pixels cover an area smaller than an individual eye, allows the eyes to be captured as two black dots.
Let's increase the pixels for this scene, from 140 to 240:
As each pixel covers a smaller area, more features continue to emerge - lips, ears, etc. and the eyes become more detailed (eyebrows, iris, etc.).
Finally, here's 4 samples ranging from 35 to 2120 pixels covering the same area:
Clearly, as we increased pixels allocated, the more fine details that can be captured.
The smaller pixel count images, regardless of how 'good' the camera or encoder was could not capture those details because the pixels were covering too large an area for them. This is what we mean by pixels determine potential.
Pixels Limits on Quality
A 1MP camera will never capture the fine details of the face of a subject at a 50' wide FoV. It simply lacks the potential, because the pixels will cover too large an area relative (25ppf) to how small a face is at the same position.
However, a 5MP came covering that same 50' wide FoV may capture the fine details. It has the potential, because the pixels will be covering small enough areas (50ppf).
This potential, though, is a maximum theoretical limit bound by very important factors like:
Ability to capture in low light scenes (which most 5MP+ cameras are terrible at).
Ability to handle wide dynamic range scenes (see example).
Quality of lens, preciseness of focus and eliminating any DoF problems.
Minimizing compression artifacts / loss of quality (see tutorial).
Angle of incidence of subject to camera (if the camera is too high or the person is looking askew from the camera, more pixels will not help).
Quality vs Pixels
Ultimately, image quality is driven by a half dozen factors combined. While pixel density / count determines the potential quality and the maximum achievable details, those other factors, that are often overlooked and ignored in PPF calculations, routinely and often dramatically constrain the actual image quality achieved.