A pixel by any other name
Let’s talk about the heart of any digital image: the pixel. And let’s talk about its finite nature. You see, in computer vision (and any digital display), each pixel is its own set of data (coordinates), and no information “fits” between them. You can make each pixel hold as much data as you like, but you can never make a “better” pixel.
Pixels and … curve fitting?
You can think of pixels as points in a curve fit. From a calculus standpoint, the more points we have in our data series, the better the regression. Why? When we perform regression on a function, we essentially amalgamate a bunch of really small mini-slopes. To get our curve fit, we calculate the slopes at smaller and smaller intervals. The more mini-slopes we have, the better the curve fit will be.
Turns out, you can kind of think about a “pixel” as akin to the point at which we calculate the slope. We want as many pixels/points as we can to create the best possible illusion of continuity. In a digital image, pixels are these “mini-slopes,” and the image is the “curve fit.” The more pixels we can cram into a display, the smaller the discrete changes between pixels become. Or put succinctly, more resolution = more pixels = smoother transitions.
Curve fitting: The more slopes we can calculate, the better our fit will be.
Resolution
The quality of digital images is limited to the quality of your display. The lower the resolution, the grainier the image will be. That’s why HDTVs were labeled things like 720p or 1080i: these values were the number of pixels in the display. Some of us grew up with Duck Hunt and 420x420 CRTs, and had to walk both ways uphill to the TV to adjust the prongs on my Nintendo adaptor.
Now, I complain when I have to couch-coop Mario Cart and have to play on a only ¼ of the screen, which is still much larger than my entire TV in the 90s. Amazing how quickly we become spoiled and whiny jerks. And while graphics cards and rendering engines have come miles and miles since Duck Hunt, we will still ultimately be bottlenecked by the screen on which we view them.
Crappy resolution Super high resolution
Tiny screen Giant screen
Sat too close, eyesight now ruined Still sat too close, eyesight still ruined
Fun aside: This is why computers suck at making circles and spheres. You can make the screen bigger and the pixels smaller until it rains in hell, but it will never be a real circle, no matter how many zany adventures it goes on.
