Area-coverage antialiasing

Area-coverage antialiasing assigns an edge pixel a value based on the fraction of its footprint covered by a geometric shape. In a simple rasterization model with constant foreground value $C_f$, constant background value $C_b$, and a uniformly weighted pixel region $P$, let $S$ be the shape. ThenEquivalently, $\alpha$ is the average of the shape's indicator function over $P$. This is a spatial average: a partially covered opaque shape can produce an intermediate pixel value without its material being transparent. Filtering the image over a finite region reduces the abrupt changes produced by deciding coverage at one sample point.^[ref]

For a worked example, take the unit-square pixel $0\le x,y\le 1$ and a white shape covering $y\le x$ over a black background. The diagonal divides the square into equal areas, so $\alpha =1/2$ and the pixel gets half the white value. A single center sample lies exactly on the edge and must choose one side by a convention; a tiny edge movement can flip that binary decision. The covered area instead changes continuously. The arithmetic applies to values proportional to light, before a nonlinear display encoding.

Exact geometric coverage and multiple sample tests are two ways of estimating this average; a finite set of samples can miss a sufficiently thin shape. Uniform footprint averaging also has limits: its abrupt filter boundary does not remove every high-frequency component, so it reduces aliasing without guaranteeing a perfectly band-limited image.^[ref]