. Why is a median filter especially effective against salt-and-pepper noise, compared to Gaussian blur?
A wildly wrong outlier pixel skews a mean a lot but barely affects a median, since the median just picks the middle-ranked value.
. On a grayscale image, what operation does erosion correspond to in a neighborhood?
Grayscale erosion generalizes binary erosion as a min filter: each pixel becomes the minimum value in its neighborhood.
. In the bilateral filter formula, what are the two factors each neighboring pixel is weighted by?
The bilateral filter combines a spatial Gaussian (G_sigma_s) with a range/intensity Gaussian (G_sigma_r), so only neighbors that are both nearby and similar in intensity get high weight.
. Why does the bilateral filter preserve a step edge while Gaussian blur smooths across it?
Even though pixels on the other side of an edge may be spatially close, their intensity difference makes the range weight near zero, so they contribute almost nothing to the output.