Computer Vision MT25, Subsampling and upsampling
Flashcards
Suppose you want to reduce the resolution of an image by a factor of $2^n$. What goes wrong with the simple approach of deleting every pixel with coordinates that are not a multiple of $2^n$?
You get aliasing problems in high-frequency regions.
Suppose you want to reduce the resolution of an image by a factor of $2^n$. One approach to do this is deleting every pixel with coordinates that are not a multiple of $2^n$, but this has aliasing problems in high-frequency regions.
What’s one way you can get around this?
Remove high-frequency details by blurring first, and then subsampling.
Suppose you want to increase the resolution of an image by a factor of $2$. One way to do this is to double the pixel coordinates, but this introduces gaps between the pixels.
If $A$, $B$, $C$, $D$ are the four corners of one “square” in the image, @state how bilinear interpolation would fill in the remaining values of the $5$ empty squares forming a cross inside the square.
and the middle has
\[\frac{A + B + C + D}{4}\]In general, this process can be seen as first averaging the values of the horizontal and vertical pixels, and then using these new values to find the value of the middle pixel.
Suppose you have four pixels arranged in a square with values $A, B, C, D$ and located at $(x _ 1, y _ 1), (x _ 2, y _ 1), (x _ 1, y _ 2), (x _ 2, y _ 2)$. Given some coordinate $(x, y)$ inside the square, @state the formula used by generalised bilinear interpolation to give a value to $(x, y)$.
where
\[\begin{aligned} w _ {11} &= \frac{(x _ 2 - x)(y _ 2 - y)}{(x _ 2 - x _ 1)(y _ 2 - y _ 1)} \\ w _ {21} &= \frac{(x - x _ 1)(y _ 2 - y)}{(x _ 2 - x _ 1)(y _ 2 - y _ 1)} \\ w _ {12} &= \frac{(x _ 2 - x)(y - y _ 1)}{(x _ 2 - x _ 1)(y _ 2 - y _ 1)} \\ w _ {22} &= \frac{(x - x _ 1)(y - y _ 1)}{(x _ 2 - x _ 1)(y _ 2 - y _ 1)} \end{aligned}\]@Define nearest-neighbour interpolation.
Interpolated values are taken from the closest point.
@State a useful property of nearest neighbour interpolation.
It only uses values already in the data.
@State a useful property of linear interpolation, compared to quadratic or cubic interpolation.
It does not create samples outside the range of interpolants.
@State a useful property of cubic interpolation.
It is differentiable everywhere.