Soeren Sandmann wrote:
- interpolate to define the image on a continuous domain
- transform
- resample
The problem I am having is that this does not match how filtering of
transforms is done in any image processing software I am familiar with.
This is how all software I am familiar with works, this replaces the
three steps you show above:
- Figure out the INVERSE transform
- For each output pixel, the x, y, and inverse transform figures out a
weighing factor for every pixel in the input image. These are weights
for input PIXELS, not weights for input "points".
- Multiply input pixels by these weights and sum to get output pixel.
For a more concrete example, our image transforms consist of translating
the output x/y into an input axis-aligned rectangle that is as close as
possible to the area of the output pixel inverse-transformed to the
input. This rectangle dimensions are then used to scale 2 1-D filters to
the right size (they are truncated sync or similar functions and the
non-zero area is about twice the size of the rectangle). These two
filters are used in a 2-pass algorithm to weigh and sum all the pixels
in the rectangle and around it to produce the output pixel.
I suspect you think you are describing mip-mapping, but a "sample" in a
mipmap is not just an X/Y position, but also a "which scaled image"
number. Mipmap is instead a compression scheme for weighted pixel
samples, where the same weight for a square of 4 sample pixels can
instead be specified as 4x weight of a single pixel in the 1/2 sized
image. (In addition I do not think mipmapping is correct for Cairo: the
filtering is very poor for non-square transforms, and the overhead is
high if the samples all come from only one or two of the scaled images.)
You cannot describe the input image as a "continuous domain" and get any
kind of sampling that is any better than putting the same number of
samples right in the middle of the pixels. In addition a number of the
filtering operations demanded by users (sharp edges on transformed
images, and sharp square pixels when zoomed in) are impossible unless
the "continuous domain" is defined as constant squares of color and thus
equivalent to rounding any "point" to the nearest pixel center.
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