Bilinear & Bicubic Interpolation

quote:

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Original post by smkc_be
Does anyone know the algorithm for Bilinear or Bicubic Interpolation for doing arbitrary scaling to a 2D image? I''ve looked all over the net, but haven''t seen any good descriptions of the technique and no listing of the algorithms. Thanks

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Bilinear is actually very simple. Bilinear interpolation between four pixels with the following orientation (hope this figure works):

+---> x
|
|
\/
y


p1 p2
x--------x
| |
| |
| |
x--------x
p3 p4

float p1, p2, p3, p4; // monochrome pixel values
float x, y; // (x,y) ranging (0..1)
float p12, p34; // temporary results
float p; // result

p12 = p1 * (1.0-x) + p2 * x;
p34 = p3 * (1.0-x) + p4 * x;
p = p12 * (1.0-y) + p34 * y;


You get the general idea: perform linear interpolation along X twice, and then perform linear interpolation along Y once (between the two "x-values).
Trilinear interpolation is similar, except you interpolate between 8 points (resulting in 7 interpolation operations).

Bicubic interpolation is also similar, but you use 16 points instead of 4 points (still 3 interpolation operations).

Linear interpolation uses the "weighting factors" (1-x) and x. Cubic interpolation uses four weighting factors (one for each point):

w1 = -(1.0/6.0)*x*(x-1.0)*(x-2.0);
w2 = (1.0/2.0)*(x*x-1.0)*(x-2.0);
w3 = -(1.0/2.0)*x*(x+1.0)*(x-2.0);
w4 = (1.0/6.0)*x*(x*x-1.0);

(snippet from some old code I had on my disk)

Hope you understand what I mean...

Anyway: here are a few words of advice:

- Cubic interpolation does not look THAT much better than linear interpolation (important for sound, not for images)
- Using interpolation for resampling images only works for upsampling (magnifying). Minification must be done using low pass filtering - and THEN interpolation (this is what is called MipMapping).

/Marcus