Hello folks,
I’ve added a new command in the standard library of G’MIC 2.9.1, and I think this could interest some of the G’MIC script writers here. I’m pretty sure this could lead to fun experimentations
Release of stable G’MIC 2.9.1 is planed for tomorrow.
The new command is named rbf
, which stands for Radial Basis Function. More precisely, it implements a RBFbased interpolation of sparse keypoints. To be honest, I’ve already been using RBFinterpolation in some of the G’MIC filters for a long time (commands x_warp
, x_morph
and clut
, to name a few), but I’ve decided it was time to provide this generic interpolation method as a standalone command that can be used to interpolate any kind of data.
It basically works like this: the command takes as input a set of K keypoints (X_k,V_k) (where k=1\dots K). The X_k represents the coordinates of keypoint k (X_k can be a 1D/2D or 3D vector), and V_k is the associated value of keypoint k (V_k can be a Ndimensional vector, with N having any value). The set of keypoints is passed to rbf
as a singlecolumn (or singlerow) vectorvalued image, where each pixel represents a keypoint.
From this, the command rbf
is able to interpolate the values of the keypoints in all 1D/2D or 3D image space. You specify the size of the interpolated image you want as a result, as well as a corresponding XYZ coordinate mapping (optionally).
To sum up, rbf
creates a smooth function that passes through given keypoints.
Beware, if the number of keypoints increases, then processing time explodes. Even if the command is parallelized, it implies a K\times K matrix inversion (K, the number of keypoints), which usually has a complexity of O(K^3) + it has a reconstruction phase with complexity O(whdK). But if the set of keypoints is small enough (I’d say <1000), then it’s a very interesting toy to play with.
A few examples:
 1D interpolation:
test1d :
20,1,1,2,[u(700),u(150,250)] # Pick random keypoints
+rbf. 700 # Interpolate keypoints
700,400,1,3,255 round. graph. ..,1,0,0,400
eval[0] "ellipse(#1,i0,i1,5,5,0,0.5,255,0,0); I"
test1d
gives:
 2D interpolation:
test2d :
sp duck
100%,100% noise_poissondisk. 10 # Pick random keypoints
1,{is},1,5 eval[2] "begin(p=0);i?(I[#1,p++]=[x,y,I(#0)])" # Create set of 2D colored keypoints
to_rgb[1] mul[0,1] dilate_circ[0] 5
+rbf[1] {0,[w,h]} c[1] 0,255 rm..
test2d
gives (after heating your CPUs a lot…):

Easy color gradient:
You can userbf
to create supereasy random color gradients:
test2d_2 :
32,1,1,5,u([400,400,255,255,255])
rbf 400,400 c 0,255
test2d_2
gives:
That’s it. I’d be interested by what you can obtain with this new command.
Note that we already had solidify
and inpaint_pde
for doing such interpolation, but having another option is still cool.