vector field on an image

Hello, I have a vector field where each vector corresponds to a pixel and which determine the movement of that pixel. Where could I find a problem description and a matlab solution to such a problem.

Also, how would I add effects, say, applying the vector field to each pixel like it was a particle in a viscous fluid. Thus the transformed image or successive images would appear liquidy (for lack of a better term). Thanks

[Walter Roberson]

Was the question edited? It shows up as new, but the wording is what I remember?

[Sean de Wolski]

2-d image and 2-d translation vectors?

[ryan webster]

yes

Answer 1

[Jan]

Even the standard RGB images match your description: Each pixel is a vector in the 3D RGB space. A generalisation to more dimensions is e.g. done by the conversion to the 4D color space CMYK or when adding an alpha channel to the RGB data. Anyhow, the components of these vectors need not be a color information, but e.g. the 4th component can be the Z-depth, temperature or anything else.

You can use any numerical transformation to implement an "effect" to your ND-array.

[ryan webster]

I see, thanks for the answer. I wasn't specific enough. The vectors are modifying the positions of the pixels. My solution was to treat every 4 pels as a square and perform a projective transform. But I'm sure there is a better solution.

For example, when a video is encoded with motion vectors, how is a P-frame reconstructed from the motion vectors and I-frame

Answer 2

[Sean de Wolski]

 I = your_image
 %Create a grid of the indices: 
 [rr cc] = ndgrid(1:size(I,1),1:size(I,2));
 %Add the displacements vectors to them:
 rr = rr+row_displ;
 cc = cc+col_displ;
 %Engine
 I2 = zeros(size(I),class(I));
 I2(sub2ind(size(I2),rr,cc)) = I;

This doesn't do any interpolation or decisions for multiple vectors to the same new pixel but will move pixels to the locations defined by their integer motion vectors.

[ryan webster]

yea but this method just looks so terrible. there has to be a better way

[Jan]

Yes. Insert some spaces after the commas and before and after the operators.