diffusion model for 2D images

I have a discussion with Image Processing researcher about using diffusion model for 2D images:

He said ... "the anti-concentration diffusion model is wrong for 2D digital subtraction angiography DSA images. Because in 2D, pixel-values (concentration) are summations in depth, and small distances in 2D can be large in 3D."

I said that 2D DSA images suffer from intensity inhomogeneity and we can apply diffusion models to correct intensity inhomogeneity problem.

What do you think?

Answer 1

[Bjorn Gustavsson]

If I get this right...

Linear diffusion you can calculate by straightforward convolution with a Gaussian kernel, and that operation should commute with the integration along the lines-of-sight your imaging system does. If you start doing non-linear diffusion this will no longer be true - you would not get the same result if you first did a non-linear diffusion of the 3-D object and then imaged that, as if you first imaged the 3-D object and then did non-linear diffusion on that. So it depends on what type of diffusion you do. This is resting on the fact that the diffusion is done with a Gaussian kernel and that those are separable. This means that you can separate the diffusion perpendicular to and along the lines-of-sight.

HTH

[Bjorn Gustavsson]

Except for the case where DSA-images are of the same kind as X-ray tomography - then its different.