Understanding correct usage of dvf2ddf

[ArjunNarayanan]

Hi,

My understanding of dvf2ddf is that it takes a velocity field and integrates it (via scaling and squaring) to produce a displacement field. The velocity tells me incrementally where a given point will move in the next time step, and the displacement field tells me where a given point will move over several time steps. (Please correct me if I am wrong 😄 )

So if dvf=1 , and I take 3 steps with monai.networks.blocks.DVF2DDF -- I expect ddf=3 . Here's an example,

from monai.networks.blocks import DVF2DDF
import torch

dvf2ddf = DVF2DDF(num_steps=3)
dvf = torch.ones([1,3,10,10,10])

ddf = dvf2ddf(dvf)
ddf_view = ddf.select(2,5)[:,:,3:7,3:7]

This gives me

tensor([[[[1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.]],
         [[1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.]],
         [[1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.],
          [1., 1., 1., 1.]]]])

When I was expecting the interior of ddf to have value 3. Am I missing something?

[ebrahimebrahim]

Almost the right idea, but there is some confusion.

The num_steps argument is not number of time steps but rather number of scaling and squaring steps. To understand scaling and squaring see section 3 of this paper. In that notation the num_steps is $N$.

The amount of "time" is always 1. When you set num_steps=3 you're saying you want to integrate out from $t=0$ to $t=1$ in $2^N=8$ time steps via $N=3$ squarings. You start with dvf / 8 as an initial ddf, treating this as an approximation of the ddf that you'd actually get if you integrated your dvf from time 0 to time $\frac{1}{8}$. Then you square that ddf (compose it with itself) three times to get to $t=1$.

[ArjunNarayanan]

Thanks for your reply, I'll take a look at the paper. Do you know how I can achieve what I am trying to do using DVF2DDF?

[ebrahimebrahim]

What are you trying to do? If you just want to integrate out to "time = 3" instead of "time = 1" then you can plug in 3*dvf instead of dvf.

[ArjunNarayanan]

I'm trying to train a model to perform 3D registration based on this tutorial. Instead of a ddf my model predicts a dvf so I tried using DVF2DDF to convert my dvf to a ddf. However, this model doesn't work (no sign of the loss going down during training).

I replaced the Warp module with my own implementation of grid warping through direct numerical integration (Euler or RK4) and this model does learn a registration field. I'm just wondering why my implementation with DVF2DDF does not work.

[ebrahimebrahim]

I vaguely remember having successful training with DVF2DDF in the past, but I am not certain. Maybe worth making another post where you share some code and ask why the loss isn't going down, if you're interested in doing that. Could be any number of things I guess 🤷

[ArjunNarayanan]

Yeah that makes sense, I'll do that. Thanks for your help!