Get Affine Transformation Matrix from TransformParameters

I'm using ITK to perform a affine coregistration on 3D MRI scans.
Now similar to what is suggested in https://github.com/InsightSoftwareConsortium/ITKElastix/blob/master/examples/ITK_Example08_SimpleTransformix.ipynb I would like to perform the affine transformation on another image but we are using another library for that.

So I would need a full affine matrix for the transformation that describes the affine coregistration.

I noticed that the registration returns the transform parameters:

```python
result_image, result_transform_parameters = itk.elastix_registration_method( ...
parameter_map = transform_parameters.GetParameterMap(0)
transform_parameters = np.array(parameter_map['TransformParameters'], dtype=float)
```

From other GitHub issues I gathered that the last 3 values of the 12 values in `transform_parameters` is for the translation and the first 9 are for the rotation. Not sure if that is correct.

Based on this I started playing around and got close to the correct affine transformation matrix (the resulting images are similar but not quite right).

```python
rotation = transform_parameters[:9].reshape(3, 3)
translation = transform_parameters[-3:][..., np.newaxis]
translation = -np.flip(translation)
reg_affine: np.ndarray = np.append(rotation, translation, axis=1)
reg_affine = np.append(reg_affine, [[0,0 ,0,1]], axis=0)
```

The translation might be right but the rotation is slightly off. What am I missing / what is wrong? Also why do I need to flip and negate the translation? Do I need to do something similar with the rotation matrix?

Would really appreciate some insight. The ITK methods are a blackbox to me.

------

Not sure what example data I can share. Here some example values for the above variables:

```python
transform_parameters = [ 9.98573286e-01, -3.92533565e-03, -7.45617495e-03, 6.11828178e-04,
9.98081930e-01, 7.21948277e-03, 2.74329272e-03, -1.22292851e-02,
1.00763651e+00, -1.52612188e-01, 8.89476641e-01, 2.55258072e+00]
```

with the resulting affine matrix:

```python
reg_affine = [[ 1.00763651e+00, -1.22292851e-02, 2.74329272e-03, -2.55258072e+00],
[ 7.21948277e-03, 9.98081930e-01, 6.11828178e-04, -8.89476641e-01],
[-7.45617495e-03, -3.92533565e-03, 9.98573286e-01, 1.52612188e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]
```