Geometric Transformation in Gradient Domain Possible? I work with images in gradient domain because I sometimes need to manipulate image gradients (i.e. Laplacian filter responses) rather than intensity values.

However, I need to apply a geometric transform (distortion) to an image already in gradient domain.

Is is then meaningful to reintegrate the distorted image back to spatial domain?

Here is my earlier question related to gradient domain reconstruction with some images.
The geometric transformation needs to be independent from the pixel coordinates $x$ and $y$. assume that $G$ is your transformation matrix:
$$
\int\frac{d^{2} (G I)}{dx dy}  = G \int\frac{d^{2} (I)}{dx dy} 
$$
is true only when $G$ is independent from the coordinates. 

The restoration will succeed with constant (i.e. global) image rotations, scalings, and shifts.