[INPUT_SEPARATOR]
First, create a Cython helper module for distance calculations.
```python
edit
file: solver.py
lines: 0-0
---
import scipy.ndimage

class Solver:
    def solve(self, problem):
        image = problem["image"]
        matrix = problem["matrix"]
        try:
            # Perform affine transformation with cubic interpolation
            transformed_image = scipy.ndimage.affine_transform(
                image, matrix, order=3, mode='constant'
            )
        except Exception:
            # Return empty list on failure
            return {"transformed_image": []}
        return {"transformed_image": transformed_image.tolist()}
---
```