Image Rotation & Inverse Mapping

The problem, from first principles

Rotation is a common augmentation: a cat tilted by ten degrees is still a cat. The obvious way to implement it is to take every input pixel and write it to its rotated position, but that leaves holes and collisions in the output, because rotated positions rarely land on pixel centres. The standard fix is inverse mapping: loop over the output pixels, rotate each coordinate backwards to find where it came from in the input, and read the input there. With nearest-neighbour sampling, round the source coordinate to the closest pixel. Output pixels whose source falls outside the image are filled with zero.

From theory to code

Implement rotate_nearest.

Constraints

• img has shape (H, W). Rotate counterclockwise by angle_deg degrees about the image centre ((H - 1) / 2, (W - 1) / 2). The output has the same shape.
• For output pixel (r, c) with dy = r - cy and dx = c - cx, the source is sy = cos(a) * dy + sin(a) * dx + cy and sx = -sin(a) * dy + cos(a) * dx + cx, rounded with np.rint.
• If the rounded source is outside the image, the output pixel is 0. For a square image, rotate_nearest(img, 90) equals np.rot90(img).
• Do not modify the input.

Hints