Reverse Mapping in Image Stacking

In reverse mapping, each pixel in the destination image is computed by sampling the appropriate location in the source image, based on a geometric transformation (e.g. translation, rotation, or affine warp).

Practical benefits for astronomical images:

• Lower background noise
• Better star shape

How It Works:

1. Loop through each pixel (dx, dy) in the destination image grid.
2. Apply the inverse transformation to compute the corresponding location (sx, sy) in the source image:
   (sx, sy) = inverse_transform(dx, dy)
3. The calculated (sx, sy) will typically fall between pixels in the source image.
4. Use bilinear interpolation to compute the final pixel value at (dx, dy):
• Identify the four neighboring pixels surrounding (sx, sy).
• Compute a weighted average based on the subpixel position.

Bilinear Interpolation Formula:

value = 
(1 - fx) * (1 - fy) * I(x, y) +
fx * (1 - fy) * I(x+1, y) +
(1 - fx) * fy * I(x, y+1) +
fx * fy * I(x+1, y+1)

Where:

• (x, y) is the integer floor of (sx, sy)
• fx = frac(sx), fy = frac(sy)
• I(x, y) is the pixel value at that coordinate in the source image

Why Use Reverse Mapping?

• Ensures that every pixel in the destination image is filled.
• Avoids gaps or overlapping pixels common with forward mapping.
• Enables accurate stacking, averaging, or sigma-clipping at consistent locations.