Bilinear Interpolation

The problem, from first principles

To resize an image you must decide what value each output pixel should have, but the output pixel generally maps to a fractional location in the input. Bilinear interpolation estimates the value there from the four surrounding input pixels, weighting each by how close it is: first interpolate horizontally along the two rows, then vertically between those results. A subtle detail decides whether your resize matches the libraries: the convention for where a pixel's coordinate sits. Treating a pixel as a unit square whose center is at index + 0.5 gives the mapping src = (dst + 0.5) * (in_size / out_size) - 0.5, which keeps the image centered when scaling.

From theory to code

Implement bilinear_resize.

Constraints

• img has shape (H, W). bilinear_resize(img, out_h, out_w) returns shape (out_h, out_w).
• For output pixel (i, j) the source coordinates are y = (i + 0.5) * H / out_h - 0.5 and x = (j + 0.5) * W / out_w - 0.5, clipped to [0, H - 1] and [0, W - 1].
• With y0 = floor(y), y1 = min(y0 + 1, H - 1) and wy = y - y0 (same for x), the value is the bilinear blend of the four neighbours with those weights.
• Do not modify the input.

Hints