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Bilinear Interpolation

Computer Vision

Medium

Resize a two-dimensional grid with corner-aligned bilinear interpolation. Map each output coordinate to the source grid:

y=i\frac{H-1}{H_{\mathrm{new}}-1}

x=j\frac{W-1}{W_{\mathrm{new}}-1}

Use source coordinate zero when the corresponding output dimension is one. Let $y_0=\lfloor y\rfloor$ , $x_0=\lfloor x\rfloor$ , $d_y=y-y_0$ , and $d_x=x-x_0$ . Clamp $y_1=y_0+1$ and $x_1=x_0+1$ to the source boundary. Then compute:

V_0=I_{y_0,x_0}(1-d_x)+I_{y_0,x_1}d_x

V_1=I_{y_1,x_0}(1-d_x)+I_{y_1,x_1}d_x

O_{i,j}=V_0(1-d_y)+V_1d_y

Return the resized two-dimensional list.

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Examples

Input: image = [[0, 10], [20, 30]], new_h = 3, new_w = 3

Output: [[0, 5, 10], [10, 15, 20], [20, 25, 30]]

Explanation: Corners remain fixed and every middle value is the linear blend of neighboring pixels.

Input: image = [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]], new_h = 2, new_w = 2

Output: [[0, 3], [12, 15]]

Hint 1

Compute source coordinates before taking their floor and fractional parts.

Hint 2

Interpolate horizontally twice, then interpolate those two values vertically.

Requirements

Use corner-aligned source coordinates
Blend the four neighboring source values
Handle output height or width equal to one
Return a two-dimensional list with the requested dimensions

Constraints

The image is a nonempty rectangular list
New height and width are positive integers

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