Alpha Matte Compositing

Implement alpha compositing for foreground/background blending, a key technique in image matting. This process involves combining a foreground image with a background image using a matte, which is a grayscale image defining the opacity of the foreground.

The matte, represented by $\alpha$ , is used to control the blending of the foreground and background colors. The compositing equation is based on the principle of linear blending, where the resulting color is a weighted sum of the foreground and background colors.

Define the foreground, background, and matte images.
Apply the compositing equation to each pixel.

C = \alpha F + (1 - \alpha) B

This technique is widely used in digital image editing.

Example:

Input:

foreground = person image
background = beach scene
alpha = person matte (1 inside, 0 outside)

Output:

Person composited onto beach

Reasoning:

For each pixel:

Where alpha=1: use foreground
Where alpha=0: use background
Where 0<alpha<1: blend smoothly

Constraints:

foreground: Foreground image (H, W, 3)
background: Background image (H, W, 3)
alpha: Alpha matte (H, W) in [0, 1]
Return: Composited image

Example:

Constraints:

Test Results