Image Wapring: Forward and inverse

Wapring

Warp source image $f(u,v)$ to target image $g(x,y)$.

Forward Warping

Left: source, right: target. Distribute color among neighboring pixels if pixel lands between two pixels.

Inverse Warping

Interpolation Method

Several methods are taken to conduct interpolation for resampling color pixels in inverse warping:

• Nearest neighbor: Round $(u,v)$ to the nearest integer coordinate.

• Bbicubic.

• Sinc.

• Trilinear interpolation: used in 3-d regular grid.

• Linear interpolation:

  $$\begin{equation} \begin{aligned} \frac{y-y_0}{x-x_0} &= \frac{y_1-y_0}{x_1-x_0} \\ y = \frac{x_1-x}{x_1-x_0}y_0 &+ \frac{x-x_0}{x_1-x_0}y_1 \end{aligned} \end{equation}$$

• Bilinear interpolation: find four integer samples nearest to $(u,v)$, then apply bilinear interpolation:

  $$\begin{equation} \begin{aligned} f(x,y) \thickapprox \frac{f(x_1, y_1)}{(x_2 - x_1)(y_2 - y_1)}(x_2 - x)(y_2 - y) &+ \frac{f(x_2, y_1)}{(x_2 - x_1)(y_2 - y_1)}(x - x_1)(y_2 - y) + \\ \frac{f(x_1, y_2)}{(x_2 - x_1)(y_2 - y_1)}(x_2 - x)(y - y_1) &+ \frac{f(x_2, y_2)}{(x_2 - x_1)(y_2 - y_1)}(x - x_1)(y - y_1) \end{aligned} \end{equation}$$