BMT at TU München

• Is the same for any point p
• Can be described by just a few numbers (parameters)

• Identity
• Scaling
• Rotation
• Mirror
• Shear

Transformations can be combined by matrix multiplication (matrix composition).

The ordering here is IMPORTANT!

Send each pixel f(x, y) to its corresponding location
(x', y')= T(x, y) in the second image.

And use Splatting to color the pixels

Destination picture might have holes

Get each pixel g(x', y') from its corresponding location
(x, y)= T^-1(x', y') in the first image.

Use Interpolation to color the pixel.

+ ensures that no holes occur

- requires and invertible warp function

Image Warping using Vector Fields

• Let (vx, vy)= F(x, y) be an arbitrary vector field and I an image.
• Question: How can we compute the value at I(x + vx, y + vy)?
• Answer: Use forward warping to propagate the pixels to a new
location.
• Problem: Same as before, resulting image will contain holes.

-> Solution:

• Answer 2: Use inverse warping with bilinear interpolation.
• Need to invert vector field F(x, y)
• Look up source pixels using F(x', y')^-1
• Interpolate using one of the presented models, e.g. bilinear

-> Vector Fields transform each pixel separately

-> Inverse warping is better, but requires invertible vector field

edge halos

blurring

aliasing

No jagged artifacts as in Nearest Neighbor

BUT blurry edges

p' = T(p) (p = 2D vector)