Image Alignment with Least Squares

We look for a rotation/transform matrix A ∈ ℝ^2×2 and a translation b ∈ ℝ² so that y^(k) ≈ A x^(k) + b for the marked point pairs. "Run" fits (Â, b̂) minimizing ∑_k ‖ y^(k) − (A x^(k) + b) ‖₂² using the method selected below: the normal equation (exact) or gradient descent (iterative).

Method: | Image:

Source (click)

Click to add a marker x^(k)

Resize: 100%

Target (drag and rotate)

y^(k) = A x^(k) + b

30°

Fitted Image

ŷ^(k) = Â x^(k) + b̂

(click "Run")

Pixel-wise Difference

|ŷ^(k) − y^(k)|.

mean |Δpx|: —