Homography plus Radial lens Distortion (HRD) model

• The definition is , where

  • is the transformation function with input of location p and output as the transformed location.
  • is the parameter vector.
  • is the radial distortion function, given the image center of , assumed to be the center of the pixel array.
  • is the usual planar homography (h is a 9-component vector formed from the 3x3 homography matrix).

• Comparison with homography model

  • The following example is the checkerboard image of the alignment on Brugge Square pair. The alignment is using homography transformation model and the yellow boxes are showing the areas of misalignment.

Zoom-in of the yellow box

(a) Homography Only	(b) HRD model

• Summary

  • It is a nonlinear model with 10 degree-of-freedom, taking into account first-order radial lens distortion.
  • It is often necessary in order to accurately align images taken by off-shelf cameras. In our dataset, three pairs required HRD model: Brugge Square, Brugge Tower, Brussels