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 9component 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.
Zoomin of the yellow box
(a) Homography Only 
(b) HRD model 





Summary
 It is a nonlinear model with 10 degreeoffreedom, taking into account firstorder radial lens distortion.
 It is often necessary in order to accurately align images taken by offshelf cameras. In our dataset, three pairs required HRD model: Brugge Square, Brugge Tower, Brussels