Transformation Format in mosaic.xform File

The transformation starts with the tag "xform = <" and ends with ">" (the inverse transformation starts with "inverse_xform = <") in the .xform file. Compared to the typical form of transformations, the ones used in GDB-ICP are centered transformations, i.e., the transformation is w.r.t. the center. The details are explained as follows:

• Affine

The text format is:
AFFINE
2
a11 a12
a21 a22
t1 t2 c1 c2

The 1st line "AFFINE" indicates it is an affine transformation. The 2nd line indicates this transformation applies to 2D coordinates. (The same idea applies to the following transformations.) The rest of lines are coefficients to the transformation in this format:

• Homography

The text format is:
HOMOGRAPHY2D
2
h11 h12 h13
h21 h22 h23
h31 h32 h33
c1 c2 d1 d2

Denoting as the 3-by-3 homography matrix and

as the homography function in inhomogeneous coordinates, the transformation is written as

• Homography with Radial Lens Distortion

  The text format is:
  HOMOGRAPHY2D_WITH_RADIAL_DISTORTION
  2
  h11 h12 h13
  h21 h22 h23
  h31 h32 h33
  c1 c2 d1 d2
  k1 k2

Denote

as the homography function (same as before) and

as the radial lens distortion function. The transformation is written as

• Reduced Quadratic
  The format is the same as Quadratic transformation. However, it has only 6 degree of freedom (instead of 12). Please refer to Dual Bootstrap paper for details.

The text format is:
REDUCED_QUADRATIC
2
b11 b12 b13
b21 b22 b23
a11 a12
a21 a22
t1 t2 c1 c2

Let

• Quadratic

The text format is:
QUADRATIC
2
b11 b12 b13
b21 b22 b23
a11 a12
a21 a22
t1 t2 c1 c2

Let