[Vxl-maintainers] vpgl_calibration_matrix over parameterization

[Matt L. <mat...@ki...>]

All,

I seem to keep running into issues related to the fact that
vpgl_calibration_matrix is over parameterized. The problem is that
vpgl_calibration_matrix is internally represented by 6 parameters but
only has 5 DOF.  The redundant ones are focal_length, x_scale, and
y_scale, which I feel should really be focal_length, and
pixel_aspect_ratio.

A common problem that arises because one constructor is

vpgl_calibration_matrix(focal_length, principle_point, x_scale=1,
y_scale=1, skew=0);

and the other is

vpgl_calibration_matrix(vnl_double_3x3 K);

In the constructor from a matrix, the focal_length is set to 1 and
x_scale=K(0,0) and y_scale=K(1,1).  So consider the following:

double focal_length = 1000.0
vgl_point_2d<double> pp(640,480);
vpgl_calibration_matrix<double> K(focal_length, pp);
vpgl_calibration_matrix<double> K2(K.get_matrix());
vcl_cout << "focal length = " << K2.focal_length();

The above prints "focal length = 1", but I would expect 1000.  In
practice this happens because we often write the camera to a file as a
matrix and then read it back in.

Does anyone have a good reason to keep the x_scale and y_scale?  Can I
replace this with pixel_aspect_ratio?

Thanks,
Matt