Hello,
I've read a lot on the PanoTools lens correction model in this user group
and over the Internet, however I still have a lot of questions. All its
disadvantages were discussed several times, but I could not a detailed
description of the mechanism itself.
I have calibrated a fisheye lens using Kannala model, which is basically a
polynomial R(theta), where R is the polar coordinates radius of current
point. Now I have a need to work with this calibration in PTGui. We use
Canon APS-C matrix crop-factor 1.62, 4272x2848 matrix in the landscape
mode, 8 mm Sigma fisheyes.
I need to express PanoTools model as a function R(theta). To accomplish
this, I can iterate all possible thetas in the [0, pi/2] range and find the
radius R, corresponding to it. This is how I do it:
1) calculate undistorted equidistant radius (used both by Panotools and
PTGui, not by Hugin, right?) R_undist = f*theta*m as undistorted radius in
pixels. I take m as a mm-to-pixel conversion factor from camera
specification: matrix width is 22.2 mm = 4272 pixels.
2) convert it to PTGui units using the condition r=1 when r=width/2 (this
is taken from PTGui documentation). r = R_undist / (width/2).
3) solve quartic equation in PTGui units: a*r^4 + b*r^3 + c*r^2 +
(1-a-b-c)*r - Rundist = 0 , which gives us r - the distorted radius
4) convert distorted radius to pixels: r_dist_px = r_dist*(width/2), so we
have a r(theta) mapping.
For backprojection theta(R) we have to do the same it the opposite
direction:
1) Convert R to PTGui units: r = R/(width/2)
2) Apply the undistorting polynomial: r_undist =
a*r^4+b*r^3+c^r*2+(1-a-b-c)*r
3) Convert r_undist back to pixels, and then to mm : r_undist_mm =
r_undist*(width/2)/m
4) Taking f*theta model into account, return r_undist_mm / f as a
backprojection angle theta.
This looks logical, but doesn't work. The radiuses don't get distorted and
undistorted as expected. I've also found this intriguing code in math.c of
libpano13. Why are the coefficients used with r, and not polynomially? The
same thing can be found in "inv_radial" function, where the polynomial is
solved. Maybe I misunderstand the whole model?
int radial( double x_dest, double y_dest, double* x_src, double* y_src,
> void* params)
> {
> // params: double coefficients[4], scale, correction_radius
> register double r, scale;
> r = (sqrt( x_dest*x_dest + y_dest*y_dest )) / ((double*)params)[4]; // r
> = r_px/scale
> if( r < ((double*)params)[5] )
> {
> scale = ((((double*)params)[3] * r + ((double*)params)[2]) * r +
> ((double*)params)[1]) * r + ((double*)params)[0]; // scale
> = a*r+b*r+c*r+d
> }
> else
> scale = 1000.0;
>
> *x_src = x_dest * scale ;
> *y_src = y_dest * scale ;
> return 1;
> }
I've also tried to understand the conversion from fov to f and back. This
is what Joost, the author of PTGui, exactly told me:
> Yes PTGui still uses the f*theta projection.
> This is how PTGui calculates the horz fov:
> hfov=4*RAD2DEG*asin(cropwidth_**mm/4.0/focallength);
> cropwidth_mm is the diameter of the cropping circle, or the width of the
> image.
> I realize that this is not consistent with the equidistant formula but it
> does match the fov for practical lenses.
However, when I use the diameter of crop circle as cropwidth_**mm (4500 px
in my case), it doesn't work correctly. I empirically found, that the
mistake is linear, and the correct conversion formula is f =
0.967555562*D/(4*m*sin(radians(fov)/4)) or
hfov=4*asin(0.967555562*D/(4*m*focallength)),
where D is the crop width in pixels, m the scale coefficient desribed
earlier. The fact that the mistake is linear makes me think I use a
different value of m? Or maybe it's more complicated.
I've contacted the author of PTGui himself, he has answered some of my
questions, but was not willing to solve the problems, so I decided to try
to get advice in this group.
Thanks in advance for any help,
Lire
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