Hallo, Am Dienstag, 24. Juli 2018 21:56:16 UTC+2 schrieb Torsten Bronger: > > Hallöchen! > > klaus...@gmail.com <javascript:> writes: > > > I found an old thread on the panotools wiki. > > > > https://wiki.panotools.org/User:Klaus/Improving_Hugin > > I find the language hard to understand, sorry. Anyway … what is the > argument against even exponents? > They introduce a singularity at r=0 (due to the branching point of sqrt(x=0) for the two-dimensional mapping function. This singularity causes a rather small radius of convergence.
The problem is not the presence of even exponents. If there were enough odd exponents, and I think one or two more would make a difference, the fit would choose coefficient values close to zero for the coefficients of the even exponents. > > > As long as there is no hard vignetting in the lens, the reasoning > > should work. > > How does the vignetting affect distortion? > Central to my reasoning is that the lens mapping function is holomorphic over the entire image area. Starting with geometric optics, ray tracing through a set of lenses gives an infinitely differentiable function for every ray specified by start point and direction. This property is conserved if one selects rays passing through an aperture in one plane and uses the averaged arrival positions. Here it is key that integration boundary is not a function of ray angle, or in other words, a function of arrival point on the image sensor. When mechanical vignetting occurs, the imaging function is no longer holomorphic at the boundary of the onset, that means that (higher) derivatives will no longer be continuous there. Sorry, that is mathematics heavy, needing a background in complex functions of two variables. But it has practical implications. -- A list of frequently asked questions is available at: http://wiki.panotools.org/Hugin_FAQ --- You received this message because you are subscribed to the Google Groups "hugin and other free panoramic software" group. To unsubscribe from this group and stop receiving emails from it, send an email to hugin-ptx+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/hugin-ptx/0cc33944-0277-42fd-876e-c97daa20556d%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
