Rogier, On Jan 6, 8:17 am, Rogier Wolff <[email protected]> wrote: > On Thu, Jan 06, 2011 at 04:45:26AM -0800, Bart van Andel wrote: > > > On Thursday, January 6, 2011 5:09:06 AM UTC+1, Tom Sharpless wrote: > > > > > It has been pointed out that the polynomial should only consist of > > > > even numbered powers, both for speed and for mathematical soundness. > > > > I'm not convinced there is anything wrong with odd powers in a radial > > > correction function; since R is always >= 0 the odd symmetry is never > > > manifested. > > > Isn't there? There is a sharp discontinuity in (the derivative of) any > > odd-powered polynomial, when mirrored around the Y-axis. Since R can only > > have positive values, this discontinuity will happen at the image "center" > > which is used to compute R from. Therefore, it makes sense to avoid odd > > powers. > > Ok. So the function y = x has exponent 1, and is not suitable. There > is a sharp corner at x=0, which mathematically manefests itself as a > discontinuity of the derivative: > > dy/dx = 1 where x > 0 > and = -1 where x < 0 (and undefined for x=0)
You are thinking of y = abs(x) = sqrt( x^^2). The first derivative of y = x is +1 everywhere. There are no discontinuities in any of the derivatives of non-negative powers of x. Regards, Tom -- You received this message because you are subscribed to the Google Groups "Hugin and other free panoramic software" group. A list of frequently asked questions is available at: http://wiki.panotools.org/Hugin_FAQ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/hugin-ptx
