James Turner wrote: >By the way, ringing at sharp edges is an intrinsic feature of higher- >order spline interpolation, right? I believe this kind of interpolant >is really intended for smooth (band-limited) data. I'm not sure why >the pre-filtering makes a difference though; I don't yet understand >well enough what the pre-filter actually does. > > Yes, ringing at edges is an intrinsic feature of higher-order spline interpolation. Eventually, the spline interpolant becomes a band-limited sinc-interpolator which will assume that edges are really points sampled from a sinc. So, if you re-sample at different points you get the "ringing" effect. But, you shouldn't see a lot of ringing below order 7.
The pre-filter obtains the spline-interpolation coefficients. The spline assumes the continuous function represented by the samples at x_i is f(x,y) = sum(c_ij beta^o(x-x_i) beta^o(y-y_i)) The "pre-filter" is computing the coefficients c_ij. You then evaluate at any point you like using the continuous function implied by the spline. The function beta^o is a spline function and depends on the order of the spline. >I'm not sure what people normally do in computer graphics, since I'm >working more with natural band-limited images, but in the case of >Stefan's "rotate_artifacts" example, wouldn't it be appropriate to >use the 1st- or 0th-order spline instead of the 2nd order? If your >real-life data are smooth enough, however, then in theory the >ringing with higher orders should go away. > > Yes, that is true. But, you really shouldn't see much ringing with a 3rd order spline, though. I studied these splines for a while, but my memory can fail me. You can look at the papers of M. Unser for much more information. Here is a link to a good review paper. http://bigwww.epfl.ch/publications/unser0001.pdf -Travis _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
