pete@octopus.UUCP (Pete Holzmann) (01/25/86)
For a digitizing application, I'm looking for any good algorithms that
can be used to generate a transformation function of (x,y) given a set
of reference tranformations.
E.g., I have N sets of (x,y) -> (x',y') values, and want a general way
to come up with F(x,y) that gives (x',y') for any (x,y).p
I've heard that applying a least squares fit to a polynomial in x,y,x^2,y^2 and
xy gives a good fit, but haven't been able to figure out how to
implement that in practical terms for my application: I keep getting
results that don't work at all.
Has anybody out there worked on problems like this? Any suggestions or
reference sources I can go to?
Thanks!
--
OOO __| ___ Peter Holzmann, Octopus Enterprises
OOOOOOO___/ _______ USPS: 19611 La Mar Court, Cupertino, CA 95014
OOOOO \___/ UUCP: {hplabs!hpdsd,pyramid}!octopus!pete
___| \_____ Phone: 408/996-7746ken@turtlevax.UUCP (Ken Turkowski) (01/28/86)
In article <191@octopus.UUCP> pete@octopus.UUCP (Pete Holzmann) writes: >E.g., I have N sets of (x,y) -> (x',y') values, and want a general way >to come up with F(x,y) that gives (x',y') for any (x,y).p How about this: Let z = (x, y, x', y') and order your N sets of 4-D points (by x and/or y). Make up an interpolating polynomial (if N isn't too large) or spline in t such that all of your data points (z) correspond to some t in [0,1]: z = z(t) Then solve for the z that minimizes the distance to a selected (x, y) in the (x, y) plane. -- Ken Turkowski @ CIMLINC, Menlo Park, CA UUCP: {amd,decwrl,hplabs,seismo,spar}!turtlevax!ken ARPA: turtlevax!ken@DECWRL.DEC.COM
frankel@megatek.UUCP (Allan Frankel) (02/02/86)
In article <191@octopus.UUCP> pete@octopus.UUCP (Pete Holzmann) writes: >E.g., I have N sets of (x,y) -> (x',y') values, and want a general way >to come up with F(x,y) that gives (x',y') for any (x,y). > For moderate N and well behaved points, try treating each (x,y) and (x',y') as a point in the complex plane and apply polynomial or rational interpolation. Allan Frankel (619) 455-5590 x2541 Megatek Corporation, 9645 Scranton Road, San Diego, CA 92121 sdcsvax!celerity! akgoa!celerity!megatek!frankel seismo!s3sun! -- Allan Frankel (619) 455-5590 x2541 Megatek Corporation, 9645 Scranton Road, San Diego, CA 92121 sdcsvax!celerity! akgoa!celerity!megatek!frankel seismo!s3sun!