[magick-users] Pinbarrel distortion correction

[Anthony Thyssen]

On Sun, 29 Mar 2009 17:22:47 -0700
Fred Weinhaus <fmw at alink.net> wrote:

| 
| 
| >The program is not available anymore and I do not have a copy.
| >I believe it is used more for photo scanning of documents and books
| >rather than real world images at a longer distance.
| >
| >However taking a straight on photo of a picket fence or equally spaced
| >houses, should be able to produce a similar set of lines. Though one
| >which an automatic coordinate extraction program would not be able to
| >directly handle.
| >
| >But I understand how the program works in automatically finding the
| >line crossings of the equally spaced parallel lines, and once it has
| >determined those coordinates the rest is much like your spread sheet
| >but with far more coordinates, spread over a larger radial range.
| >
| >That allows for better matching by least squares function fitting.
| >Something IM already does for handing large numbers of 'control
| >points' than the minimum needed for affine, perspective, or (still
| >undocumented) polynomial distortions, in pixel coordinates.
| >
| >
| >FYI  Polynomial Distortion
| >   -distort polynomial  'order,  coordinate-pairs, ....'
| >Where order is largest X or Y power of for the polynomial
| >and determines the minimum number of coordinates needed
| >   order    function       minimum coodinates
| >     0       constant         1
| >     1       affine           3
| >    1.5      bilinear         4
| >     2       quadratic        6
| >     3       cubic           10
| >     4       quartic         15
| >     5       quintic         21
| >
| >For example a cubic distortion (order 3)
| >distorts the image using the reverse mapping function
| >    Xsrc =  a0 + a1*x + a2*y                        # affine terms
| >         + a3*x*y                                   # bi-linear term
| >         + a4*x^2 + a5*y^2                          # quadratic terms
| >         + a6*x^3 + a7*x^2*y + a8*x*y^2 + a9*y^3    # cubic terms
| >
| >and a similar but completely separate Y coordinate mapping function.
| >
| 
| 
| Anthony,
| 
| Currently your least squares fit only works with X,Y coordinate to 
| fit an X equation and a Y equation. I am not sure you have anything 
| that will work directly with fitting a single polynomial in 
| R=sqrt(X^2+Y^2). Or do you?
| 
I was thinking of extracting coordinates in terms of radii, then
feeding them into the polynomial just a X coordinates, so as to get the
verbose best fit polynomial X formula.  Then the parameters can be
scaled appropriately for their order to get the barrel parameters.

It is an Idea, but I need an image of parallel lines to try out.



  Anthony Thyssen ( System Programmer )    <A.Thyssen at griffith.edu.au>
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