LensCorrection Pre-release

[Silvercup]

Hello

I finished writing a script to correct the barrel/pinchcusion photographic objectives, using Helmut Dersch's formula:

Normal Mode: r_src = (a * (r_dest ^ 3) + b * (r_dest ^ 2) + c * r_dest + d) * r_dest
Inverse Mode: r_src = 1/(a * (r_dest ^ 3) + b * (r_dest ^ 2) + c * r_dest + d) * r_dest

a,b,c,d parameters are the radial distortion/correction coefficients for the X,Y dimension equation.

The coefficient a,b,c,d represents scaling and the radial terms control pincushion and barrel distortion. The higher order coefficients affect the pixels further from center. The whole expression has a scaling effect. Thus, to avoid overall scaling, keep a+b+c+d=1. For normal mode, pincushion correction and barrel distortion are achieved using a,b,c positive and barrel correction and pincushion distortion are achieved using a,b,c negative.
For a+b+c+d>1, the image will be scaled smaller and for a+b+c+d<1, the image will be scaled larger.
Typical values are: d near 1 and a,b,c near zero.
For inverse mode, the situation above is reversed. Thus for inverse mode, pincushion correction and barrel distortion are achieved using a,b,c, negative and barrel correction and pincushion distortion are achieved using a,b,c,d positive.
For a+b+c+d<1, the image will be scaled smaller and for a+b+c+d+e>1, the image will be scaled larger.
Values of a=0,b=0,c=0,d=1, makes no change in the image in the appropriate dimension.
Coefficients a,b,c,d,e are floating point values.

Some examples:

Original



Corrected



Original



Corrected





And now I need some help. I can implement a, b, c, d coefficients for X and Y independiently i.e. ax, bx, cx, dx  and ay, by, cy, dy. But theoretically, this formula
can correct chromatic aberration with independent coeficients for each RGB channels Redax, Redbx....Blueyc, Blueyd. You can shift x and y points, choose center of image, etc. A lot of controls.

I don't know how to implement this controls: simple text controls, sliders? SpinBox don't alow negative and decimal values.

And this for Juan. I got error calculations with standart formula r_src = (a * (r_dest ^ 3) + b * (r_dest ^ 2) + c * r_dest + d) * r_dest so I implemented r_src=(a*(r_dest*r_dest*r_dest) + b*(r_dest*r_dest) + c*r_dest + d)*r_dest. What I'm doing wrong?

Thanks

[georg.viehoever]

Hi Silvercup,

this was always on my wishlist, see http://pixinsight.com/forum/index.php?topic=1476.0.

As for the controls: I have been using NumericControl (Sliders) in my scripts, see for example http://pixinsight.com/forum/index.php?topic=1159.msg9587#msg9587 .

Georg

[Enzo De Bernardini]

This is a somewhat old post, but I ask: can this improve, even slightly, coma issues?

Enzo.

[Juan Conejero]

Hi Silvercup,

For some strange reason I overlooked this post completely. Now I've seen it and this looks like a very interesting and promising work (and yes it has been in Georg's wish list for a long time ).

And this for Juan. I got error calculations with standart formula r_src = (a * (r_dest ^ 3) + b * (r_dest ^ 2) + c * r_dest + d) * r_dest so I implemented r_src=(a*(r_dest*r_dest*r_dest) + b*(r_dest*r_dest) + c*r_dest + d)*r_dest. What I'm doing wrong?

The ^ operator does not work as you expect in JavaScript. In PixelMath, ^ is the raise (exponentiation) operator, but JavaScript borrows most of the C/C++ operator syntax so ^ stands for the bitwise XOR operator.

So you must call Math.pow( x, y ) which returns the result of x^y. Using this method, your expression would be:

r_src = (a*Math.pow( r_dest, 3 ) + b*Math.pow( r_dest, 2 ) + c*r_dest + d) * r_dest;

Although I personally would implement it using successive multiplications and a Horner scheme:

let(r_dest2 = r_dest*r_dest, r_dest3 = r_dest2*r_dest) r_src = (a*r_dest + b)*r_dest3 + c*r_dest2 + d*r_dest;

or, much better, using the Math.poly() method:

r_src = Math.poly( r_dest, [d, c, b, a] );

Let us know if you make progress with this extremely interesting script. Any chance you finish it so we can include it into the next release?