unwrapl — Unwraps phased images linearly
[unwrapped_phase, phase_jumps] = unwrapl(image[,threshold,step,direction])
Phased images are obtained in various interferometry domains. The phase (coded in gray levels) is represented as the altitude of each pixel. Because the phase is modulo (2*pi or 1 when working with gray levels), the absolute altitude is not known.
This function unwraps a phased image (gray levels) in the simplest manner: linearly. It works this way:
Very simple and quite fast algorithm. But very noise sensitive. Images to treat should be of excellent quality.
For those not familiar with phase unwrapping, I tried to write a very detailed example.
stacksize(1e7); // images are memory-expensive
pw=gray_imread(SIPDIR+'images/photonics/pyramide_wrapped.jpg'); //phase wrapped
xset("window",0); //create a 1st window to display the original image
xbasc();xselect();imshow(pw);
xtitle("original wrapped phase")
//we try to show the object in 3D:
//because of phase jumps, it's not very good
xset("window",1);//the best of all: in a 3rd window, show the object in 3D
xbasc();xselect();
//we take 1 point on 4 to draw the object (faster and more beautifull than
//drawing all the points)
plot3d1(1:4:size(pw,'r'),1:4:size(pw,'c'),pw(1:4:$,1:4:$));
xtitle("original wrapped phase in 3D")
//now we unwrap the phase linearly:
//In this example we don't need any additionnal parameters
//because the image is of good quality.
//be a little patient for this operation
puw=unwrapl(pw);//phase unwrapped
//and we show the result
xset("window",2);//show the unwrapped phase in 2D: we have to put it in the 0-1 range
//to display it properly
xbasc();xselect();imshow(normal(puw));
xtitle("unwrapped phase");
xset("window",3);//we can now show the original object in 3D
xbasc();xselect();
// Again, we take 1 point on 4 to draw the object
plot3d1(1:4:size(puw,'r'),1:4:size(puw,'c'),puw(1:4:$,1:4:$));
xtitle("unwrapped phase in 3D");
An easy introduction to these problems can be found in "Methods for 2-D phase unwrapping in Matlab" by Jiri Novak.
A more complete one: "Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms" by Zebker and Lu (Journal of Optical Society America, vol 15, n3, march 98)