Re: [Numpy-discussion] iterate along a ray: linear algebra?

4 Jul 2006


      I've found some matlab code that seems to do the same sort of thing.
Interestingly enough it just uses trigonomotry to do find the x,y positions
in the matrix that correspond to the ray at a particular angle. I had
origionally discarded this idea because I thought there must be a more
efficient way to do it, but perhaps not. I still have a lot to learn about
numpy :)

Stephen

(sorry for the double post to you Torgil)

On 7/3/06, Torgil Svensson  wrote:
...
I've done something similar a few years ago (numarray,numeric). I
started roughly at the middle and did 64 points from a reference point
(xc,yc). This point together with a point at the edge of the image
(xp,yp) also defined a reference angle (a0). (ysize,xsize) is the
shape of the intensity image.
I used the following code to calculate points of interest:
na=64
xr,yr=xsize-xc,ysize-yc
a0=arctan2(yp-yr,xp-xc)
if a0<0: a0+=2*pi
ac=arctan2([yr,yr,-yc,-yc],[xr,-xc,-xc,xr])
if numarray:
    ac[ac<0]+=2*pi
else:
    ac=choose(ac<0,(ac,ac+2*pi))
a1,a2,a3,a4=ac
rmaxfn={
    0: lambda a: a<=a1 and xr/cos(a-0.0*pi) or yr/cos(0.5*pi-a),
    1: lambda a: a<=a2 and yr/cos(a-0.5*pi) or xc/cos(1.0*pi-a),
    2: lambda a: a<=a3 and xc/cos(a-1.0*pi) or yc/cos(1.5*pi-a),
    3: lambda a: a<=a4 and yc/cos(a-1.5*pi) or xr/cos(2.0*pi-a)
    }
angles=arange(a0,a0+2*pi,2*pi/na)
if numarray:
    angles[angles>=2*pi]-=2*pi
else:
    angles=choose(angles>=2*pi,(angles,angles-2*pi))
nr=int(ceil(sqrt(max(yc,yr)**2+max(xc,xr)**2)))
crmax=array([int(floor(rmaxfn[floor(a*2/pi)](a))) for a in angles])
cr=outerproduct(ones(na),arange(float(nr)))
ca=outerproduct(angles,ones(nr))
x=cr*cos(ca)+xc
y=cr*sin(ca)+yc
After this I did cubic spline interpolation in the image with these
points and did something useful. I don't know how relevant this is to
you and it doesn't use the linear algebra package but it might give
you some hint.
If you find out a nifty way to do your rays please post on this thread.
Sidenote -- Watch my explicit float argument to arange and even
putting in pi there in one case. There's a discussion on this list
that floats in arange are troublesome
...
I am in the process of implementing an image processing algorithm that
requires following rays extending outwards from a starting point and
calculating the intensity derivative at each point. The idea is to find
...
point where the difference in intensity goes beyond a particular
On 6/30/06, stephen emslie  wrote:
the
threshold.
...
Specifically I'm examining an image of an eye to find the pupil, and the
edge of the pupil is a sharp change in intensity.
How does one iterate along a line in a 2d matrix, and is there a better
way
...
to do this? Is this a problem that linear algebra can help with?
Thanks
Stephen Emslie
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