David Young

Yeoh cs: There are no general rules for setting those parameters. It depends on the original image and the purpose of doing the transform.

rmax determines the "field of view" of the transform. That is, it gives the radius of the region of the original image that is sampled.

nw determines the resolution at the outside ring. If you want to capture the full detail of the original image, with one transform pixel for each original pixel, you need to make nw equal to 2*pi*rmax. However, this results in massive oversampling nearer the centre, so you may want a smaller value.

I normally set only one of rmin and nr, and allow the other to default, so that the pixels in the sampled image have an aspect ratio of 1. There is always a "hole" at the centre of a log-polar image, and rmin determines how big this hole is. Near the centre of the log-polar image the original image is grossly oversampled, and the smaller rmin is, the worse this is.

In the end though, you have to look at what you are using the log-polar image for, and use either theoretical arguments or empirical tests to decide the parameters.

Very helpful and useful (rating and comments based only on gamma and gammaln functions). Suggestions:

1. The code to allocate storage:

 f = 0.*z; % reserve space in advance

is not needed (indeed is wasteful), as preallocation is only useful ahead of a loop or to set up an array of a specific shape.

2. It might be worth switching to logical indexing rather than linear indexing - this would avoid the use of find() and the reshape at the end.

3. gammaln(z) returns infinities for abs(imag(z)) greater than about 226 and real(z) < 0. This is due to overflow of sin() in the reflection formula, but it is an unnecessary restriction as log(sin(z)) can be computed without overflow over a larger set of values than can sin(z). For example, we can use log(sin(x + iy)) (x and y real) is approximately equal to y + log(0.5i * exp(-1i * x)) for large positive y, and the approximation is good to machine accuracy if y > 18 or thereabouts. (For negative y the approximation is -y + log(-0.5i * exp(1i * x)).) Replacing log(sin()) by a call to a logsin() function that uses these approximations greatly extends the set of valid arguments.

wow, thanks a lot for the code David, helped with my project a lot!

just one question,

for example, if i were to set npeaks to 5, this will result in 5 circles being detected. however, i would only like one of the circle.

hence, is there a parameter i can set to eliminate the other circles? or do i have to add on to your code?

thank you so much!

Young: thx for ur advice, 1 more question .... how to defined the rmin /rmax /nr /nw value of different pattern ?