Re: Fit sphere to planar circles

On Apr 7, 1:24 pm, "Sven" <sven.holco...@xxxxxxxxxxxxxxxxxx> wrote:
Hi all,

I'm trying to find the center and radius of a mostly spherical body in a voxel volume (femoral head in a CT scan, to be precise).

My approach so far has been to use hough circle detection in the area of interest, looped over each slice. This detection works best around the hemisphere (rather than pole) regions of the sphere, and I am using some logic to cull away any false positive circles detected by the hough transform.

My question is this: what is the best way to fit a sphere to a series of planar circles?

My data is currently in the form of:
circs = [...
  240.5275  145.0197 -564.5000   20.5078;
  241.1135  146.1915 -559.5000   22.8516;
  241.1135  146.1915 -554.5000   23.4375;
  241.6994  146.7775 -549.5000   23.4375;
  241.1135  146.7775 -544.5000   22.2656;]

The columns are the X, Y, and Z locations of 5 circle origins, and their radii.

I'm confident that the average of the X and Y columns represent the X and Y sphere centre, but I don't know the best way to get the Z location.

A simple average of Z locations is inaccurate because the detected circles are not necessarily centrally detected along the Z-direction.

Any thoughts? Perhaps I could try to fit a curve to the radii values and find its peak, but I'm not sure how to fit anything robustly to so few data points.

Any help would be very welcome.
Thanks,
Sven.

Sven,

I have a similar problem and I abandoned the hough transform. I assume
you have grayscale images. What I do is replicate slices to bring z
resolution ~equal to xy resolution, then I do a fft convolution with a
spherical mask (there is an fspecial3 on file exchage, you need some
normalization though) at the radius of interest. If you don't know the
radius, you can iterate over multiple radii. Take the pixel
coordinates corresponding to the max of the convolution.

Any thoughts on/need of computing the entropy of the pixels within the
sphere without requiring a supercomputing center? I'm actively
researching this. Let me know if you want to chat more about this.

Thanks,
Trance.
.

Relevant Pages

  • Re: Maximizing the sum of the radii of packed disks
    ... radii for n circles was always under r*sqrt. ... Apparently, it's unity. ... I meant the radius of the large circle. ...
    (sci.math)
  • Re: Concentric Circles Loosing It
    ... introduction to Java, ... I've managed that, managed to get the 3 circles centered, ... > however, when I minimise and maximise the Applet, ... It sounds as if the value of the radius is being decremented each time the ...
    (comp.lang.java.help)
  • Re: converting points to circles
    ... > we need to transform points in Oracle spatial to circles with a ... > given radius in Oracle spatial. ... GEOMETRY SDO_GEOMETRY ... CREATE OR REPLACE FUNCTION Point2Circle( ...
    (comp.databases.oracle.misc)
  • Re: Rate Gyros and Accelerometers
    ... The force due to gravity is inverse with the square of the radius outside a spherical body, and decreases linearly from the surface to the center IFF the body is of uniform density. ...
    (comp.dsp)
  • Re: Known lengths of edges of an abitrary polygon, seek for area
    ... >>>Right now I'm looking at the pentagon. ... >>>might be 2 possible radii. ... >>angle for that chord decreases as the radius increases. ... >angles add up to 0. ...
    (sci.math)