http://imagej.273.s1.nabble.com/FitCircle-circle-fitting-class-tp3691194p3691199.html
>>
>>
>> On Sep 11, 2009, at 4:17 , Michael Doube wrote:
>>
>>> Hi Johan
>>>
>>> From the practical standpoint rather than than the mathematical
>>> perspective:
>>>
>>> the Hough transform finds shapes within data; e.g. you supply an
>>> image and the Hough transform finds the shape (line, circle...) in
>>> it - there is an ImageJ plugin for this here:
http://rsbweb.nih.gov/ij/plugins/hough-circles.html>>
>> Strictly speaking, THE Hough transform finds lines. Other "Hough-
>> like" transforms can be built using the basic ideas of:
>>
>> a) a quantized parameter space
>> b) a voting procedure which turns edge-elements into a set of
>> parameters
>> c) peak finding in the quantized parameter space.
>>
>> Shapes such as circles and ellipses are relatively easy to put into
>> this framework, usually involving a paramter space of Translation,
>> Orientation, and Scale. Circles don't need Orientation.
>>
>> Arbitrary shapes can be handled by the "Generalized Hough
>> Transform". Here, you need a discrete model of the shape, which
>> can be used to build a table that implements the voting rule (for
>> each edge-element, which parameter settings might have generated
>> that edge-element).
>>
>> The Hough transform, the Hough-like transforms, and the Generalized
>> Hough Transform are 3 distinct concepts.
>>
>>
>>>
>>> My FitCircle class finds the single best-fit circle for a set of
>>> (x, y) points. So if you have n coordinates in a 2D array (double
>>> [n][2]; I have displacement from a mean axis vs axis distance) you
>>> can call e.g. FitCircle.hyperStable(coordinates), which returns
>>> the centre and radius of the best fitting circle.
>>>
>>> Chernov has written a huge, detailed manual on the methods which
>>> you can read here:
http://www.math.uab.edu/~chernov/cl/book.pdf .
>>> I'm still suspicious that my Taubin fits are buggy as they break
>>> when supplied with samples from an arc of less than 2*PI radians.
>>> So far, the Hyper fits are doing well in terms of stability and
>>> speed.
>>>>>
>>
>> Here, we see the strength of a Hough-like transform - typically it
>> can do a superior job of identifying an occluded shape.
>> Recognizing the correct circle from a small arc of that circle is
>> easy for a Hough-like circle fitter - but problematic for other
>> approaches.
>>
>