I have a bunch of points where the best circle is fitted into them. The algorithm is based on the least squares approach to fit a circle.My question is, how would error analysis be performed. I am thinking of something like: ∑ i ( r i − r ( actual ) ) 2 where r i are the distances from the center of the fitted circle to the point, and r a c t u a l is the actual radius of the circle.Any suggestions or insights on how to proceed?

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I have a bunch of points where the best circle is fitted into them. The algorithm is based on the least squares approach to fit a circle.My question is, how would error analysis be performed. I am thinking of something like:      ∑          i        (      r    i    −      r          (      actual      )            )    2   where       r    i   are the distances from the center of the fitted circle to the point, and       r          a      c      t      u      a      l       is the actual radius of the circle.Any suggestions or insights on how to proceed?

lodosr · Accepted Answer

Given   f  (  x  ,  y  )  :=  a  (      x    2    +      y    2    )  +  b  (  x  y  )  +  c  x  +  d  y  +  e  , a circle is determined by   f  (  x  ,  y  )  =  0. For error analysis of a list of points   [  (      x    1    ,      y    1    )  ,  …  ,  (      x    n    ,      y    n    )  ] that should be on the circle, you can use       ∑    i    f  (      x    i    ,      y    i        )    2    .

I have a bunch of points where the best circle is fitted into them. The algorithm is based on the le

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