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Source code for algebraic (non-iterative) ellipse fitting using positional and 
tangential constraints
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ellipse_fit_with_gradients.c
  Given as input a sequence of points in the form [x_i, y_i], and their 
  gradients [gx_i, gy_i], this file outputs the parameters of the ellipse 
  [cx, cy, a, b, orientation] that approximates the input data; (cx,cy) denotes
  the centre of the ellipse, (a,b) the major and minor axes, and orientation is 
  the angle between the major axis and Ox. The function expects also a buffer 
  that is used internally to compute the coefficients of a linear system.
  This code requires lapack library. The version 3.3.1 was used.

test_ellipse_fit_with_gradients.c
  This code reads some test data from a text file, and calls the ellipse fitting
  function, allocating and deallocating the buffer needed by this function. 
  The text file has the form:
  
  pts_size
  x0 y0 gx0 gy0 
  x1 y1 gx1 gy1
  ...
  
  The first line contains the number of points, and each of the next lines 
  contains the Cartesian coordinates and gradient of each point.

  The code prints in console the parameters of the ellipse.

To compile the test code type 'make'. Make sure you have lapack library 
installed.

To run, type ./test_fit file_name.txt 

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Additional files:

draw_ellipse.m 
  Matlab function to draw an ellipse [cx,cy,a,b,orientation].

sample_data.txt, sample_data_arc1.txt, sample_data_arc2.txt
  Examples of input files to run the ellipse fitting test; the first one 
  contains points sampled along the entire contour of an ellipse, and the other
  two contain points sampled on incomplete contours. 

sample.pgm
  Image from which the points contained in the sample text files above were 
  extracted.

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For details about this ellipse fitting technique, see

  A Parameterless Line Segment and Elliptical Arc Detector with Enhanced Ellipse
  Fitting, V. Patraucean, P. Gurdjos, R. Grompone von Gioi, ECCV2012.

If you use this code in your work, please cite the above paper.

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Contact:
  Viorica Patraucean
  University of Cambridge, Department of Engineering 
  [email protected]