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What's in a Set of Points? (Straight Line Fitting)
April 1992 (vol. 14 no. 4)
pp. 496-500

The problem of fitting a straight line to a planar set of points is reconsidered. A parameter space computational approach capable of fitting one or more lines to a set of points is presented. The suggested algorithm handles errors in both coordinates of the data points, even when the error variances vary between coordinates and among points and can be readily made robust to outliers. The algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework. It is observed that certain extensions of the Hough transform can be turned to be equivalent to well-known M estimators, thus allowing computationally efficient approximate M estimation.

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Index Terms:
parameter estimation; statistical analysis; least squares approximations; straight line fitting; parameter space computational approach; optimality criteria; Hough transform; M estimators; curve fitting; least squares approximations; parameter estimation; statistical analysis; transforms
N. Kiryati, A.M. Bruckstein, "What's in a Set of Points? (Straight Line Fitting)," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 4, pp. 496-500, April 1992, doi:10.1109/34.126810
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