This issue is solved, after line fitting, by implementing an additional step necessary to merge adjacent lines corresponding to the same linear structure.
As a result, Figure 3 is obtained by applying this line fitting approach (setting ETh to 50 and including the merging step) to the clusterized dataset shown in Figure 2.
This section presents description and results of the numerical simulations carried out to assess absolute performance of the PCA when used for line fitting and to get a comparison with the traditional LS method , for which a fast version is implemented .
Since the goal of these simulations is to assess line fitting performance of the PCA method over sets of points distributed according to a linear pattern, a realistic reproduction of the operation of a range sensor (e.g., 2D LIDAR) is not carried out.
On the other hand, [m.sub.L] is set to 0 as line fitting performance is independent of the orientation of the linear dataset.
The spectrum is to be modeled by a pair of line fitting segments on a logarithmic frequency scale.
For the low index region, the mean-square error between the magnitude and the line fitting (first slope) to be minimized is given by
For the low index line fitting, index j of the summation goes from 1 to L and for the high index line fitting, index j of the summation goes from L + 1 to N/2.
Finally, the mean index, the two coefficients ([a.sub.l0], [a.sub.l1]) used for the envelope line fitting of the low indices, and the other two coefficients ([a.sub.h0], [a.sub.h1]) used for the envelope line fitting of the high indices form the five-dimensional intermediate features.
where P is the number of dimensions of the feature vector and [X.sub.feat] and [N.sub.est] represent the line fitting features of the input signal and estimated noise, respectively.