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line extraction. In section 2 we give a brief review of the subject. The proposed
line extraction procedure is explained in section 3 through section 5.
In section 3 a sequential line estimation procedure is presented. Using di-
rectly the line equation in polar coordinates, we have developed an Extended
Kalman Filter (EKF) for sequential line estimation, being noise variance un-
known and depending on measured distance. Our filter formulation is equivalent
to regression models formulation, so we get all the statistical properties, test for
hypothesis contrast, etc., known for regression models theory.
Kalman filters need initial values for their parameters, the only place for
collecting this information are the measures. A set measures, called seed, is used
to get an initial estimation for the filter parameters, a clustering procedure,
section 4, is used to determine good seeds positions. This clustering procedure is
based in scale-space techniques, we have develop a statistic filter to reduce the
number of contour curves due to noise, making the procedure more reliable and
ecient.
In section 5 the designed EKF ability is used for detecting outliers to detect
segments ends, overlapped segments compete for common measures and finally,
due to filter statistical properties, test from model regression theory to merge
similar segments are applied.
Section 6 presents some uses of segmentation results for making robot navi-
gation safer when using center of area methods: better split points location and
moveable split points.
2 Line Extraction Review
It is not intended in this section to make a detailed review of the subject (inter-
ested reader is referred to [9]) but just to highlight the aspects directly motivating
our work or more related to it. First question attracting our attention was the
existence of distance thresholds and the second one was noise effects and models.
Distance thresholds are usual criteria to determine if a point belongs to a
segment based on distance between points. Some known methods using distance
threshold are: Split and Merge [5], Iterative End Point Fit [4], Successive Edge
Following [3], Random Sample Consensus Algorithm (RANSAC) [6] and Line
Tracking [14]. Our objections to distance thresholds are two. First, taking mea-
sures radially there is no limit, theoretically, for distance between two consecutive
segment points, it depends on incidence angle. Second, points belonging to non
concurrent segments could be misclassified if they are close to each other.
Second question to consider is noise models, specially in probabilistic meth-
ods. When noise variance is used in the noise model, it is supposed to be constant
and known, in section 1 we commented the possible big influence of the reflexion
surface on the measure error. We have not found comments in literature men-
tioning explicitly the possibility for unknown, changing or high variances, but
we can give some references where fixed known variance is theoretically required
[18], or used in experiments [4,9]. Normally this variance is the value found in
device technical specifications plus some constant.
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