Line Generalization: Least Square With Double Tolerance
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A new approach to line generalization using a least squares method with double tolerance (LS:DT) is introduced in this work. In this technique, ‘anchor points’ that preserve the line caricature are first identified, using the Douglas & Peucker technique. Once these anchor points are located, a least squares line that passes through a set of identified points using the anchor points as guides is constructed. As a result, a least squares line that begins and ends at projected anchor points will be established. In order to control the allowable projected distance for the anchor points, a shift tolerance is used. With the introduction of the shift tolerance, the least squares lines are adjusted to enhanced the generalization effects. Since the least squares lines are not linked together, common intersection points (IP) are established. Joining together the corresponding IP and projected points then forms the generalize line. It is found that, apart from exhibiting a ‘global approach’ towards generalization, LS:DT are capable of minimising length and areal (polygonal) distortion with respect to the original line and area while still preserving its caricature. Another advantage of LS:DT is its capability to perform generalization either by the Douglas & Peucker technique, least squares or a combination of the two by specifying the appropriate shift tolerance.