Detection of critical points: the first step to automatic line generalization
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Date
1987-06
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Ohio State University. Division of Geodetic Science
Abstract
Computers have played and are continuing to play a major role in the field of cartography. However, the process of map production especially when a change in scale is required (which is usually the case) cannot be made automatic despite the concerted effort by many mapping agencies and private firms. The bottleneck for this has been the process of line generalization. There does not exist a satisfactory method which can generalize lines automatically as the scale of the map changes. Moreover, the problems of raster to vector conversion, critical points detection, and data compression are equally important to cartography. The problems of data compaction and raster to vector conversion are solved by the process of finding critical points in the raster data by using the method of zero-crossings of the convoluted values of the second derivative of the Gaussian with the signal derived from the digitized data. The problem of automatic line generalization from any larger scale to any smaller scale is also solved by finding the zero-crossings. The data compaction in vector data is achieved by analyzing the eigenvalues of the normalized symmetric scatter matrix derived from the data. The evaluation of the generalized lines is performed by comparing the corresponding lines generalized by zero-crossings algorithm with those performed by cartographers. The following are the most important results of this research: 1. The zero-crossings algorithm achieves line smoothing and data compaction in one step. 2. The zero-crossings method of line generalization gives results which are very close to those obtained by conventional cartographers even when there is a great change in scale. 3. When there is a drastic reduction in scale in the process of line generalization, one needs to preserve the basic shape of the feature and not the critical points. 4. The zero-crossings algorithm of critical points detection can mimic critical points detection by humans. Moreover, this algorithm provides an useful method of raster to vector conversion. 5. The zero-crossings method is fast because it requires neither the computation of square roots nor does it require matrix manipulation.