Comparative Study of Positional Accuracy Evaluation of Line Data
2.2 Pont-correspondence method
In applying point-correspondence method, virtual measurement points are generated along the measurement line with constant interval and "virtual error vectors" are drawn connecting the virtual points on the measurement line and "virtual points" along a "true" or reference line. The "virtual measurement points" on the true line are determined so as to minimize the total
sum of square length of the virtual error vectors. This method is based on assumption that aperture generate nodes of a measurement line to minimize "overall" errors or maximinze agreement between the true line and the measurement. In evaluating the "overall" errors or agreement, we assume that the operators generate "virtural" check points along the measurement line or the true line with constant interval interfal to evaluate distance or errors between the true line and the measurement (Fig2). To put it concretely, this method follows the bellow procedures.
Figure 2: Point-correspondence method
- Generate "virtural" check points along the measurement line with constant interval.
- From the virtual points, draw error vectors to true or reference line.
- Determine or adjust the end or error vectors on the true line to minimize total square of length of vectors.
- In the minimization process, set constraint conditions that order of the end points of the error vectors on the measurement line should be consistent with the order of another end points on the true line.
Since errors are evaluated in term of least square of errors and it is is assumed that distribution of errors follow normal or Gaussian distribuion, square of lengths of errors corresponds to the likelihood of errors. With this method, we can estimate bias of errors easily, but when there are not correspondence points and there are two correspondence points, algorithms of determining the point-correspondence should be devised.
2.3 Hausdorff distance
Suppose that
e1 is width of buffer from the true line which contains all of the measurement line, and that
e2 is width of buffer from the measurement line which contains all of the true line. Min
{
e1 ,
e2 } is called hausdorff distance. Since width of buffer that contains all length of the line, it is sensitive to large errors.
2.4 Elimination of bias-error elements
Methods proposed above are for evaluating random errors and not for evaluating systematic errors, for instance, bias, rotation, and difference of scale. So it is necessary to eliminate them. With point-correspondence method, we can estimate systematic errors.
3. Case study
In his study, we use two types of road data of Sagamihara city in Kanagawa prefecture from different data sources. One is data from digitized road ledger (1/500 scale), which is regarded as a reference data, and another is data from aerial survey (1/2500 scale), which is regarded as a measurement line. We picked a part of these data and evaluated errors using proposed methods.
Figure 3: Sample road data
