Carlos López fing.uy/~carlos

1. On the improving of elevation accuracy of Digital Elevation Models: a comparison of some error detection procedures Carlos López http://www.fing.edu.uy/~carlos Centro de Cálculo Facultad de Ingeniería Montevideo URUGUAY

2. Our goals: • Improve elevation accuracy of grid-based DEM • Use general methods as far as possible • Satisfy both DEM producer & end user needs

3. Some assumptions... • a better value for the elevation can be obtained, but it might be too expensive to acquire it directly (GPS?) • once detected, the errors are corrected (“perfect inspector” hypothesis) • the editing cost is proportional to the number of candidate points

4. Organization of the presentation • Description of the three procedures • Results for the Mt. Sainte Victorie DEM • Discussion • Conclusions

5. The method by López (1997) (IJGIS 1997, 11, 7, 677-689) • A brief presentation of PCA • The method for an elongated DTM • The generalization to any DTM

6. A brief presentation of PCA • attempts to explain the behavior of clouds of points in Rw reducing the dimensionality of the data • it is usually applied to tabular (not raster!) datasets • the starting point is the cloud; all ordering among points (profiles) is lost

7. The elongated DTM case • The process requires two phases: • Identify the ¨suspicious¨ profiles • Analyze each of those profiles trying to pick in each the best candidate(s) for being an error • Any other procedure for tabular dataset can be used instead

8. Some remarks... • Even though we use PCA, our approach is not the standard one used in image processing • We do not use nor assume at all any model of covariance in respect with distance for the elevation • We locate errors based only upon the elevation (we will not consider slope neither curvature)

9. The generalization to any DTM • Any DTM can be considered as build from elongated ones, without intersection • We might look within each of those to locate errors • The procedure can be applied row-wise as well as column-wise • The most likely errors are those which are candidates both for column and row-wise analysis

10. The method of Felicísimo (JP&RS 1994, 49, 4, 29-33) • Compares a local best fit with a low order polinomial; the gross errors are obtained after an analisys of the residual • It is based on very simple hypothesis • uncorrelated errors in space • gaussian distribution of the errors • It can be easily implemented

11. Some problems of both methods • The assumptions of errors weakly correlated in space do not hold at least in the considered example. • Moreover, the performance of both method decreases if the spatial correlation increases

12. The modified procedure (TOG 2000, 4, 1, 43-64) • Since adjacent profiles are too correlated, we formed the strip choosing every kth. row from the DEM. • The implementation and the rationale are almost exactly the same as before. • It considers as a particular case the previous code.

13. The experiment • We used a SPOT derived DEM as a test bed, and consider another DEM of higher accuracy as the ground truth. • Once a location is selected, we correct the noisy DEM using the values from the other. The same point cannot be corrected twice. • We corrected as much as 15 per cent of the DEM. Various measures of the accuracy were recorded.

14. Discussion(1) • The new method outperforms the previous in the low effort region • The Felicísimo’s method in the long run gets mostly systematic errors • The RMSE might drop from 12.7 m to 11.0 m by checking only 1 per cent of the DEM; the max error drops from 193 m to 100 m • For efforts over 2.5 per cent the Felicisísimo’s method becomes better

15. Discussion(2) • Given a DEM, there are some parameters to be defined for our method. The suggested rules gave reliable values. • Once a suspicious point is suggested, some action needs to be taken. Different users might have different goals. • Despite the complexity of the details, the procedure requires only modest computer resources.

16. Conclusion (1) • Some advantages of the procedure • It is valid for any raster dataset • It might be of use both for data producers as well as for end users • It has some free parameters which can be tailored for specific needs, but we provide rules suitable for a first guess • It does not require any “model” for the dataset, neither at local nor global scale

17. Conclusion(2) • Some drawbacks of the method presented • It has been tested only with one DEM • It left unexploited some (maybe) important information from the dataset like the spatial correlation • Future work • should compare the methods with other DEM’s representative of different terrain characteristics