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On the improving of elevation accuracy of Digital Elevation

Models: a comparison of some error detection procedures

Carlos Lópezhttp://www.fing.edu.uy/~carlos

Centro de CálculoCentro de CálculoFacultad de Ingeniería Montevideo URUGUAYFacultad de Ingeniería Montevideo URUGUAY

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Our goals:

Improve elevation accuracy of grid-based DEM

Use general methods as far as possible Satisfy both DEM producer & end user

needs

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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

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Organization of the presentation

Description of the three procedures Results for the Mt. Sainte Victorie DEM Discussion Conclusions

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The method by López (1997)

A brief presentation of PCA The method for an elongated DTM The generalization to any DTM

(IJGIS 1997, 11, 7, 677-689)

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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

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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

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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)

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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

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The method of Felicísimo

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

(JP&RS 1994, 49, 4, 29-33)

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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

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The modified procedure

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.

(TOG 2000, 4, 1, 43-64)

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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.

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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

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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.

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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

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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