1. Main guide is the paper itself
Some text is in kth2.doc
Main guide is the paper itself

2. Carlos López http://www.fing.edu.uy/~carlos
Locating some types of random errors in Digital Terrain Models (to appear in Int. J. of G.I.S.)
Carlos López
Environmental and Natural Resources
Information Systems
Royal Institute of Technology

3. Let’s analyze the title
Locating
We will pick candidates to be errors
some types of random errors
the errors are synthetic, not real
they are weakly or no correlated at all
in Digital Terrain Models
but it might work as well in other raster datasets

4. What does locating mean?
whole dataset
correct values
errors A
error’s definition:
II = # A
+ #
I = # B
+ # B
candidates for being errors
candidates for
being correct

5. What is a random error? We do not attempt to locate systematic errors
Our error model simulates weakly or totally uncorrelated errors in space
Its size are supposed to be typical for this DTM
What’s the difference between an error and a blunder?

6. Organization of the paper
PCA in brief
The method for an elongated DTM
Generalization to any DTM
The Monte Carlo experiment
Results for the Stockholm DTM
Discussion
Conclusions

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

8. The elongated DTM case The process requires two phases:
We will look first for ¨unlikely¨ profiles
Later we will analyze each of those profiles trying to pick in each the best candidate(s) for being an error
Let’s see how to do it...

9. 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 Monte Carlo experiment
Each simulation requires that:
We seed the DTM with errors, randomly located and also of random size
We applied the methodology at least for five steps
We evaluate some statistics like Type I and II errors, RMS, etc.
We repeated everything 50 times, in order to obtain average values

11. We require an error model...
An error model is supposed to produce errors with similar spatial correlation and size like those of interest; it might include both random and sistematic errors
The error model is strongly related with the methodology used to create the DTM
We only made a crude approximation since our model is valid for weakly or no correlated at all random errors

12. Results for the Stockholms DTM (1)
We used as a testbed an available DTM of Stockholm, with 1 m height and 50 m horizontal resolution. Its size is 7.5x5 km.
Height ranges from 0 to 59 m. We assumed that integer errors in [-4,+4] are typical
We used two different models to simulate some degree of spatial correlation

13. Results for the Stockholms DTM (2)
As expected, it was easier to locate isolated errors
For spike like, one can be very confident in the first two steps (90%) using parameter appropriate for end users
On the other hand, lowering the remaining errors requires slightly different options, which might be appropriate for DTM producers

14. Discussion
Given a DTM, there are some parameters to be defined. We suggested some rules as a guidance, which might differ depending on the user’s goals
Despite though the complexity of the details, the procedure requires only modest computer resources

15. 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
It does not require any “model” for the dataset, neither at local nor global scale

16. Conclusion (2) Some drawbacks of the work presented
It has been tested only with one DTM
The error model might simulate only a small amount of real random errors
Confidence levels should arise from the Monte Carlo experiment
It left unexploited some (maybe) important information from the dataset