application of the wavelet transform to filtering

APPLICATION OF THE WAVELET TRANSFORM TO FILTERING AIRBORNE LASER SCANNING DATA

mgr inż. Krzysztof Sośnica

Krzysztof Sośnica Institute of Geodesy and Geoinformatics

Juniorstav 2010

ALS


ALS (Airborne Laser Scanning)

Filtering

Advantages:

Wavelet transform

-independence from light condition,

Algorithm of filtering Results Summary

-independence from weather, - good penetration of afforested areas.

Krzysztof Sośnica Instytut of Geodesy and Geoinformatics

Juniorstav 2010

ALS

Filtering Wavelet transform Algorithm of filtering Results Summary


Test Data – ‘Widawa’ Project

Krzysztof Sośnica

APPLICATION OF THE WAVELET TRANSFORM TO FILTERING

Instytut of Geodesy and Geoinformatics

Juniorstav 2010

ALS

Test Data – ‘Widawa’ Project


AIRBORNE LASER SCANNING DATA

The prototype scanner ‘ScaLARS’

Krzysztof Sośnica




Juniorstav 2010

ALS

Filtering

Data filtering Digital Surface Model

Wavelet transform Algorithm of filtering Results Summary Digital Terrain Model

+

Surface objects

Krzysztof Sośnica



Juniorstav 2010

ALS


Data filtering of LIDAR signal

Filtering Wavelet transform Algorithm of filtering

-based on a moving polynomial models,

- based on Fourier transform, - based on wavelet transform.

Results

-based on adaptive TIN models,

Summary

-other methods.


Juniorstav 2010

ALS



Wavelet transform

Krzysztof Sośnica



Juniorstav 2010

ALS


Signal decomposition Raw Data

Filtering

Approximation 1 Wavelet transform Algorithm of filtering Results Summary

Approximation 2

Approximation 3

Detail 3

Detail 2

Detail 1


Juniorstav 2010

ALS



Krzysztof Sośnica



Juniorstav 2010

ALS

Algorithm of filtering based on discrete fast * wavelet transform * *



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Juniorstav 2010

ALS



Wavelet transform


Juniorstav 2010

ALS



Wavelet transform


Juniorstav 2010

ALS



Results

Krzysztof Sośnica




Juniorstav 2010

Results – time of filtering

ALS

The relation between time of filtering and a total number of points

Filtering Wavelet transform Algorithm of filtering

The time of computations in s

14,00

12,00

10,00

8,00

6,00

4,00

2,00

Results 0,00 0

Summary

0,5

1

1,5

2

2,5

3

Total points number (in millions)

3,5

4

y = 3E-06x + 0,174


Juniorstav 2010


ALS Errors I type -

Filtering

surface recognized as objects

Errors II type -

Wavelet transform Algorithm of filtering Results Summary

objects recognized as surface

Appropriate recognition – surface recognized as surface

Appropriate recognition – objects recognized as objects


Juniorstav 2010

ALS


Results


The result of filtering in the sloping terrain. As shown in figure, the wavelet approximation of the surface is adapted to the ground: vegetation is eliminated, while slope remains intact.

Krzysztof Sośnica




Juniorstav 2010

Results

ALS

Number of errors in test areas

Wavelet transform Algorithm of filtering Results

Errors in % and time of computation in s

Filtering 18 16 14 12 10 8 6 4 2

Error type II [%]

0 Total error [%] 4 1

Error type I [%]

2

Summary

No of test area

3 Time of computation [s]

5 6 averrage


Juniorstav 2010

ALS



Summary - the algorithm of two-steps filtering has been developed. This method makes the process of filtering in the domain of wavelet frequency, where high frequencies of the signal correspond to surface objects. Low frequencies are basically responsible for the physical surface of the ground. - the algorithm works properly in the flat area, as well as in hilly and mountain terrains, - the accuracy of algorithm was estimated on 95%, - the possibility of filtering of 1 million of points in the time of 3.4 seconds


Juniorstav 2010

ALS



References •Borkowski A., Sośnica K. „ZASTOSOWANIE DYSKRETNEJ TRANSFORMACJI FALKOWEJ DO FILTRACJI DANYCH LOTNICZEGO SKANINGU LASEROWEGO”, Kraków 2010, Archiwum Fotogrametrii, Kartografii i Teledetekcji, •Sośnica K. „Noise Reduction in Airborne Laser Scanning Signal Based on Discrete Wavelet Transform", IGSM 2009, ETH Zurich 2009, •Sośnica K. „Data Analysis of LIDAR Signal Based on Wavelet Transform", SECON 2009, Wojskowa Akademia Techniczna w Warszawie 2009, •Axelsson P., 2000. DEM generation from laser scanner data using adaptive TIN models. International Archives of Photogrammetry and Remote Sensing Vol. XXXIII/B, Amsterdam 2000. •Bartels M., Wei H., 2006. Towards DTM generation from LIDAR data in hilly terrain using wavelets. Whiteknights. The University of Reading. [online] http://www.cvg.reading.ac.uk/projects/LIDAR. •Białasiewicz J.T., 2000: Falki i aproksymacje, Wydawnictwo Naukowe-Techniczne, Warszawa 2000 •Borkowski A., Jóźków G., 2006. Wykorzystanie wielomianowych powierzchni ruchomych w procesie filtracji danych pochodzących z lotniczego skaningu laserowego. Archiwum Fotogrametrii, Kartografii i Teledetekcji, Vol.16, s.63-73 •Elmqvist M., 2002. Ground surface estimation from airborne laser scanner data using active shape models. ISPRS, Commission III, Symposium Photogrammetric Computer Vision, September 9–13, Graz, 114–118. •Kraus K., Pheifer N., 2001: Advanced DTM generation from LIDAR data. International Archives of Photogrammetry and Remote Sensing, Vol. XXXIV-3/W4, Annopolis, Mary-land, 23-30. •Marmol U., 2002: Analiza częstotliwościowa jako metoda filtrowania profili powierzchni topograficznej. Materiały Ogólnopolskiego Sympozjum Naukowego: Fotogrametria i teledetekcja w społeczeństwie informacyjnym. Białobrzegi k/Warszawy, 2002. •Thuy Vu T., Tokunaga M., 2002: Designing of wavelet-based processing system for air-borne laser scanner segmentation. Space Technology Applications and Research – Asian Institute of Technology, Commission V WG V/6, Thailand. •Vidaković B., Müller P., 2005: Wavelets for Kids. A Turiorial Introduction. Duke Uni-versity, Institute of Statistics and Decision Sciences, 2005

Thank you for your kind attention

mgr inż. Krzysztof Sośnica