Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

baltsavias, emmanuel p.

Bibliographic data

Monograph

Persistent identifier:: 856473650

Author:: Baltsavias, Emmanuel P.

Title:: Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

Sub title:: Joint ISPRS/EARSeL Workshop ; 3 - 4 June 1999, Valladolid, Spain

Scope:: III, 209 Seiten

Year of publication:: 1999

Place of publication:: Coventry

Publisher of the original:: RICS Books

Identifier (digital):: 856473650

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: TECHNICAL SESSION 4 FUSION OF SENSOR-DERIVED PRODUCTS

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: INTEGRATION OF DTMS USING WAVELETS. M. Hahn, F. Samadzadegan

Document type:: Monograph

Structure type:: Chapter

International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 3.2 Integration of DTMs The integration concept consists of three steps: Step 1: Calculate a wavelet decomposition with M levels for the high resolution DTM and its associated covariance matrix. The number of levels is chosen in such a way that the coarsest scale level fits to the resolution of the second DTM. Step 2: The low-pass filtered coarse scale representation of the first DTM and the second DTM are merged together using weighted least squares averaging. The weights result from the inverted covariance matrices of both DTMs. This means that for the low-pass filtered DTMl the corresponding low-pass filtered covariance matrix Cl is used (Eqs. 1 and 2) and for DTM2 the given second DTM with its covariance matrix C2. Weighted least squares averaging is of course only one possibility among others. Other widely applied techniques for DTM interpolation like least squares prediction or Wiener filtering may be used, if they promise better results. Step 3: The merging result of both DTMs together with the calculated covariance matrix can be considered as the representation of the integrated DTM on scale level M. By using the reconstruction formulas (Eqs. 3 and 4) the estimates for the integrated DTM together with its accuracy can be calculated on all scales and in particular on the finest scale. Generalisation from two to several DTMs can be simply carried out by repeating the three steps. As soon as two DTMs are integrated the resulting height and accuracy data are taken as a new DTM which can be integrated with a third one. A fourth and fifth DTM and so on may follow. From the viewpoint of computational efficiency it might be reasonable to integrate coarser DTMs first and move on by integrating the higher resolution DTMs. But more important for the computational efficiency of the overall processing is the implementation of the wavelet decomposition and reconstruction formulas. The elaboration with the block-circulant matrices according to Eqs. 1-4 is very convenient to understand the structure of the transform but for efficiency reasons a recursive implementation, essentially based on discrete convolutions, is required. For more details about the fast wavelet transform refer to Mallat (1989). In the next section, we visualise results of the wavelet decomposition and reconstruction, in particular those relating to the first and third step of the integration process and discuss the achievements by focussing on the accuracy. 4. EXPERIMENTS 4.1 Illustration of Integration Results In the experimental investigation we first want to visualise the overall DTM integration process, in particular for the terrain surface, over a number of scale levels. For that purpose, we use two DTM samples. The first one represents a rather smooth area, the other one a region with undulating terrain. The densely sampled rather noisy DTMs for both areas can be seen in Figures 2 and 4 together with another three lower scale levels of the DTM pyramid. On the coarse level, merging with a second DTM is carried out by least squares averaging as outlined in section 3. The second DTM given on the lower scale is not shown, as it looks fairly similar to the integration result on that 2ÜJ0 , 1530 6DÜ n 400 - 200 >. 100 1000-. 800. firm... 40 1000 20 Fig. 2. Experiment with smooth terrain. The noisy high resolution DTM and three lower scale levels are shown.

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