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 to obtain an improved DTM which benefits from the existing ones. Typically, two DTMs, which represent a certain area on different scales or resolutions, are considered. For example, one DTM might be densely derived by image matching techniques from aerial or space images and a second one might be measured with GPS or with analytical photogrammetric instruments. The latter one is expected to be a sparse but more accurately measured DTM, which represents the terrain shape on a coarse scale. Other examples might be the integration of existing DTMs with new measured DTMs from radar or laser data. The next section briefly sketches the idea of multiscale wavelet processing. A concept for the integration of DTMs, which may differ in scale and accuracy, is presented in section 3. First experiments are presented to demonstrate the applicability of the approach (section 4) and give some insight into the accuracy behaviour of the integrated DTM over scale. 2. WAVELET TRANSFORMATION AND MULTISCALE PROCESSING Wavelet theory is explained in detail for example in the textbook of Louis et al. (1997). In the following, we briefly outline the idea of multiscale analysis using wavelets for one dimensional signals. Splitting a signal into parts of varying detail is the key to the fast computation of the discrete wavelet transform (Mallat, 1989). The decomposition of signal/= s+d, with s representing the smooth and d the detail part, can be carried out by discrete low-pass and high-pass filtering. By identifying s with the lower resolution signal / on scale level i and f A with the signal on the finer scale level i-1, the lower resolution signal will be obtained from f_x by low-pass filtering with a low-pass of response function /. The detail signal d is computed by high-pass filtering with impulse response h. I corresponds to the so-called scaling function, h to the wavelet function of the discrete wavelet transform. The convolutions can be elegantly formulated using multiplication with block-circulant matrices. L and H are the block-circulant matrices corresponding to the filter kernels l and h. The convolutions then read as follows: d i =Hf i _ l This process is referred to as the decomposition of the signal / and L and H are the decomposition operators. Recursive application of the decomposition formulas leads to further splitting of the smooth part over a selected number of M scale levels. By reversing this process the synthesis equation fi-l ~ L fi + H*d t of the wavelet transform is obtained. This reverse process is referred to as the reconstruction of the signal in which the finer representation is calculated from coarser levels by adding the details according to the synthesis equation. Decomposition includes a subsampling by a factor of two and reconstruction the corresponding oversampling. Based on this short description of the wavelet transform, we are now prepared to present our concept for DTM integration based on wavelets. Related work on multiresolution approximation in the area of physical geodesy is discussed in Li (1996). For a deeper understanding of the wavelet theory we refer to the textbook of Louis et al. (1997). 3. A CONCEPT FOR DTM INTEGRATION BASED ON WAVELETS For the explanation of the concept, we restrict ourselves to two given DTMs. The generalisation to multiple DTMs will become obvious at the end of the discussion. Assume that one DTM with high resolution and a second one with low resolution are given. The first one is considered a fine scale representation of the surface of some terrain and the second one a coarse scale representation of the same terrain surface. We further assume that accuracy measures for both DTMs are given and represented by the corresponding covariance matrices. For simplicity, we presume that the grid width of both DTMs is related by a factor 2 M . 3,1 Multiscale Representation of a DTM The first step of the integration process is to represent the high resolution DTM in a series of scales. The sequence of low-pass filtered and subsampled data results in a DTM pyramid generated by the wavelet transform. An example is plotted in Figure 1. Basically, it shows a familiar picture of a DTM pyramid, which is often generated in photogrammetry by image matching and finite element modelling using image pyramids (Ackermann and Hahn, 1991). But this, of course, does not imply any close relation between the generation processes of the wavelet representation and the finite element modelling. The formulas for the wavelet decomposition and reconstruction given in section 2 have to be adapted for the formulation of the DTM integration process. The wavelet decomposition for two-dimensional data can be conveniently formulated by using matrix notation based on the Kronecker product <£>. The wavelet DTM representation on level j calculated from the finer level DTM on level j-1 reads as follows (x is used to address the DTM, dx for the detail signal of the DTM) x“=(L®L)x“ 1 di.“ = (L ® H)i“, = (H ® In addition to the decomposition of a DTM, its corresponding covariance matrix C must be also decomposed. For this second moment information, the law of error propagation applies giving

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