A Way to Automatic Reconstruction of a Real 3D-City Surface
In accordance with those conclusions, a first draft of an algorithm for automatic reconstruction of a real 3D-city surface is depicted briefly in Figure 5. It adopts the idea stated in Chapter 3, where orthonormal fractal wavelets, the principles of image inversion, sampling theorem, least squares estimation technique, and a ‘from-coarse-to-fine’ strategy are utilized. In each level of the image pyramid, significant wavelet coefficients are automatically determined and selected and used as candidate unknown parameters for the lower level with finer resolution, so that an efficient operations are available.

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Compute the image pyramid data.
Define approximation of DTM: horizontal plane or better data if available.
Compute a better DTM by the image pyramid method: From the top to the bottom level: For the top level:
Determine a_j0k and w_j0k ,"k.
Automatically select significant wavelet coefficients w_j0k , "k. Prolong the significant wavelet coefficients to the lower level.
For the lower levels:
Determine jk w for those candidates of significant wavelet coefficients.
Automatically select significant wavelet coefficients w_jk , "k.
Prolong the significant wavelet coefficients to the lower level. For the bottom level:
Determine w_jk for those candidates of significant wavelet coefficients.
Automatically select significant wavelet coefficients w_jk , ".k.
Output the computed DTM and ortho image and its covariance matrix as well.

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Figure 5. First draft of an algorithm for automatic reconstruction of a real 3D-city surface

Conclusions
It is concluded that the proposed wavelet-based approximation algorithm can describe an entire geometrical function with local (pseudo) break points and/or –lines, where conventional piecewise representation is not needed. Some topics must be further and continuously studied, e.g. the first draft of algorithm shown in Figure 5 will be exactly developed and tested. Furthermore, a really 3D representation will be further studied, where one changes the current model Z(X,Y) with only one Z-value at a horizontal position (X,Y) to the other with the capability for representing more Z-values at a (X,Y).

Reference

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