A concept and algorithm for 3D city surface modeling

To realize a better representation of complete three-dimensional (3D) city models in Taiwan, this paper proposes an alternative concept and algorithm for 3D geometrical city surface modelling based on wavelets and least squares adjustment. The reasons why wavelets are adopted as an alternative module are stated. Firstly in this algorithm, a wavelets-based module for surface modelling makes it convenient to depict different types of city surfaces, where it enables an operator to choose a proper father wavelet in an interactive manner. It also can describe a fractal surface if fractal wavelets are adopted. Secondly, observations are acquired manually or (semi-)automatically. Simultaneously, any observation is recorded with a predefined code that defines a specific topology relationship with others. Then, the well-known least-squares adjustment is utilized to let the adopted wavelet surface function fit all observations, where the surface parameters, namely wavelet coefficients, in a local small stereo model (image window) are directly estimated and observation errors are filtered out. The surface function and observation equations are linear so that both estimation of initial values for unknown parameters and Gauss-Newton iteration are not needed. Current personal computer (PC) makes it possible to complete all computations in a short duration of time. It also provides quality figures, namely a covariance matrix, and enables a (near) real-time visual check on a DPW (Digital Photogrammetry Workstation). The afore-mentioned processes are done in each small window. Finally, a 3D city surface in a large area can be reconstructed by collecting the results in all windows, where neighbouring windows have a proper overlap. Some preliminary test results are also shown.