A new algorithm for automatic precise reconstruction of a real object surface

This paper proposes some wavelet-based mathematical models and algorithms for representing any 'real' signal such as a 2D curve or a 3D surface. In contrast with conventional methods that describe almost only a smooth approximation, these models are more powerful which can describe effectively not only smooth signals but also multi-resolution fractal ones. By adopting a designed algorithm, they can also resolve the problem caused by Gibbs effect so that they still can represent a discontinuous signal accurately. Test results of 2D curves and 3D surfaces are shown and analyzed. Based on those conclusions drawn from experimental tests and theoretical analyses, a new algorithm for automatic reconstruction of a real 3D object surface using airborne sensor data (e.g. aerial images) is presented as well. The test results show that high precision representation of a real 3D object surface is realizable. Moreover, the proposed wavelet-based algorithm can describe an entire geometrical object surface with local (pseudo) break points and/or -lines, where conventional piecewise representation is not needed.