Multiresolution discontinuity-preserving surface reconstruction

This paper proposes a single multiresolution framework for both surface fitting and discontinuities identification in the surface reconstruction problem. In particular, the Mallat-Zhong wavelet transform modulus maxima (WTMM) representation is employed for representing the surface which allows the discontinuity detection and surface fitting to be carried out simultaneously in a cooperative manner under the same multiresolution framework. On the one hand, the multiresolution feature analysis inherent in the WTMM representation helps characterize the strength of the different significant features, and thus by updating the WTMM surface in a number of energy-minimization processes, the discontinuities can be detected and tracked across various resolution levels. On the other hand, the detected discontinuities in turn control spatially the suitable degree of smoothness at various image positions when the surface is fitted to the input data in the energy-minimizing processes. In this way, the discontinuity detection and the surface fitting processes mutually assist each other. Experimental results show that a piecewise smooth surface can be reconstructed without discontinuity being over-smoothed.