It is desirable to combine both the surface reconstruction phase with the detection of discontinuities into a single framework. Wavelet Modulus Maxima representation proposed in [9] can be used to achieve this goal.
This representation has a property that there exists strong correlation between the wavelet coefficients across scales. Noise would usually show up in the first few wavelet bands with its effect decreases drastically in the higher wavelet bands. In contrast strong edges will have their effects showing across all wavelet bands. Hence, by tracking the effects across wavelet bands, we can establish whether the response is due to noise or not, and how strong the edge is [10].
This representation thus allows tracking of discontinuities in
a multiresolution fashion, i.e., a robust performance in
discontinuity detection can be achieved which enhances the surface
being reconstructed from the sparse data.
Please refer to the following for details
N.F. Law and R. Chung,
``Interpolation with Multiscale Analysis of Discontinuity'',
Proceedings of the Fifth European Conference on Computer Vision
(ECCV' 98),
June 1998, University of Freiburg, Breisgau, Germany,
Vol 2, pp. 202-214.