Abstract
Samples taken at scattered points of a finite-support two-dimensional signal can be interpolated to recover an approximation of the original signal. Given a bound on the number of samples, where should they be placed to enable the most accurate reconstruction? Or, given an error bound for the reconstruction, what is the minimum number of samples required, and where should they be placed? In this paper we introduce search schemes that provide good candidate solutions to these problems, for digital signals. Natural Neighbour Interpolation is used in iterative sample removal and movement processes to obtain sparse sample patterns. For pictures and Digital Elevation Models, fewer samples are required if the interpolant is onlyC 0 continuous at the data sites, than if it isC 1. Retained samples lie on the ridges and valleys of the laplacian.
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Robinson, J.A., Ren, M.S. Data-dependent sampling of two-dimensional signals. Multidim Syst Sign Process 6, 89–111 (1995). https://doi.org/10.1007/BF00981566
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DOI: https://doi.org/10.1007/BF00981566