16 September 1994 Homotopy and critical morphological sampling
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Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.186035
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States
Abstract
In pattern recognition tasks, it is often convenient to alter the sampling rate of the signal, either to convert to a more appropriate scale/resolution, or to produce an image pyramid and perform the task in an multiresolution fashion. In many of these applications, the mse criteria optimized by the Shannon Sampling Theorem is not appropriate, and other sampling strategies should be considered. In this paper we present a new Critical Sampling Theorem, and extends the results to the case where the connection between several parts of the signal (i.e., the homotopy of the set) is of primary interest. The results are presented for binary signals in an hexagonal grid. Extension for square grids with some specific cases of connectivity criteria is also presented. The results show that it is possible to preserve homotopy while using a sampling density 3 to 4 times smaller than required by previous results. This can be used to reduce the sample density or to improve the detail preservation, and has the potential of improving many multiresolution techniques.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Dinei A. F. Florencio, Dinei A. F. Florencio, Ronald W. Schafer, Ronald W. Schafer, } "Homotopy and critical morphological sampling", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); doi: 10.1117/12.186035; https://doi.org/10.1117/12.186035
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