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P System Implementation of Dynamic Programming Stereo

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Abstract

Designing parallel versions of sequential algorithms has attracted renewed attention, due to recent hardware advances, including various general-purpose multi-core and many-core processors, as well as special-purpose FPGA implementations. P systems consist of networks of autonomous cells, such that each cell transforms its input signals in accord with its symbol-rewriting rules and feeds the output results into its immediate neighbours. Inherent massive intra- and inter-cell parallelisms make P systems a prospective theoretical testbed for designing efficient parallel and parallel-sequential algorithms. This paper discusses the capabilities of P systems to implement the symmetric dynamic programming stereo (SDPS) matching algorithm, which explicitly accounts for binocular or monocular visibility of 3D surface points. Given enough cells, the P system implementation speeds up the inner algorithm loop from O(nd) to O(n+d), where n is the width of a stereo image and d is the disparity range. The implementation gives also an insight into a more general SDPS that accounts for a possible multiplicity of solutions of the ill-posed problem of optimal stereo matching.

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Acknowledgements

The authors wish to acknowledge the contributions of P. Delmas, M.J. Dinneen, Y.-B. Kim, J. Morris, D. Nicolescu and the assistance received via the University of Auckland FRDF grants 9843/3626216 and 3624475.

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Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Georgy Gimel’farb, Radu Nicolescu & Sharvin Ragavan

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  1. Georgy Gimel’farb
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  2. Radu Nicolescu
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  3. Sharvin Ragavan
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Correspondence to Georgy Gimel’farb.

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Gimel’farb, G., Nicolescu, R. & Ragavan, S. P System Implementation of Dynamic Programming Stereo. J Math Imaging Vis 47, 13–26 (2013). https://doi.org/10.1007/s10851-012-0367-6

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