By Andrea Frosini, Maurice Nivat (auth.), Reinhard Klette, Joviša Žunić (eds.)
This quantity provides the complaints of the tenth foreign Workshop on Combinatorial photo research, held December 1–3, 2004, in Auckland, New Zealand. earlier conferences happened in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we obtained 86 submitted papers from 23 nations. each one paper was once evaluated by way of not less than self sustaining referees. We chosen fifty five papers for the convention. 3 invited lectures by means of Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) accomplished this system. convention papers are awarded during this quantity below the subsequent topical half titles: discrete tomography (3 papers), combinatorics and computational versions (6), combinatorial algorithms (6), combinatorial arithmetic (4), d- ital topology (7), electronic geometry (7), approximation of electronic units through curves and surfaces (5), algebraic ways (5), fuzzy picture research (2), picture s- mentation (6), and matching and popularity (7). those topics are handled within the context of electronic picture research or computing device vision.
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The main problem with the admissibility condition is that it considers all detector values separately. For example, the measured effect of an atom can never be equal to its lower bound for all detectors simultaneously. For a given configuration which has been constructed up to block the fitting procedure constructs an exact configuration for which the atom positions lie in the prescribed cells such that the of to the measured data is minimal: If the of the resulting exact configuration is larger than a constant D (the fitting cutoff), we can conclude that the configuration is most likely not a good partial solution to the reconstruction problem and it is discarded.
The samples that we consider are typically very thin, around 10 atoms thick, so only linear combinations with equally small coefficients can lead to such problems. The detector measurements always contain a certain amount of noise. A high noise level may also result in a solution to the reconstruction problem that is different from the actual measured atom configuration. We now choose a particular set of atom projection functions for demonstrating the basic concepts of our model and our algorithm.
J. Palenstijn Fig. 10. Test configurations with their projections On the Reconstruction of Crystals Through Discrete Tomography 5 37 Discussion The experimental results show that our algorithm is able to reconstruct all test sets accurately when there is no noise. Noise is clearly a problem for our algorithm. When reconstructing atom configurations for which we know in advance that they contain only a single atom type, the tolerance for noise is much higher than for the case of multiple atom types.