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Issue title: Formal Models - Computability, Complexity, Applications
Article type: Research Article
Authors: Nicolescu, Radu | Gimel’farb, Georgy | Morris, John | Delmas, Patrice | Gong, Rui
Affiliations: Department of Computer Science, The University of Auckland, Auckland, New Zealand. [email protected]
Note: [] Address for correspondence: Department of Computer Science, The University of Auckland, Auckland, New Zealand
Note: [] Also works: Faculty of Engineering, Mahasarakham University, Mahasarakham, Thailand
Abstract: We propose a novel approach to justify and guide regularisation of an ill-posed one-dimensional global optimisation with multiple solutions using a massively parallel (P system) model of the solution space. Classical optimisation assumes a well-posed problem with a stable unique solution. Most of important practical problems are ill posed due to an unstable or non-unique global optimum and are regularised to get a unique best-suited solution. Whilst regularisation theory exists largely for unstable unique solutions, its recommendations are often routinely applied to inverse optical problems with essentially non-unique solutions, e.g. computer stereo vision or image segmentation, typically formulated in terms of global energy minimisation. In these cases the recommended regularisation becomes purely heuristic and does not guarantee a unique solution. As a result, classical optimisation algorithms: dynamic programming (DP) and belief propagation (BP) – meet with difficulties. Our recent concurrent propagation (CP), leaning upon the P systems paradigm, extends DP and BP to always detect whether the problem is ill posed or not and store in the ill-posed case an entire space of solutions that yield the same global optimum. This suggests a radically new path to proper regularisation: select the best-suited unique solution by exploring statistical and structural features of this space. We propose a P systems based implementation of CP and set out as a case study an application of CP to the image matching problem in stereo vision.
Keywords: concurrent propagation, ill-posed problems, regularisation, multiple solutions, stereo matching, P systems, membrane computing, parallel and distributed computing models, actor model
DOI: 10.3233/FI-2014-1026
Journal: Fundamenta Informaticae, vol. 131, no. 3-4, pp. 465-483, 2014
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