Academic Journal
A New Original Vector Ordering based on Search of the Minimum Error Sequence by Recursive Analysis of n-ary trees
| العنوان: | A New Original Vector Ordering based on Search of the Minimum Error Sequence by Recursive Analysis of n-ary trees |
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| المؤلفون: | Ouattara, Sié, Kouassi, Adles, Clément, Alain |
| المساهمون: | Institut National Polytechnique Félix Houphouët-Boigny Yamoussoukro (INP-HB), Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Université d'Angers (UA) |
| المصدر: | ISSN: 0973-1768 ; Global Journal of Pure and Applied Mathematics ; https://hal.science/hal-02116162 ; Global Journal of Pure and Applied Mathematics, 2018, 14 (9), pp.1237-12349 ; https://www.ripublication.com/gjpam.htm. |
| بيانات النشر: | HAL CCSD Research India Publications |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | Vector ordering, tree, Vectorial mathematical morphology, Mean square error, Minimum cost, Morphological Operators, Multicomponent Image, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing |
| الوصف: | International audience ; The elaboration of a vector ordering in vectorial mathematical morphology is tricky. This has been the subject of many works because the extension of a scalar order to the vector case does not seem obvious. Therefore, if we stick to Barnett's classification in 4 groups of orders, we find that the first group called marginal order orders the vectors by component and independently, it introduces false colors and the order is not total. The second group is the partial order, it performs a classification in ordered partitions and does not provide a classification of the vectors of the same partition. The third called reduced order is based on a bijective transformation of vectors into scalars, its implementation requires the choice of a referent that is generally arbitrary. The last group is the conditional order, its principle is based on the lexicographic order used in the dictionaries, and in this case the proximity between the vectors is not guaranteed. Indeed, in our previous work, we contributed to the improvement of the conditional orders by choosing adaptive and non-arbitrary absolute referents. Additional constraints have been proposed to make these orders constitutes a lattice on the space considered. The relevance of the choice of referent is questionable and always makes parametric proposed conditional orders, which weakens their performance. Thus, the purpose of this paper is to propose a new original, simple, natural and non-parametric order to order vector attributes or "color" based on the choice of sequences subject to an error constraint minimal. Our goal is to be able to tend towards a universal order for the ordering of the vector attributes. The new vector orderthat we present in this work is natural and original. The general idea of its conception is inspired by an observation of the functioning of the order of real numbers, in particular the natural numbers. Consider a sequence of numberx1, x2,., xpofRorNof lengthp. Considering all possible permutations of sequences ... |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-02116162; https://hal.science/hal-02116162; OKINA: ua17935 |
| الاتاحة: | https://hal.science/hal-02116162 |
| رقم الانضمام: | edsbas.F5C65E85 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |