A fully conservative parallel numerical algorithm with adaptive spatial grid for solving nonlinear diffusion equations in image processing
In this paper we present simple yet efficient parallel program implementation of grid-difference method for solving nonlinear parabolic equations, which satisfies both fully conservative property and second order of approximation on non-uniform spatial grid according to geometrical sanity of a task....
| Published in: | Supercomputing frontiers and innovations Vol. 6, № 1. P. 14-18 |
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000660353 Перейти в каталог НБ ТГУ |
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| 024 | 7 | |a 10.14529/jsfi190103 |2 doi | |
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| 039 | 9 | |a 201907091321 |c 201907081707 |d VLOAD |y 201907081654 |z Александр Эльверович Гилязов | |
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| 100 | 1 | |a Bulygin, Andrey D. |9 165606 | |
| 245 | 1 | 2 | |a A fully conservative parallel numerical algorithm with adaptive spatial grid for solving nonlinear diffusion equations in image processing |c A. D. Bulygin, D. A. Vrazhnov |
| 504 | |a Библиогр.: 9 назв. | ||
| 520 | 3 | |a In this paper we present simple yet efficient parallel program implementation of grid-difference method for solving nonlinear parabolic equations, which satisfies both fully conservative property and second order of approximation on non-uniform spatial grid according to geometrical sanity of a task. The proposed algorithm was tested on Perona-Malik method for image noise ltering task based on differential equations. Also in this work we propose generalization of the Perona-Malik equation, which is a one of diffusion in complex-valued region type. This corresponds to the conversion to such types of nonlinear equations like Leontovich-Fock equation with a dependent on the gradient field according to the nonlinear law coefficient of diffraction. This is a special case of generalization of the Perona-Malik equation to the multicomponent case. This approach makes noise removal process more flexible by increasing its capabilities, which allows achieving better results for the task of image denoising. | |
| 653 | |a Шредингера нелинейное уравнение | ||
| 653 | |a нелинейное уравнение диффузии | ||
| 653 | |a Перона и Малика метод | ||
| 653 | |a Леонтовича-Фока уравнение | ||
| 655 | 4 | |a статьи в журналах |9 879358 | |
| 700 | 1 | |a Vrazhnov, Denis A. |9 106039 | |
| 773 | 0 | |t Supercomputing frontiers and innovations |d 2019 |g Vol. 6, № 1. P. 14-18 |x 2409-6008 | |
| 852 | 4 | |a RU-ToGU | |
| 856 | 4 | |u http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000660353 | |
| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=195456 | ||
| 908 | |a статья | ||
| 999 | |c 195456 |d 195456 | ||