Finite difference formulation of shape detection using Poisson's equation
Master of Science in Engineering Mathematics
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| Format: | Dissertation |
| Language: | English |
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Universiti Malaysia Perlis (UniMAP)
2017
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| Online Access: | http://dspace.unimap.edu.my:80/xmlui/handle/123456789/76681 |
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my.unimap-766812022-11-02T01:49:40Z Finite difference formulation of shape detection using Poisson's equation Siti Hajar, Azizan Nursalasawati, Rusli, Dr. Poisson's equation Poisson's equation -- Numercial solutions Differential equations, Elliptic Master of Science in Engineering Mathematics Object can be detected or compared its similarity to other shapes, when shape detection is successfully described in computer vision. In this study, three geometry shapes are used in shape detection which are square, circle and ellipse. The two dimensional (2D) Poisson’s equation is used to detect these shapes because Poisson’s equation can be used for various types of shape detection. In order to approximate the Poisson’s equation, the discretization process is conducted using an implicit finite difference method. The Jacobi and Gauss-Seidel methods have been used to solve linear equation of 2D Poisson’s equation. The numerical algorithms are developed in MATLAB R2012b software. In the solution process, the Gauss-Seidel method used less number of iterations compared to Jacobi method to detect square, circle and ellipse. Numerical solutions for these methods are compared and the results obtained using these methods are found to be efficient and suitable to obtain the original shape. The simulation results of 2D Poisson’s equation have been successfully predicted for the shape detection. 2017 2022-11-02T01:49:40Z 2022-11-02T01:49:40Z Dissertation http://dspace.unimap.edu.my:80/xmlui/handle/123456789/76681 en Universiti Malaysia Perlis (UniMAP) Universiti Malaysia Perlis (UniMAP) Institute of Engineering Mathematics |
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Universiti Malaysia Perlis |
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Asia |
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Malaysia |
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Universiti Malaysia Perlis |
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http://dspace.unimap.edu.my/ |
| language |
English |
| topic |
Poisson's equation Poisson's equation -- Numercial solutions Differential equations, Elliptic |
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Poisson's equation Poisson's equation -- Numercial solutions Differential equations, Elliptic Siti Hajar, Azizan Finite difference formulation of shape detection using Poisson's equation |
| description |
Master of Science in Engineering Mathematics |
| author2 |
Nursalasawati, Rusli, Dr. |
| author_facet |
Nursalasawati, Rusli, Dr. Siti Hajar, Azizan |
| format |
Dissertation |
| author |
Siti Hajar, Azizan |
| author_sort |
Siti Hajar, Azizan |
| title |
Finite difference formulation of shape detection using Poisson's equation |
| title_short |
Finite difference formulation of shape detection using Poisson's equation |
| title_full |
Finite difference formulation of shape detection using Poisson's equation |
| title_fullStr |
Finite difference formulation of shape detection using Poisson's equation |
| title_full_unstemmed |
Finite difference formulation of shape detection using Poisson's equation |
| title_sort |
finite difference formulation of shape detection using poisson's equation |
| publisher |
Universiti Malaysia Perlis (UniMAP) |
| publishDate |
2017 |
| url |
http://dspace.unimap.edu.my:80/xmlui/handle/123456789/76681 |
| _version_ |
1751537957634834432 |