เรียนอะไรบ้างใน SEAMS School on Partial differential equations for image processing: theory and numerics ?
เนื้อหาที่เรียนมีทั้งหมด 5 หัวข้อ โดยผู้เชี่ยวชาญ 5 ท่าน ดังนี้
1. Scientific python by Marília Pires, University of Évora, Portugal ️🇵🇹
This practice presents the main features of a free software to solve mathematical equations derived from concrete problems. This course is done on computer.
- Presentation of python
- Basics (number, characters, function)
- Linear and nonlinear systems.
2. Finite difference methods for PDE by Noppadol Chumchob, Silpakorn University, Thailand 🇹🇭️
- Brief overview of ordinary and partial differential equations
- Elliptic PDE
1D, 2D elliptic problems, Convergence theory
- Parabolic PDE
1D heat equation, Stability, Convergence theory for time-dependent problems
- Image processing-image restoration.
3. Exact solutions of smoothing PDE, by Nabil Bedjaoui, University of Picardie, France 🇨🇵️
- Separation of variables, Fourier series
- Fourier transform
- Convolution, Green’s function
- Image restoration, Filtering.
4. Hyperbolic PDE by Joaquim Correia, University of Évora, Portugal 🇵🇹️
- Dynamics of image processing & parabolic-hyperbolic models
- Image denoising and restoration & viscosity solutions, shock capturing
- Linear and nonlinear models (transport, waves and optics, dissipation and dispersion)
- Characteristics, entropies, viscosity-dispersive solution(s)
- Curves and signals & metrics, dynamic geometry and scales.
5. Computer implementation, Youcef Mammeri, University of Picardie, France 🇨🇵️
This lecture is dedicated to the implementation of methods presented in the other lectures. This course is done on computer.
- 1D Finite differences implementation
- Fast Fourier Transform
- 2D implementation, Kronecker product
- Examples of simple image processing
- Scipy routines for image manipulation.