MA3111: MATHEMATICAL IMAGE PROCESSING, Fall 2025

MA3111: MATHEMATICAL IMAGE PROCESSING, Fall 2025

Instructor: Prof. Suh-Yuh Yang (楊肅煜)

Office: M315, Hong-Jing Hall
Phone: 03-4227151 ext. 65130
E-mail address: syyang@math.ncu.edu.tw
Homepage: http://www.math.ncu.edu.tw/~syyang/

Office Hours: Tuesday 10:00~12:00 am or by appointment.

Teaching Assistant: 饒祥弘, E-mail: 113221006@cc.ncu.edu.tw

Prerequisites: MA1018/MA2030/MA2044, and some knowledge of programming language Matlab

Textbook: No textbook but some references

[AK2002] G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Second Edition, Springer Verlag, New York, 2002.

[CS2005] T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods, Society for Industrial and Applied Mathematics, Philadelphia, 2005.

[TUM2019] D. Cremers, Computer Vision I: Variational Methods, Online Resources, Departments of Informatics & Mathematics, Technical University of Munich, Germany, 2019/2020. https://vision.in.tum.de/teaching/online/cvvm

[GW2018] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Fourth Edition, Pearson Education Limited, New York, 2018.

Course Objective: This course is concerned with the mathematical study of image processing. Its two objectives are

to introduce basic concepts and engineering approaches applicable to digital image processing and develop a further study foundation.

to provide some mathematical techniques for studying several fundamental questions in image processing, such as how to restore a degraded image and how to segment it into meaningful regions.

General Information: This course will cover the following topics

Basic concepts of digital image processing
Intensity transformations and spatial filtering
Variational methods for image denoising
Variational methods for image deblurring
Multi-focus image fusion and guided filter
Image dehazing: atmospheric scattering model and dark channel prior
Variational methods for image contrast enhancement
Image inpainting: variational methods and sparse representation
Variational image segmentation: Mumford-Shah and Chan-Vese models
Principal component pursuit problems

Assignments: will be assigned approximately every two weeks and announced at ee-class. The students are encouraged to discuss homework with other classmates. Direct copying is absolutely not allowed.

Course Transparency Set: (in PDF)

Grading Policy: assignments 30%, midterm 30%, final 30%, and others 10% (學期總成績)

Last updated: September 01, 2025