MA3111: Mathematical Image Processing Syllabus and Introduction
Suh-Yuh Yang (楊肅煜)
Department of Mathematics, National Central University Jhongli District, Taoyuan City 32001, Taiwan
http://www.math.ncu.edu.tw/∼syyang/
Syllabus
Instructor:Prof. Suh-Yuh Yang (楊肅煜) Office: M315, Hong-Jing Hall
Phone: 03-4227151 extension 65130
Office hours: Tuesday 10:00∼12:00 am or by appointment.
Teaching assistant: 廖唯廷/研究室: M201, Tel: 65145, E-mail:
Prerequisites: MA1018/MA2030/MA2044, and knowledge of MATLAB:http://matlab.math.ncu.edu.tw/
Assignments: will be assigned approximately every two weeks.
The students are encouraged to discuss homework with other classmates.Direct copying is absolutely not allowed.
Exams:there will be a midterm exam and a final presentation/report.
Grading policy:assignments 40%, midterm 30% and final 30%.
Course objective
This course is concerned with the mathematical study of image processing. Its two main objectives are
(1) to introduce basic concepts and engineering approaches applicable to digital image processing and develop a further study foundation.
(2) 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.
No textbook but some references
(1) [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.
(2) [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.
(3) [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 (4) [GW2018]R. C. Gonzalez and R. E. Woods,Digital Image
Processing, Fourth Edition,Pearson Education Limited, New York, 2018.
Important dates
The period for adding and dropping a course: 09/08-09/28, 2021 The period for withdrawing a course: 10/29-12/10, 2021
Moon Festival: September 21 (Tue), 2021,no class!
Midterm: 11/10 (Wed), 2021
Sports Day: November 17 (Wed), 2021,no class!
Final presentation: 01/04-05, 01/11-12, 2021
Digital image processing
Interest in digital image processing methods stems from two principal application areas:
(1) improvement of pictorial information for human interpretation;
(2) processing of image data for tasks such as storage, transmission, and extraction of pictorial information.
The need to extract information from images and interpret their content has been the driving factor in the development of modern image processing techniques and tools.
Image processing is a multidisciplinary field. It overlaps with other areas such asimage analysis/understanding (影像分析/影像 了解) and computer vision (電腦視覺).
image processing =⇒ image analysis/understanding
=⇒ computer vision
This course will cover the following topics
(1) Basic concepts of digital image processing (2) Basic image processing operations in MATLAB
(3) Intensity transformations and spatial filtering
(4) Variational methods for image denoising: ROF model (5) Multi-focus image fusion: local variance and guided filter (6) Variational methods for image contrast enhancement (7) Variational methods for image inpainting
(8) Feature extraction and image stitching: panorama
(9) Image segmentation: Mumford-Shah and Chan-Vese models (10) Sparse dictionary learning for image processing
Image denoising
(e)
(a) original
(f)
(b) noisy
(g)
(c) ROF
(h)
(d) adaptive
Image fusion
(e) Source1 (f) Source2
(g) LSDGF1 (h) LSDGF2
Panorama: image stitching
(T) 8 source images; (B) stitched image
Contrast enhancement I
(T) stitched image; (B) contrast enhanced image
Contrast enhancement II
(L) low-light images; (R) contrast enhanced images
Image inpainting I
(L) corrupted images; (R) inpainted images
Image inpainting II
(L) ground truth images; (M) original images; (R) inpainted images Generative Adversarial Network (GAN, 生成對抗網路)
Image segmentation
origin image initial contour
23 Iterations segmentation = 0.005
(i)
origin image initial contour
23 Iterations segmentation = 0.005
(j)
origin image initial contour
23 Iterations segmentation = 0.005
(k)
origin image initial contour
23 Iterations segmentation = 0.005
(l)
Medical image segmentation (variational method)
Input image Initial contour
21 iterations Segmentation
(m)
Input image Initial contour
21 iterations Segmentation
(n)
Input image Initial contour
21 iterations Segmentation
(o)
Input image Initial contour
21 iterations Segmentation
(p)
(m) input image; (n) initial contour; (o)&(p) segmented images
Medical image segmentation (snake method)
(T) Human’s cardiac CT, human’s lung CT, brain CT, and ultrasound (B) Deformation processes by AeGVF
