Math 155, Lecture 1, Winter 2019

Mathematical Imaging

Lecture: MWF 1.00PM - 1:50PM, MS 6627.

Discussion Section: Thursday 1.00PM - 1:50PM, MS 5117.

Instructor: Luminita A. VESE
Office: MS 7620D
Office hours (Instructor): 10-15 minutes after class for short questions; and Wednesday 2pm; or by appointment.
E-mail: lvese[at]math.ucla.edu

Teaching Assistant: Siting LIU. E-mail: siting6[at]math.ucla.edu
Office: MS 3905.
Office hours (T.A.): Tuesday 4-5PM, Thursday 2-3PM.

Textbooks:

R.C. Gonzalez and R.E. Woods, Digital Image Processing, Prentice-Hall, 2018 (4th Ed.) (2nd and 3rd editions are very good; I will be using these).

Pre-requisites: courses Maths 32B and Maths 33B, Maths 115A and PIC 10A.

Math 155 is an introductory course on mathematical models for image processing and analysis. The students will become familiar with basic concepts (such as image formation, image representation, image quantization, change of contrast, image enhancement, noise, blur, image degradation), as well as with mathematical models for edge and contour detection (such as the Canny edge detector), filtering, denoising, morphology, image transforms, image restoration, image segmentation, and applications. All theoretical concepts will be accompanied by computer exercises.

Useful Links:

PIC Lab: 2000 Math Sciences Building
http://www.pic.ucla.edu/piclab/

Textbook website

MATLAB documentation

More about Matlab

Quick Matlab Documentation (thanks to Prof. Chris Anderson, UCLA)

Class Web Page: http://www.math.ucla.edu/~lvese/155.1.19w/

Tutorial: Image Processing with Matlab (Pascal Getreuer)

Sections studied in the lecture (3rd Edition):

Introduction

1.4 Fundamental Steps in Digital Image Processing

2.3.4. A Simple Image Formation Model

2.4 Image Sampling and Quantization: 2.4.1, 2.4.2, 2.4.3, 2.4.4.

Chapter 3: Sections 3.1, 3.2 (3.2.1-3.2.4 except Bit-plane slicing), 3.3, 3.4, 3.5, 3.6.

Chapter 4: Sections 4.2, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11.

Chapter 5: Sections 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10.

Chapter 10: Sections 10.2.5, 10.2.6.

...

Assignment Policy: There will be weekly homework assignments with theoretical questions and computer projects. Homework will be assigned every week and collected every Friday in class. The lowest homework score will be dropped.

Examinations:

One Midterm Exam: Friday, February 15, time 1-2pm.

One Final Exam: Friday, March 15, time 1-2pm (during the last day of lecture).
These are closed note and closed book written exams.
Sample questions for the final

Grading Policy: HW 30%, Midterm 30%, Final 40%

Class materials:

SampleMatlabCode.m

Sample code in Python (thanks to Jacob Moorman) samplePython.py

Illustration of shifting the center of the FT in 1D

Matlab code for the example above of computing the DFT in 1D and shifting the center

Matlab code reproducing the result in Fig. 4.3, using the DFT and IDFT
Fig4.03(a).jpg

Additional images for optional projects

Fig. 5.13(a): Circuit image corrupted by additive Gaussian noise of zero mean and variance 1000

Fig. 5.14(a): Circuit image corrupted by salt-and-pepper noise

Fig. 5.19(a): Florida image

Fig. 5.20(a) Mars image

The following material is obtained from the book web page (including review material for students, solutions (student version), projects):

http://www.imageprocessingplace.com/

Errata to the textbook