## 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:**

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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/
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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.

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Sample questions for the final__

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

** Class materials:**

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SampleMatlabCode.m__

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

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Illustration of shifting the center of the FT in 1D__

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

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Matlab code reproducing the result in Fig. 4.3, using the DFT and IDFT__

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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):
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http://www.imageprocessingplace.com/__

__Errata to the textbook__

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Review material offered by the book authors__

**Homework Assignments, Projects & Practice Problems:**

**HW #1** Due on: Friday, January 18

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HW1.pdf__
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HW1.tex__

Image to download Fig3.08(a).jpg

**HW #2** Due on: Friday, January 25

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HW2.pdf__
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HW2.tex__

**HW #3** Due on: Friday, February 1

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HW3.pdf__
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HW3.tex__

Image to download Fig3.37(a).jpg

**HW #4** Due on: Friday, February 8

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HW4.pdf__
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HW4.tex__

Image to download Fig3.40(a).jpg

Image to download Fig5.26a.jpg

**HW #5** Due on: Friday, February 15

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HW5.pdf__
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HW5.tex__

Image to download Fig5.26a.jpg

**HW #6** Due on: Friday, February 22

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HW6.pdf__
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HW6.tex__

Image to download Fig4.11(a).jpg

**HW #7** Due on: Friday, March 1

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HW7.pdf__
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HW7.tex__

Image to download Fig5.26(a).jpg

**HW #8** Due on: Friday, March 8

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HW8.pdf__
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HW8.tex__

Image to download Fig5.07(a).jpg (original circuit board X-ray)

Image to download Fig5.07(b).jpg

Image to download Fig5.08(a).jpg

Image to download Fig5.08(b).jpg

**HW #9** Due on: Friday, March 15

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HW9.pdf__
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HW9.tex__

Image to download Fig5.26(a).jpg

Image to download Fig10.15a.jpg