Math 155, Lecture 1, Winter 2018

Mathematical Imaging

Lecture: MWF 1.00PM - 1:50PM, MS 5118.

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

Instructor: Luminita A. Vese
Office: MS 7620D
Office hours (Instructor): After the lecture and Wednesdays 2-3pm.

E-mail: lvese[at]

Teaching Assistant: Jacob Moorman. E-mail: jdmoorman[at]
Office: MS 3921.
Office hours (T.A.): Thursdays 12:30pm-2:00pm.

  • R.C. Gonzalez and R.E. Woods, Digital Image Processing, Prentice-Hall, 2008.

    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
  • Textbook website
  • MATLAB documentation
  • More about Matlab
  • Quick Matlab Documentation (thanks to Prof. Chris Anderson, UCLA)
  • Class Web Page:
  • 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 on theoretical questions and computer projects. Homework will be assigned every week and collected every Friday in class. The lowest homework score will be dropped.

  • One Midterm Exam: Wednesday, February 14, 1-1:50pm (during lecture).
  • One Final Exam: Friday, March 16, 1-1:50pm (during last lecture).
    These are closed note and closed book written exams.
    Sample questions for the final

    Grading Policy: HW 30%, Midterm 35%, Final 35%

    Class materials:
  • SampleMatlabCode.m
  • Sample code in Python (thanks to Jacob Moorman)
  • 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

    The following material is obtained from the book web page (including review material for students, solutions (student version), projects):
  • Errata to the textbook
  • Review material offered by the book authors

    Homework Assignments, Projects & Practice Problems:

    HW #1 Due on: Friday, January 19
    HW1.pdf HW1.tex
    Image to download Fig3.08(a).jpg

    HW #2 Due on: Friday, January 27
    HW2.pdf HW2.tex

    HW #3 Due on: Friday, February 2
    HW3.pdf HW3.tex
    Image to download Fig3.37(a).jpg

    HW #4 Due on: Friday, February 9
    HW4.pdf HW4.tex
    Image to download Fig3.40(a).jpg

    Image to download Fig5.26a.jpg

    HW #5 Due on: Friday, February 16
    HW5.pdf HW5.tex
    Image to download Fig5.26a.jpg

    HW #6 Due on: Friday, February 23
    HW6.pdf HW6.tex
    Image to download Fig4.11(a).jpg

    HW #7 Due on: Friday, March 2
    HW7.pdf HW7.tex
    Image to download Fig5.26(a).jpg

    HW #8 Due on: Friday, March 9
    HW8.pdf 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 16
    HW9.pdf HW9.tex
    Image to download Fig5.26(a).jpg
    Image to download Fig10.15a.jpg