Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 Lecture 2: Digitalization and Basic Waveforms
Extracted mostly from Broughton and Bryan Discrete Fourier
Analysis and Wavelets WileyInterscience, 2008
Weihong Guo (Case Western Reserve)
Math 473Intro. Img. Proc. Comp. Vis.
1 / 23
Outline
1
Digit
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 HW2 Solutions
Problem 1
Solution:
We loaded the image T1Brain.mat and take the Fourier transform of the image matrix I to form the kspace data
K
K = f f tshif t(f f t2(I).
%load T1Brain.mat;
%loads the T1 image I
K = fftshift(fft2(I); %Fourier
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473: Introduction to Image Processing and Computer Vision
Homework 1 Sketchy Solutions
1. Follow steps in book.
2. Verify that L2 (N) = cfw_(x0 , x1 , ),
k=0
xk 2 < is a vector space. L2 (N) is often called 2 .
Proof. Vector addition in this space
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Fall 2014 Math 473 HW 2
Instructions: show all steps to get full credits. Print Matlab code and results and turn in together with written parts. Submit Matlab code to blackboard in the format of HW 2 LastN ame.zip.
Matlab code is due 9:30am of the due day
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Fall 2014 Math 473 HW 1
Instructions: show all steps to get full credits. Print Matlab code and results and turn in together with written parts. Submit Matlab code to blackboard in the format of HW 1 LastN ame.zip.
Matlab code is due 9:30am of the due day
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 Lecture 3: Discrete Fourier transform (DFT)
and its applications in denoising and compression
Extracted mostly from Broughton and Bryan Discrete Fourier
Analysis and Wavelets WileyInterscience, 2008
Weihong Guo (Case Western Reserve)
Math 473Int
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 Lecture 4: Convolution and lter design
Extracted mostly from Chapter 4 of Broughton and Bryan
Discrete Fourier Analysis and Wavelets WileyInterscience, 2008
Weihong Guo (Case Western Reserve)
Math 473Intro. Img. Proc. Comp. Vis.
1 / 31
Outline
1
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 Lecture 6: Filter banks and discrete wavelet
transform
Extracted mostly from Chapter 6 of Broughton and Bryan
Discrete Fourier Analysis and Wavelets WileyInterscience, 2008
Weihong Guo (Case Western Reserve)
Math 473Intro. Img. Proc. Comp. Vis.
Introduction to Mathematical Image Processing and Computer Vision
MATH 473

Spring 2014
Math 473 Lecture 1: Introduction
Weihong Guo
Department of Mathematics, Applied Mathematics and Statistics
Case Western Reserve University
Weihong Guo (Case Western Reserve)
Math 473Intro. Img. Proc. Comp. Vis.
1 / 12
Outline
1
Prerequisite, scope, learni