EE4780
2D Discrete Fourier Transform (DFT)
2DDiscreteFourierTransform
2D Fourier Transform
F (u , v ) =
f [m, n]e j 2 ( um+ vn )
m = n =
2D Discrete Fourier Transform (DFT)
1
F [k , l ] =
MN
M 1 N 1
f [m, n]e
l
k
j 2 m + n
N
M
m=0 n =0
2D DFT is a samp
Louisiana State University
Department of Electrical and Computer Engineering
EE 4780 Introduction to Computer Vision
Spring 2008
Problem Set 1
Assigned: January 27, 2008
Due: February 4, 2008. Email your files to the TA, Ming Zhang [mzhang4@lsu.edu].
Prob
Louisiana State University
Department of Electrical and Computer Engineering
EE 4780 Introduction to Computer Vision
Spring 2008
Problem Set 2
Assigned: February 15, 2008
Due: February 25, 2008. Turn in a hardcopy of your solutions to the class. Also emai
Louisiana State University
Department of Electrical and Computer Engineering
EE 4780 Introduction to Computer Vision
Spring 2008
Problem Set 3
Assigned: April 14, 2008
Due: April 23, 2008
Teamwork: The problem set will be done in teams of two. Each team m
Final
BahadirK.Gunturk
2
BahadirK.Gunturk
3
BahadirK.Gunturk
4
BahadirK.Gunturk
5
BahadirK.Gunturk
6
There are two blurred observations of an image. In Fourier domain:
G1 = H1 F + N1
G2 = H 2 F + N 2
Derive the formula for F that minimizes the following c
using the derivative of the Gaussian function as the wavelet function. Based on their analysis, a simple and computationally efficient algorithm is proposed here.
Corner is a relative term. Corners are largely dependent on the
shape of the object under co
Contents:
A.zip: code compatible with Matlab 2007a and older
B.zip: code compatible with Matlab 2007b and newer
data.zip: test data
instructions.pdf: this file
Instructions:
Unzip the selected file (A.zip or B.zip) in Matlab current directory (C:/./Matlab
ComputerVision
Stereo Vision
PinholeCamera
Bahadir K. Gunturk
2
Review:PerspectiveProjection
x' y' f '
=
x
y
z
Bahadir K. Gunturk
3
Stereo
scene point
p
p
image plane
optical center
p
Bahadir K. Gunturk
p
4
StereoConstraints
M
Image plane
Y1
Epipolar Line
EE4780
Image Segmentation
ImageSegmentation
Group similar components (such as, pixels in an
image, image frames in a video) to obtain a compact
representation.
Applications: Finding tumors, veins, etc. in medical
images, finding targets in satellite/aeria
EE4780:Introductionto
ComputerVision
Introduction
EE4780
Instructor: Bahadir K. Gunturk
Office: EE 225
Email: bahadir@ece.lsu.edu
Tel: 8-5621
Office Hours: MW 10:00 12:00
Bahadir K. Gunturk
2
EE4780
We will learn the fundamentals of digital image processi
EE4780
Bilateral Filter
BilateralFilter
K is the normalization constant
K=
x+ N
e ( I ( y ) I ( x ) )
2
2
2
2
/ 2 r y x / 2 d
e
y= x N
Intensity (range)
proximity
( x ) = 1
I
K
x+ N
e
Spatial (domain)
proximity
2
( I ( y ) I ( x ) ) / 2 r
2
e
2
2
y x /
EE4780
Huffman Coding Example
HuffmanCodingExample
Suppose X is a source producing symbols; the symbols comes from the alphabet A=cfw_a1, a2, a3,
a4, a5.
Suppose that the probability of each symbol is as follows: cfw_0.4, 0.2, 0.2, 0.15, 0.05.
Form the Hu
EE4780
Image Enhancement (Frequency Domain)
FrequencyDomainFiltering
Compute the Fourier Transform of the image
Multiply the result by filter transfer function
Take the inverse transform
Bahadir K. Gunturk
2
FrequencyDomainFiltering
Bahadir K. Gunturk
3
F
EE4780
Image Enhancement
ImageEnhancement
The objective of image enhancement is to process an
image so that the result is more suitable than the original
image for a specific application.
There are two main approaches:
Image enhancement in spatial domain:
ImageAnalysis
Image Restoration
ImageRestoration
g ( x, y ) = h ( x, y ) * f ( x, y ) + n ( x , y )
Image enhancement tries to improve subjective image quality. Image restoration tries to recover the original image.
BahadirK.Gunturk
EE4780
2
NoiseModels
EE4780:Introductionto
ComputerVision
Linear Systems
Review:LinearSystems
We define a system as a unit that converts an input function
into an output function.
Independent System operator
variable
Bahadir K. Gunturk
2
LinearSystems
Let
where fi(x) is an ar
EE4780
Matlab tutorial
MATLAB
Review your matrix-vector knowledge
Matlab help files are helpful to learn it
Exercise:
f = [1 2; 3 4]
g = [1; 1]
g = [1 1]
g
z = f * g
n=0:10
plot(sin(n);
plot(n,sin(n); title(Sinusoid); xlabel(n); ylabel(Sin(n);
n=0:0.1:10
EE4780
Morphological Image Processing
Example
Two semiconductor wafer images are given. You are supposed to
determine the defects based on these images.
Bahadir K. Gunturk
2
Example
Bahadir K. Gunturk
3
Example
Absolute value of the difference
Bahadir K.
ComputerVision
Optical Flow
Some slides from K. H. Shafique [http:/www.cs.ucf.edu/courses/cap6411/cap5415/] and T. Darrell
Correspondence
Which pixel went where?
Time: t
Bahadir K. Gunturk
Time: t + dt
EE 7730 - Image Analysis II
2
MotionFieldvs.OpticalFl
ComputerVision
Radiometry
Radiometry
Radiometry is the part of image formation concerned
with the relation among the amounts of
light energy emitted from light sources,
reflected from surfaces,
and registered by sensors.
Bahadir K. Gunturk
2
Foreshortenin
A Novel Fingerprint Matching Algorithm Based on Minutiae and
Global Statistical Features
Peng Shi, Jie Tian, Senior Member, IEEE, Qi Su, and Xin Yang
Abstract-The performance of Automated Fingerprint
Identification System (AFIS) is highly defined by the s