Time-Frequency Analysis and
Wavelet Transform Oral
Presentation
Advisor: 丁建均 and All Class Members
Student: 李境嚴
ID: D00945001
What’s Today?
XIII. Applications of Time–Frequency Analysis
(1) Finding Instantaneous Frequency
(11) Acoustics
(12) Biomedical Engineering
(2) Signal Decomposition
(3) Filter Design
(4) Sampling Theory
(5) Modulation and Multiplexing
(13) Spread Spectrum Analysis
(14) System Modeling
(15) Image Processing
(6) Electromagnetic Wave Propagation
(7) Optics
(8) Radar System Analysis
(9) Random Process Analysis
(16) Economic Data Analysis
(17) Signal Representation
(18) Data Compression
(19) Seismology
(10) Music Signal Analysis
(20) Geology
Wavelet Transform
Laws Texture
Kernel (Windows)
3
What’s Today?
 Study of Classification of Lung Tumor Based on
CT/PET Images
 Technique of studying image ( gray level)
 Training skill of machine learning
Why Image Processing?
 Gray level studying
 DSP, Kernel( window)
 Resolution of image
 4000*3000, 1024*768, 640*480, 320*240
 How about in Biomedical Image?
Why Image Processing?
 The Biomedical Image Today
 CT:

512*512
 PET:
128*128
Why Image Processing?
Brain v.s. Lung Tumors
Outline




Introduction and Back ground
Technique
Experiments
Discussion and Conclusion
Introduction




Introduction and Back ground
Technique
Experiments
Discussion and Conclusion
Introduction
 Lung Tumor
 High Death Ratio
 Nerve-less
Introduction
Image Load
Preprocessing
CoRegistration
Registration
Down / Up sampling ; Wavelet Transform
Classification
Feature
Feature
Extraction
Extraction
Wavelet ; Laws Texture ; Other Methods
ROI
Introduction--Wavelet Transform
 Wavelet Transform:
J. J. Ding, 09月15日上課資料 , P 43
Introduction--Wavelet Transform
Ivan W. Selesnick, Wavelet Transforms, 2007
Introduction--Wavelet Transform
Introduction
y (2 n  1)  c ( n )  d ( n )
Ivan W. Selesnick, Wavelet Transforms, 2007
y (2 n )  c ( n )  d ( n )
Introduction--Wavelet Transform
Ivan W. Selesnick, Wavelet Transforms, 2007
Ivan W. Selesnick, Wavelet Transforms, 2007
Introduction--Wavelet Transform
Introduction--Wavelet Transform
 Wavelet Transform:

Improvement???
Haar !!
Introduction--Wavelet Transform
 Haar Transform:
Introduction--Wavelet Transform
Wavelet Transform
Haar Transform
Introduction--Wavelet Transform
 Wavelet Transform:
J. J. Ding, 09月15日上課資料 , P 46
Introduction--Wavelet Transform
Introduction—Laws Texture
 Laws features
 The texture energy measures developed by
Kenneth Ivan Laws at the University of Southern
California have been used for many diverse
applications. These measures are computed by first
applying small convolution kernels to a digital
image, and then performing a nonlinear windowing
operation.
http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml
Introduction—Laws Texture
 Laws features
 3 element kernel
 5 element kernel
 High order kernel
M.T. Suzuki, Y. Yaginuma, H. Kodama, A Texture Energy Measurement Technique for 3D
Volumetric Data, 2009 IEEE International Conference on Systems
http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml
Introduction—Laws Texture
 Laws features
 3 element kernel
 Level: [1 2 1];
 Edge: [-1 0 1];
 Spot: [-1 2 -1];
M.T. Suzuki, Y. Yaginuma, H. Kodama, A Texture Energy Measurement Technique for 3D
Volumetric Data, 2009 IEEE International Conference on Systems
http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml
Introduction—Laws Texture
 Laws features
Introduction—Laws Texture
 Laws features
 5 element kernel
 L5 = [1, 4, 6, 4, 1];
 E5 = [−1,−2, 0, 2, 1];
 S5 = [−1, 0, 2, 0,−1];
 R5 = [1,−4, 6,−4, 1];
 W5 = [−1, 2, 0,−2, 1];
% ripple
% wave
M.T. Suzuki, Y. Yaginuma, H. Kodama, A Texture Energy Measurement Technique for 3D
Volumetric Data, 2009 IEEE International Conference on Systems
http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml
Introduction—Laws Texture
 Laws features
Introduction—Laws Texture
 Laws features
 Image processing --- 2D case
L5L5
E5L5
S5L5
R5L5
W5L5
L5E5
E5E5
S5E5
R5E5
W5E5
L5S5
E5S5
S5S5
R5S5
W5S5
L5R5 L5W5
E5R5 E5W5
S5R5 S5W5
R5R5 R5W5
W5R5 W5W5
M.T. Suzuki, Y. Yaginuma, H. Kodama, A Texture Energy Measurement Technique for 3D
Volumetric Data, 2009 IEEE International Conference on Systems
http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml
Introduction—Laws Texture
 Laws features
Introduction—Laws Texture
L5L5
S5S5
W5W5
E5E5
R5R5
Introduction-- Background
 CT - computed tomography
 PET - Positron emission tomography
Introduction-- Background
 CT - Computed Tomography
 Digital geometry processing is used to
generate a three-dimensional image of the
inside of an object from a large series of
two-dimensional X-ray images taken
around a single axis of rotation .
 http://translate.google.com/translate?hl=zh-TW&langpair=en|zhTW&u=http://en.wikipedia.org/wiki/X-ray_computed_tomography
Introduction-- Background
 PET - Positron Emission Tomography
 A nuclear medicine imaging technique that produces a three-dimensional image or
picture of functional processes in the body. The system detects pairs of gamma
rays emitted indirectly by a positron-emitting radionuclide (tracer), which is
introduced into the body on a biologically active molecule. Three-dimensional
images of tracer concentration within the body are then constructed by computer
analysis. In modern scanners, three dimensional imaging is often accomplished
with the aid of a CT X-ray scan performed on the patient during the same session,
in the same machine.
 If the biologically active molecule chosen for PET is FDG, an analogue of glucose,
the concentrations of tracer imaged then give tissue metabolic activity, in terms of
regional glucose uptake. Although use of this tracer results in the most common
type of PET scan, other tracer molecules are used in PET to image the tissue
concentration of many other types of
http://en.wikipedia.org/wiki/Positron_Emission_Tomography
Introduction-- Background
 PET - Positron emission tomography
 FDG ( Fludeoxyglucose) :
 氟代脱氧葡萄糖
http://en.wikipedia.org/wiki/Positron_Emission_Tomography
Background
CT
V.S.
PET
Technique




Introduction and Back ground
Technique
Experiments
Discussion and Conclusion
Technique





Feature Extracting – 1 (on CT)
Down sampling (for co-registry)
Overlap CT/PET( Down/Up Sampling)
Feature Extracting – 2 (on PET)
Machine Learning
Background
CT V.S. PET
Technique –
Feature Extracting – 1 (on CT)
 Feature Extracting – 1 (on CT)
 Volume
 Rectangular Fit
 Histogram features
Laws features
Wavelet
：
：
：
Technique –
Feature Extracting – 1 (Wavelet)
2D Case
Energy 
1
MxN
Entropy 
1
MxN
M
N

2
I (i, j )
i 1 j 1
M
N

i 1 j 1
2
I (i , j )
norm
2
2
log(
I (i , j )
norm
2
)
Technique –
Feature Extracting – 1 (Wavelet)
3D Case
Energy 
1
MxNxL
Entropy 
1
MxNxL
M
N
L

i 1
M
j 1 k 1
N
L
(
i 1
2
I (i, j , k )
j 1 k  1
2
I (i , j , k )
norm
2
2
) log(
I (i , j , k )
norm
2
)
Technique –
Feature Extracting – 1 (Laws Texture)
2D Case
Energy 
1
MxN
M
N

i 1 j 1
2
I (i, j )
Technique –
Feature Extracting – 1 (Laws Texture)
3D Case
Energy 
1
MxN
M
N

i 1 j 1
2
I (i, j )
Technique –
Down sampling (for co-registry)
 Down sampling (for co-registry)
Raw Image
Low Pass
(Average)
High Pass 1
(X direction)
High Pass 2
(Y direction)
High Pass 3
(Corner)
Technique –
Down sampling (for co-registry)
 Down sampling (for co-registry)
Raw Image
Low Pass
(Average)
High Pass 1
(X direction)
High Pass 2
(Y direction)
Down-samples Image
High Pass 3
(Corner)
Technique –
Feature Extracting – 2 (on PET)
 Feature Extracting – 2 (on PET)




SUV
Leveled SUV
Largest Region’s SUV
Other probability features
Technique –
Feature Extracting – 2 (on PET)
 Feature Extracting – 2 (on PET)
PAWITRA MASA-AH, SOMPHOB SOONGSATHITANON, A novel Standardized Uptake Value (SUV)
calculation of PET DICOM files using MATLAB, NEW ASPECTS OF APPLIED INFORMATICS, BIOMEDICAL
ELECTRONICS & COMMUNICATIONS
Technique –
Feature Extracting – 2 (on PET)
 Feature Extracting – 2 (on PET)
Tumor
Level 1
Level 2
Level 3
Level 4
Level 5
Sub SUV
Sub SUV
Sub SUV
Sub SUV
Sub SUV
Feature
Feature
Feature
Feature
Feature
Technique –
Machine Learning
 Machine Learning




Logistic
Neural Network
SVM (Support Vector Machine)
J48
Experiments





Introduction
Background
Technique
Experiments
Discussion and Conclusion
Experiments
 Sorry, they are now in America
Discussion and Conclusion





Introduction
Background
Technique
Experiments
Discussion and Conclusion
Discussion and Conclusion
 Discussion:
 Relation between Image Processing, DSP,
and TWD
 Kernel of Image Processing
 Development of Each kernel
Discussion and Conclusion
 Relation between Image Processing, DSP, and TWD
 TWD:
 Analyzing signal with mathematically way, either
enhancement of complexity of equation and reducing the
amount of computation.
 DSP:
 Dealing the signal with discrete time work.
 DIP:
 Take advantage of these two to give us more probabilities
on studying images.
Discussion and Conclusion
 Kernel of Image Processing
 Similar to the window function on short time signal
analysis
 Either Gaussian filter (low pass filtering, averaging)
and edge detection (high pass filtering) are applied
to turn into features
Discussion and Conclusion
 Development of Each kernel
 Low pass filter
 High pass filter
Discussion and Conclusion
 Development of Each kernel
 Low pass filter
 Down sample ( average)
 [1 1]
 Laws texture (level)
 [1 2 1], [1 4 6 4 1]
 Gaussian blur (normal distribution)
 [1 8 12 16 12 8 1]
Discussion and Conclusion
 Development of Each kernel
 High pass filter
 Down sample ( change)
 [1 -1]
 Laws texture (edge, ripple)
 [-1 -2 0 2 1], [1,−4, 6,−4, 1]
 Gaussian Laplace Filter
 Subtract by two Gaussian filter with same mean,
different STD.
Discussion and Conclusion
 Development of Each kernel
 High pass filter
 Down sample ( change)
 [1 -1]
 Laws texture (edge, ripple)
 [-1 -2 0 2 1], [1,−4, 6,−4, 1]
 Gaussian Laplace Filter
 Subtract by two Gaussian filter with same mean,
different STD.
Discussion and Conclusion
 Development of Each kernel
 High pass filter
Discussion and Conclusion
 Development of Each kernel
 High pass filter
Discussion and Conclusion
 Conclusion:
 Image processing is right an example which
implement DSP and TWD.
 Texture Feature give doctors more clues for
diagnosing
 More kinds of kernel provide more feature for
machine learning.