2. Works plan
 - Introduction
 - Principal of « Gauss blur » filter
 - Mathematic expression for three techniques (t-f-
z) test.
 -Algorithm
 Results
 Conclusion and perspective

3. Works plan
 - Principal of « Gauss blur » filter
 - Mathématic expression for three techniques (t-f-
z) test.
 -Algorithm
 The results
 Conclusion & perspective
Introduction

4. Bokeh (derived from japenese, noun boke, meaning "blur" ) is a photographic term
referring to the aesthetic quality of the out-of-focus areas of an image produced by
a camera lens using a shallow depth of field.
- A Gaussian blur is the result of blurring an image by a Gaussian function . It is a
widely used effect in graphics software, typically to reduce image noise and reduce
detail.
- Mathematically, applying a Gaussian blur has the effect of reducing the image's
high-frequency components ;a Gaussian blur is thus a low pass filter .
INTRODUCTION
Bokeh image.

5. The problematic : what's the main of gauss
blur filter? Which technique (t, f or z)-
test is more precise ? With or without
gauss blur, the results are more precise?

6. Works plan
- Introduction
-
-Mathématic expression for three techniques (t-f-z)
test.
-Algorithm
The results
Conclusion & perspective
Principal of « Gauss blur » filter

7. - The Gaussian blur is a type of image-blurring filter that uses a Gaussian function (which is also used for the
normal distribution in statistics) for calculating the transformation to apply to each pixel in the image.
- In two dimensions, it is the product of two such Gaussians, one per direction:
- Relation between variance & fwhm(full width at half maximum) :
fwhm=2.35482* σ
Principal of GAUSS BLUR

8. 20 40 60 80
20
40
60
80
20 40 60 80
20
40
60
80
Original image Image blurred using Gaussian blur with σ = 5.
Exemples
Original image Image blurred using
Gaussian blur with σ = 2.

9. Works plan
 Introduction
 - Principal of « Gauss blur » filter

 -Algorithm
 The results
 Conclusion & perspective
mathematic expression for three techniques (t-f-z) test

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............................
βββ
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Estimate β by least square method
STATISTIC STUDING FOR LINEAR MODEL
1. Simple Linear Regression

11. ])([ 2^
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- Minimise quadratic error(by least square) between data :
...
Linear matrix εβ += XY
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la différence between reel data & estimated data :
YY
∧∧
−=ε
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12. 1-2 estimateβ
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Where : « + » pseudo-inverse design byMOORE–PENROSE,
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P: nomber of parameter
M: Nber of observation(scans)
M-P : Freedom

13. ⋅⋅⋅⋅⋅
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* F-FISHER Expression:
DETECTION ACTIVITIES OF ( t & f -test et z test ) equations with ho hypothesis
.
*
statistic form with t-test :
n-m = df=M-P
R2
: variation of data base Y
F: random variable of Fisher-Snedecor with m+1 & n-m degree of freedom.
:mean of sample x
sampleoflongth:n
sampleofvariance:σ
lemeanofsamp:µ
*Equation of Z-test

14. Works plan
 - Introduction
 - Principal of « Gauss blur » filter
 -Mathematic expression for three techniques (t-f-z)
test.
 The results
 Conclusion & perspective
Algorithm

15. 7-comparaison between graphic results with or without gauss blur & directly on the
pathologic image.
ALGORITHM
1. A picture MRI must be converted by software (DICOM) from "jpg" has to
authorize the language "Matlab" to read.
2. Identification of a sample image by the application of doctor.
3. Filtrate image obtained using gauss blur (convolution between the image and
the real function gauss).
4. Application of the method of Student-t, f-fisher and z- test to see if there is a
significant difference between samples.
5. Comparison between techniques t-test, f-test and z-test to determine which
technique is more accurate and graphically on the pathologic directly.
6. Comparison between a best result with filter or without it.

16. Works plan
 - Introduction
 - Introduction
 - Principal of « gauss blur « filter
 - Mathematic expression for three techniques (t-f-
z) test.
 -Algorithm

 Conclusion & perspective
The results

17. Our protocol is for a patient with age 46 years who would
feel vomiting and fainting jet, he didn't accept medical
treatment. The patient is made a scanner MRI with
injection of contrast. The machine used radiography with
type "Siemens", and with the field b = 1.5tesla. The
sequences applied in T1 and T2. The results obtained
show us: an attendance tumor in
frontal with three structures :
calcifications eparses, cystic and fleshy .
So presence of a cyst-like extra- cerebral mass effect on
the cortex.
protocol done : 25/03/2010
Analyse data of protocol
RESULTS
Frontal
occipital
parietal
temporal
parietal

18. Image pathologic with jpg format
Normal Image
Plot l’expression
de gauss
MRI filter with gauss blur for surface
183*183
Exemples: Filtrer of IRM & fMRI images with expression of gauss blur for σ=3
50 100 150
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150
0 50 100 150
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(X1-X2)=fwhm=8mm
Fmri image
filtre of image
5 10 15 20
0
0.2
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0.6
0.8
1
183*183
Reel Image of brain with png
format .
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0 5 10 15 20
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1
50 100 150
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19. 35X35
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-2.5
-2
-1.5
-1
-0.5
0
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1
x 10
-3
t:blue
z:green
f:red
-3 -2 -1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distribution of (t & f) statistic, N
t&f
Density
Reject if t&f>2.035
Prob = 0.025
zone accepte H0
zone de rejet H0
F-test
Z-test
T-test

20. -2 -1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distribution of (t & f) statistic, N
t&f
Density
Reject if t&f>1.987
Prob = 0.025
zone accepte H0
zone de rejet H0
90X90
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0 20 40 60 80
0
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-2 -1 0 1 2 3 4 5
0
0.05
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0.15
0.2
0.25
0.3
0.35
0.4
Distribution of z statistic, N
z
Density
Reject if z>1.999
Prob = 0.025
zone accepte H0
zone de rejet H0
f
z
t
0 10 20 30 40 50 60 70 80 90
-8
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-4
-2
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12
x 10
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t:blue
z:green
f:red
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21. 20 40 60 80 100
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Distribution of (t & f) statistic, N
t&f
Density
Reject if t&f>1.981
Prob = 0.025
zone accepte H0
zone de rejet H0
115X115
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40
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Distribution of (t & f) statistic, N
t&f
Density
Reject if t&f>1.976
Prob = 0.025
zone accepte H0
zone de rejet H0
-3 -2 -1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distribution of z statistic, N
z
Density
Reject if z>2.008
Prob = 0.025
zone accepte H0
zone de rejet H0
155X155
0 20 40 60 80 100 120 140 160
-8
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160X160
0 20 40 60 80 100 120 140 160
-2
-1
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x 10
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t:blue
z:green
f:red

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Distribution of (t & f) statistic, N
t&f
Density
Reject if t&f>1.973
Prob = 0.025
zone accepte H0
zone de rejet H0
-3 -2 -1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distribution of z statistic, N
z
Density
Reject if z>2.074
Prob = 0.025
zone accepte H0
zone de rejet H0
190X190
0 20 40 60 80 100 120 140 160 180 200
-10
-8
-6
-4
-2
0
2
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x 10
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t:blue
z:green
f:red

25. 50 100 150 200
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240X240
-3 -2 -1 0 1 2 3 4 5
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0.05
0.1
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0.2
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Distribution of z statistic, N
z
Density
Reject if z>2
Prob = 0.025
zone accepte H0
zone de rejet H0
-2 -1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distribution of t statistic, N
t
Density
Reject if t>1.97
Prob = 0.025
zone accepte H0
zone de rejet H0

26. 50 100 150
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155X155
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27. 20 40 60 80 100 120 140
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145X145
115X115
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28. 20 40 60 80
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29. Works plan
 - Introduction
 - Principal of « Gauss blur » filter
 - Mathematic expression for three techniques (t-f-
z) test.
 -Algorithm
 The results
Conclusion & perspective

30. From these studies we can distinct:
-To have a precise result we must use the filter spatial with gauss blur.
-From the three techniques we distinct that t & f are applied for little &
middle matrix and z-test is applied for big matrix as the demonstration
of theory study.
-Our study is applied for comparison between two models a new and
old one in different specialty.
-To be sure by your results, we proposed to pass by the three
techniques (t,f&z) in every scan.
CONCLUSION & PERSPECTIVE