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# P1161211140

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### P1161211140

1. 1. Works plan  - Introduction  - Principal of « Gauss blur » filter  - Mathematic expression for three techniques (t-f- z) test.  -Algorithm  Results  Conclusion and perspective
2. 2. Works plan  - Principal of « Gauss blur » filter  - Mathématic expression for three techniques (t-f- z) test.  -Algorithm  The results  Conclusion & perspective Introduction
3. 3. 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.
4. 4. 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?
5. 5. Works plan - Introduction - -Mathématic expression for three techniques (t-f-z) test. -Algorithm The results Conclusion & perspective Principal of « Gauss blur » filter
6. 6. - 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
7. 7. 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.
8. 8. Works plan  Introduction  - Principal of « Gauss blur » filter   -Algorithm  The results  Conclusion & perspective mathematic expression for three techniques (t-f-z) test
9. 9.                 +                 ×                 =                 nmnn m pmpp m npnn p nmnn m eee e ee eee xxx x xx xxx yyy y yy yyy             21 31 2221 11211 21 31 2221 11211 21 31 2221 11211 21 31 2221 11211 ............................ βββ β ββ βββ Estimate β by least square method STATISTIC STUDING FOR LINEAR MODEL 1. Simple Linear Regression
10. 10. ])([ 2^ 1 2 YYS N j j T −=== ∑ = ∧∧ εεε 2 1 1 ∑ ∑= ∧ =                 −= N i M j jii jXYS β S is less, for all m : 0.).(2 1 1 =         −−= ∂ ∂ ∑ ∑= = ∧ ∧ N i M j jiimi jxYx m S β β - Minimise quadratic error(by least square) between data : ... Linear matrix εβ += XY . la différence between reel data & estimated data : YY ∧∧ −=ε .
11. 11. 1-2 estimateβ YXXX TT YX ..).( 1 .ˆˆ − =+ =β Where : « + » pseudo-inverse design byMOORE–PENROSE, ( ) ( ) 12 12 ' '')ˆ'( ˆ ˆ − − =         =         = XXcVar XXcVarccVar T T σ σβ β β pM X pM s pM T − ≈ − = = − 2 22 ˆ σ εε σ ( ) β ∧ = ... XXY T T XWhere ( )j M j ji N i mii N i mi xxYx β ∧ === ∑∑∑ = . 111 - Variance estimation P: nomber of parameter M: Nber of observation(scans) M-P : Freedom
12. 12. ⋅⋅⋅⋅⋅ ⋅ == + ∧ CxxC C estimateiance aramterestimatedpcontrast t T )(' ' var 2 σ β * 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
13. 13. Works plan  - Introduction  - Principal of « Gauss blur » filter  -Mathematic expression for three techniques (t-f-z) test.  The results  Conclusion & perspective Algorithm
14. 14. 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.
15. 15. Works plan  - Introduction  - Introduction  - Principal of « gauss blur « filter  - Mathematic expression for three techniques (t-f- z) test.  -Algorithm   Conclusion & perspective The results
16. 16. 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
17. 17. 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 50 100 150 0 50 100 150 0 50 100 150 50 100 150 50 100 150 (X1-X2)=fwhm=8mm Fmri image filtre of image 5 10 15 20 0 0.2 0.4 0.6 0.8 1 183*183 Reel Image of brain with png format . 50 100 150 50 100 150 200 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 50 100 150 50 100 150 200
18. 18. 35X35 10 20 30 10 20 30 0 10 20 30 0 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 -2.5 -2 -1.5 -1 -0.5 0 0.5 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
19. 19. -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 20 40 60 80 20 40 60 80 0 20 40 60 80 0 20 40 60 80 -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>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 -6 -4 -2 0 2 4 6 8 10 12 x 10 -3 t:blue z:green f:red 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80
20. 20. 20 40 60 80 100 20 40 60 80 100 0 50 100 0 20 40 60 80 100 -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>1.981 Prob = 0.025 zone accepte H0 zone de rejet H0 115X115 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 0 20 40 60 80 100 120 -2 -1 0 1 2 3 4 5 6 7 x 10 -3
21. 21. 50 100 150 50 100 150 0 50 100 150 0 50 100 150 -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>1.976 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 -6 -4 -2 0 2 4 6 x 10 -3 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150
22. 22. 50 100 150 50 100 150 0 50 100 150 0 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 160X160 0 20 40 60 80 100 120 140 160 -2 -1 0 1 2 3 4 5 6 x 10 -3 t:blue z:green f:red
23. 23. 50 100 150 50 100 150 0 50 100 150 0 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 -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>1.973 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 4 x 10 -3 t:blue z:green f:red
24. 24. 50 100 150 200 50 100 150 200 0 50 100 150 200 0 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 240X240 -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 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
25. 25. 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 160X160 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 155X155 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 190X190 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150 50 100 150
26. 26. 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 145X145 115X115 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100
27. 27. 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 90X90 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 50X50 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 35X35 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50
28. 28. Works plan  - Introduction  - Principal of « Gauss blur » filter  - Mathematic expression for three techniques (t-f- z) test.  -Algorithm  The results Conclusion & perspective
29. 29. 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