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https://er.chdtu.edu.ua/handle/ChSTU/8357| Title: | Автоматизація виявлення патологій при масовому аналізі рентгенівських знімків |
| Authors: | Трембовецька, Руслана Володимирівна Завальнюк, Віталій Євгенович |
| Keywords: | цифрова обробка медичних зображень;рентгенівські діагностичні зображення;просторова фільтрація;частотна фільтрація;відновлення зображень;MATLAB |
| Issue Date: | 15-Dec-2025 |
| Abstract: | У роботі досліджено методи цифрової обробки рентгенівських діагностичних зображень у середовищі MATLAB з метою автоматичного поліпшення їх якості шляхом просторової та частотної фільтрації й відновлення. The work investigates methods of digital processing of X-ray diagnostic images in MATLAB aimed at automatic quality enhancement through spatial filtering, frequency filtering, and image restoration. |
| URI: | https://er.chdtu.edu.ua/handle/ChSTU/8357 |
| Appears in Collections: | 174 Автоматизація, комп'ютерно-інтегровані технології та робототехніка (Робототехнічні системи та автоматизація) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Диплом-магистр_Завальнюк В.pdf Restricted Access | КРМ Завальнюк В. | 7.37 MB | Adobe PDF | View/Open Request a copy |
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.
:
,
( ). :
,
D0 , ( ) -
.
48
D0 .
,
:
(3.7)
D0 – , ,
H(u, v) = 1 H(u, v) = 0,
; D(u, v) – (u, v) -
. , ' - , D(u, v)
:
(3.8)
m n – .
,
,
( ), . 3.3.
" "
:
, ( D0). ,
- , ,
( ).
, ,
.
49
. 3.3. :
, :
( ),
—
. H(u, v)
,
3600 .
D0
, .
, ( )
PT.
(u,v);u = 0,1,1...M −1;v = 0,1,1...N −1.
(3.9)
P(u, v) :
(3.10)
F(u, v) – ' - f(x, y). r( )
,
, . .:
50
(3.11)
.
.
. 3.4.
« »: )
; )
( \text{sinc}); )
( ); ) ,
' ; )
( ) ( ); )
,
( )
, ,
D0.
.
:
1. (Undersizing D0):
.
51
—
, .
2. (Oversizing D0):
,
. :
,
.
, ,
, ( " ").
' .
: ( )
( ).
.
,
(
' ) \text{sinc}(x)
.
( )
, .
" " , . 3.4.
(intensity profile)
. ,
.
52
, ,
,
.
n
D0 :
(3.12)
. 3.5.
. 3.5.
,
( )
.
- ,
.
53
,
( " "),
.
n :
•
, , , .
• ,
.
(n=2).
( )
.
. 3.6
n ( 1, 2, 5 20.
. 3.6. :
1, 2, 5 20
:
(3.13)
D(u, v) = D0 (D0 – )
0,667 . . 3.7
D0.
54
. 3.7.
D0
, '
. ,
'
, ,
, .
.
,
,
, .
-
.
3.5
, ,
'
' . ,
( ) .
55
(
) .
'
.
H_{HP}(u, v)
H_{LP}(u, v) :
(3.14)
Hlp(u, v) – .
:
, .
:
(3.15)
D0 – , D(u, v) – (u, v)
( ).
. 3. 8
,
.
. 3.8. :
;
;
56
,
, ,
« » , .
.
,
.
H(u, v) :
n, , D_0,
.
, ,
:
(3.16)
. 3. 9
,
,
.
' , .
' .
57
. 3.9. -
, -
, -
,
D , : D2
0 (u,v)
(3.17)
. 3. 10
,
, .
' , .
. 3.10. -
, -
, -
58
3.6 High-boost
, ,
, , ,
,
( ) ' - .
« ».
,
.
.
.
, ,
f(x, y) flp(x, y):
fhp ( x, y ) = f ( x, y ) − flp ( x, y ). (3.18)
,
:
fhp ( x, y) = ⋅ f ( x, y ) − flp ( x, y ). (3.19)
,
.
.
:
Hhfe (u,v) = a + b ⋅ Hhp (u,v) , (3.20)
Hhp (u,v) – .
0, 25 0, 5;
b – 1, 5 2, 5 ( , b > a).
59
b > 1 ,
.
. ,
, .
,
.
3.7 MATLAB
' MATLAB
fft2, :
F = fft2 (f ) , (3.21)
f – , F – ' f(x, y).
:
S = abs (F ) (3.22)
abs ( ) F.
' -
fftshift :
Fc = fftshift2(F ) (3.23)
Fc – ' - .
,
,
.
:
S 2 = log (1+ abs (Fc)) (3.24)
60
' ifft2,
:
f = ifft2 (F ) (3.25)
F – ' , f – .
' -
:
f = real (ifft2(F )) (3.26)
MATLAB
. ( )
:
[name]=X1:dX:Xk (3.27)
name – ' , , X1 -
, Xk - , dX - ,
(
1). - . - ,
:
[name]=[X1:dX:Xk]’ (3.28)
' .
. MATLAB
meshgrid, ,
, .
. meshgrid
:
[X, Y]=meshgrid(x, y) (3.29)
( ).
: X
x, Y — y.
61
:
x = (0,1, 2) , y = (0,1). (3.30)
0 1 2 0 0 0
x = y = ,
0 1 2 1 1 1 (3.31)
,
.
, f (x,
y) :
1) f (x, y) size;
u v,
x y;
2) '
fft2 F (u, v);
3) ( ,
); H (u, v),
,
;
4) G (u, v)
H (u, v) F (u, v);
5) g (x, y)
'
G (u, v) ifft2;
6) ,
real.
62
3
1. ,
' . ,
, — ,
.
2. ( , ,
). ,
« » ( ),
.
3. ,
. ,
,
.
63
4
MATLAB
. ,
' .
, ,
, .
.
, '
.
4.1 /
. 4. 1 /
.
. 4.1. /
f(x,
y) H \eta(x, y),
g(x, y).
\hat{f}(x, y),
.
H \eta.
64
:
(4.1)
h ( x, y ) – ,
.
:
(4.2)
' -
.
4.2
( ), .
,
. , - (
' ) , , ,
.
, ' . ,
.
,
,
.
' -
. , , « ».
,
..
65
,
.
, ,
.
, .
Z. F(Z)
Z , z
, , Z
z, . . F(z) = P(Z<z).
z, F( ) = 0 F(+ ) = 1.
F(z) ,
F(z), p(z) = F (z).
.
,
.
,
( ) , ,
.
z
:
(4.3)
z – , – z, –
z.
. 4. 2 .
66
:
(4.4)
:
(4.5)
. 4. 2 .
( - )
:
(4.6)
a > 0, b – .
:
(4.7)
. 4. 2 .
67
. 4.2.
:
(4.8)
a > 0
:
(4.9)
. 4. 2
. ,
b = 1.
:
(4.10)
:
68
(4.11)
. 4. 2
.
( )
:
(4.12)
b > a, b .
a , , .
(Pa Pb) , .
« ».
,
' . , -
( )
.
, (saturation)
(clipping). , ,
:
• (a): ( '
).
• (b): (
).
«
» .
. 4.2,
69
4.3
,
,
.
, ' ,
' . '
.
.
, , ,
.
:
(4.13)
zi – S, p(zi) –
.
,
.. , ,
,
.
a b,
..
70
4.4
,
:
(4.14)
:
(4.15)
, – η ( x, y ) N (u, v) , ,
g ( x, y ) G (u, v) .
G (u, v) N (u, v) ,
N (u, v)
G (u, v) .
, ,
.
,
. Sxy
- m×n
(x, y).
g(x, y) Sxy.
fˆ(x, y) (x, y)
, Sxy:
(4.16)
,
1/m·n.
, .
71
,
, ,
,
, .
-
.
, ,
. ,
.:
(4.17)
. ,
.
,
– 50- ,
..
100- ,
, , :
(4.18)
.
« » ,
Sxy . 0-
, ,
:
(4.19)
72
.
« »
.
:
(4.20)
.
, - .
4.5
,
(
H). ,
Fˆ(u, v) ' -
' -
( ):
(4.21)
N(u, v),
(x, y), :
(4.22)
, ,
, (
' - F(u, v)), N(u, v)
73
' - . ,
,
H(u, v) ,
,
.
,
, ,
H(u, v)
.
.
, H(0, 0) h(x, y)
H(u, v) . ,
..
-
,
.
4.6
. ,
,
, ,
..
.
, fˆ f,
74
.
e .:
(4.23)
E{·} .
, :
1) ;
2) , ;
3) ' .
,
, .:
(4.24)
G(u,v) ' - ; H(u, v) –
, H*(u, v) – H(u, v); H(u,v)2 =
H*(u,v) H(u,v) – ; S (u,v) = N(u,v)2 –
; S f (u,v) = F(u,v)2 –
.
, . , ,
. ,
, .
, ,
, , H(u, v) S (u, v)
..
' Fˆ(u, v). ,
75
, ,
.
, N(u,v)2 ,
.
.
, ,
.
(4.25)
K – .
.
4.7 MATLAB
MATLAB
imnoise, :
(4.26)
f - , g - , type - , parameters
- .
MATLAB
: doc imnoise.
, imnoise
double [0, 1]. ,
64 400
76
uint8 (8- ), 64/256,
– 400/(256)2.
statmoments,
n :
[v, unv]=statmoments(p, n) (4.27)
p – , n - , v -
,
[0, 1], unv -
.
,
,
fspecial:
(4.28)
w – , m n -
.
medfilt2, : f = medfilt2 (g, [m, n])
g - , m n -
, f - .
,
, :
(4.29)
(4.30)
MATLAB
deconvwnr, :
(4.31)
fr – , g - , PSF -
( ).
77
, /
, .
, / :
fr = deconvwnr (g, PSF, NSPR) (4.32)
, (NACORR)
(FACORR), :
fr = deconvwnr (g, PSF, NACORR, FACORR) (4.33)
-
( ) '
ifft2.
' fft2,
abs .
/ (NSPR)
.
MATLAB
fspecial :
(4.34)
fspecial PSF,
len , theta
.
, PSF,
imfilter :
(4.35)
f - , g - , PSF -
( ), 'Circular'
.
78
4
1. ,
.
' , '
.
2. ( , , )
. , («
»)
( ), .
3.
. , (
)
,
.
79
5
MATLAB
5.1
( 5.1) MATLAB ' cat (
uint8):
.5.1.
IPT:
isbw , : 1, RGB
, 0, .
80
isgray , : 1,
RGB , 0 .
isind , : 1,
RGB , 0 - .
isrgb , : 1,
RGB , 0 ..
.
.
,
( ) ( ).
, .
,
.
81
imhist - :
:
(
5.2)
.5.2.
( 5.3)
82
. 5.3.
improfile -
[r c]=size(M);
N=improfile(M, [1 c], [1 r]);
plot(N),grid ( 5.4).
.5.4.
mean2 - :
m=mean2(cat)
83
m=130.7960
std2 -
:
m1 = std2(cat)
m1 = 41.4871
' cat1
( 5.5):
,
.5.5
:
M1 = rgb2gray (RGB1);
corr2 - :
k=corr2(M,M1)
k =1
imabsdiff -
Z=imabsdiff(cat, cat1);
imshow(Z); ( 5.6)
84
.5.6
imadd -
A=imadd(cat,cat1);
imshow(A); ( 5.7)
.5.7
8) - mean2.
85
avarage = mean2 (m)%
avarage = 130.7960
std2 -
[6].
sko = std2 (m)%
sko = 41.4871
10) .
corr2
, ,
. ' .
, '
, ' , [6].
- ( 5.8, a). ,
, - ,
( 5.8, .).
>> h=fspecial('average', 15); %
M1 = imfilter(cat,h,'replicate'); %
figure, imshow(cat1); %
figure, imshow(cat); %
.5.8. : )
, )
86
:
>> k = 0.9983 %
1, ,
.
11) imabsdiff - .
uint8.
Z = imabsdiff (cat, cat1); %
imshow (Z); % ( 5.9)
. 5.9
,
1.
12) imadd
..
>> A=imadd(M,M1); % 1
87
imshow (A); % ( 5.10)
.5.10.
( + 1).
13) imcomplement - ,
.
RGB
:
,
..
>> M=imcomplement(cat1); %
>> imshow (M)% ( 5.11)
88
.5.11.
:
,
.
14) imsubtract - 1
.
0..
>> A = imsubtract (M, M1); %
imshow (A)% ( 5.12)
.5.12
89
(M1- ).
- .
15) cpstruct2pairs - cpstruct
. Cpstruct
.
Control Point Selection Tool,
:
>> cpselect (M, M1); % ( 5.13)
.5.13 Control Point Selection Tool
cpselect .
, , -
Export Points To Workspace File..
16) cp2tform -
.
Control Point Selection Tool 2 :
>> cpselect(M,M1); %
:
>> J=imrotate(cat, 30); % -
>> cpselect(J, cat, input_points, base_points); %
>> t=cp2tform(input_points, base_points, 'linear conformal') %
90
t = ndims_in: 2
ndims_out: 2
forward_fcn: @fwd_affine
inverse_fcn: @inv_affine
tdata: [1x1 struct]
5.2
MATLAB
.
fspecial ( ), ordfilt2 ( ) medfilt2
( ).
fspecial.
, :
• ( );
• "Laplacian of Gaussian" (LoG),
;
• ( );
• .
,
.
unsharp 0.5.
, (imfilter) 'replicate'
.
% ( )
h = fspecial('unsharp', 0.5);
%
M1 = imfilter(M, h, 'replicate');
%
91
figure, imshow(M1);
.5.14. ,
. ,
,
.
fsamp2
( - ).
- ( ),
H, h.
.
(
) .
• . 5.15, .
• . 5.15, .
92
( ).
. 5.15, [7].
%
[f1, f2] = freqspace(15, 'meshgrid');
% .
%
% ( " " " ").
dist = abs(f1) + abs(f2);
% ( [0, 1])
H = dist / max(dist(:));
% 3D-
mesh(f1, f2, H), colormap(cool(32));
% - 3x3
h = fsamp2(f1, f2, H, [3 3]);
%
figure, colormap(cool(32)), freqz2(h);
%
double
i = mat2gray(filter2(h, im2double(M)));
% ( [0, 0.8] [0, 1])
M = imadjust(M, [0 0.8], []);
% ( . 5.15, )
figure, imshow(M);
93
. 5.15.
: ) ( ) - ;
) - ; )
.
.
,
( ).
3) (McClellan transformation)
h = ftrans2(b)
- . ,
- b
h.
( ). :
1. - 16-
0.2\pi. ( )
. 5.16, .
94
2.
ftrans2.
. 5.16, .
. 5.16, .
. 5.16.
: ) ( )
- ; ) -
; )
.
.
4) roifilt2 -
.
5) B=imfilter(A, H) - A
H ( 5.17).
>> h=fspecial('motion', 50, 45); %
rgb2=imfilter(M, h); %
figure, imshow(rgb2), title('Filtered'); %
95
.5.17. ,
imfilter
,
.
, ,
.
, ,
( / ).
, ,
.
,
, " "
.
.
. ,
. '
:
>> I1=imnoise(M, 'gaussian', 0, 0.01); %
figure,imshow(I1) % ( 5.18)
96
.5.18.
,
. ,
.
1.
MATLAB
wiener2.
(AWGN).
:
,
.
( )
( ) N ×M .»
>> Id=wiener2(I1, [10 10]); %
imshow (Id)%
97
5.3
>> L=watershed(gradmag); %
Lrgb=label2rgb(L); % RGB-
figure, imshow(Lrgb), title('Lrgb') % (
5.19)
.5.19.
,
,
( ) .
(Foreground markers extraction).
,
. «
» (Opening-by-Reconstruction) « »
(Closing-by-Reconstruction).
.
' ,
imregionalmax.
98
5.4
MATLAB,
( , ),
histeq, imadjust
imfilter ( fspecial).
)
( ) . MATLAB
histeq.
.
,
( , ).
(grayscale), ( )
, " "
[6, 7].
>> figure, imhist(M); % (
5.20, )
I=histeq(M, 80); %
figure, imshow(I); % (
5.20, )
figure, imhist(I); % (
5.20, )
99
.5.20. :
) , )
,
.
:
( " "
),
. " "
, .
)
( ),
.
( - )
MATLAB imadjust [6, 7].
>> figure, imhist(M); % (
41, )
I=imadjust(M, [0 75]/255, [ ], 1); %
figure, imshow(I); % (
5.21, )
100
figure, imhist(I); % (
5.21, )
.5.21. - :
) )
( -
)
.
. ,
( ):
.
. , Adjust Contrast tool
.
(Windowing/Leveling),
.
101
. 5.22. Adjust Contrast tool
5
1.
MATLAB.
'
.
2. ,
(wiener2)
,
, .
3. .
,
, -
,
.
4. ,
.
102
, ,
'
103
, ,
' .
,
.
,
.
.
.
,
. ,
.
-
' , ( , ' ,
) .
.
MATLAB
, .
: ,
.
:
. ,
,
,
, .
104
1.
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