Nghiên cứu một số kỹ thuật nội suy ảnh

HỌC VIỆN CÔNG NGHỆ BƯU CHÍNH VIỄN THÔNG







NGUYỄN VĂN HẠT



NGHIÊN CỨU MỘT SỐ KỸ THUẬT NỘI SUY ẢNH

Chuyên ngành: Truyền dữ liệu và Mạng máy tính
Mã số: 60.48.15

Người hướng dẫn khoa học: PGS. TS ĐỖ NĂNG TOÀN


TÓM TẮT LUẬN VĂN THẠC SĨ KỸ THUẬT




HÀ NỘI – 2012


1
PHẦN MỞ ĐẦU
             


 
  











: Nghiên cứu một
số kỹ thuật nội suy ảnh 
 
 
Mục đích của đề tài
, 
   , 
 

.


 
 

2

 1: 
 

 


 





















3
CHƢƠNG 1: KHI QUT VỀ X L NH V NI SUY NH

1.1 Khi qut về x l ảnh





 . 


















.

Hình 1.1 Qu trình x l ảnh





















:















  




,   











.


























. .






 , 





, . 

.

 


. 















:







Hình 1.2 Cc bƣớc cơ bản trong một hệ thống x l ảnh






























4

1.2 Những vấn đề cơ bản trong x l ảnh
1.2.1 Ảnh và điểm ảnh



               

1.2.2 Độ Phân giải của ảnh
Định nghĩa: 

1.2.3 Mức xám của ảnh






1.2.4 Nắn chỉnh biến dạng



 





 

5







Hình 1.3 Ví dụ về nắn chỉnh hình biến dạng

 

1.2.5 Các kiểu ảnh
a. Ảnh chỉ số



b. Ảnh cường độ


c. Ảnh nhi phân


d. Ảnh RGB
 


6
1.2.6 Quan hệ giữa các điểm ảnh





1.2.7 Một số thuộc tính của ảnh
a. Đường viền: 

b. Biên ảnh: 

1.2.8 Toạ độ ảnh
a. Toạ độ pixel



b. Toạ độ không gian


1.3 Nội suy ảnh
1.3.1 Khái niệm nội suy ảnh





 
 




7





1.3.2 Các vấn đề với nội suy ảnh




.
1.3.2.1 
     

1.3.2.2 





1.3.2.3 




1.3.2.4 






8

1.3.2.5 


 



Ảnh ban đầu




15 

.
1.3.3 Một số hướng tiếp cận nội suy ảnh


               
C
 

Sau nội suy
Thay đổi kích cỡ

Bóp méo

9
CHƢƠNG 2: MT SỐ KỸ THUẬT NI SUY NH













p







2.1 Nội suy ảnh dựa vào cc điểm lng giềng
2.1.1 Khái quát nội suy ảnh dựa vào các điểm láng giềng
   


.
2.1.2 Phương pháp nội suy ảnh dựa vào các điểm láng giềng
P


10
t 



. 




 



. M
. M
 
, 
 
2.1.2.1    

     
cao   ban .   chung,
       cao  .
      
        
   nhi    ).
Trong  l       cong,
      
     .
P    4
  trong      

11
thu     , 
  .      
s  xung quanh   .
2.1.2.2 N   hai
     
pixel i, j)     (,
2j)       
.   
Bước 1    
2.1.A)   trung  
Bước 2:      2.1.B)
 ,  trung  
 4 ).

Hình 2.1 Hai bƣớc nội suy dựa vào cấu hình của bốn nƣớc lng giềng
        
      

  . C    
     .
P  ,    
         
           FCBI (Fast Curvature Based
Interpolation).       qua 
      hai   

12
 sung  .    
 ICBI (Iterative Curvature Based Interpolation) 

2.1.2.3 N FCBI
    , 
thay  c          
     , ta     
trong    hai    
 i sinh 
    
  . Ta    
  khi     ,  
hai    .


Hình 2.2 Nội suy dựa trên một khu phố 12-pixel
 thu   nhanh   
   . ta     
        
       .

13
2.1.2.4  ICBI
     
  cho    
   (2i + 1; 2j + 1).
Sau khi   hai   (   
),      , 
       
 o.
2.1.2.5  NN(Natural Neighbor Interpolation)
 m (DEM)      
.  NNI (Natural Neighbor
Interpolation)   DEM  
   . M (DEM)  
   qua DEM . K  
 , (  .
a. Sơ đồ Voronoi của nội suy láng giềng tự nhiên
 
Ta ,
v 
2
 {p
1
p
n

 Vor
S
 S.
b. Phương pháp nội suy láng giềng tự nhiên

g       
. NNI    2D.    
 , cho  truy  q trong 
gian R
2
,     S trong R
2
  
 q. Sau ,     q :
v (q)  w
p
v(p) (2.14)



Wp   , v    (
   ). DEM  NNI 

14
 a .   
Voronoi i         
hai   Voronoi       DEM.
c. Cột chuyển nhượng nội suy láng giềng tự nhiên
T   song song
.  
 
 ,


d. Xây dựng lưới DEM nội suy láng giềng tự nhiên

 DEM       cho 
. Q     l .  
 DEM,  ta  xem   
. N NO_DATA". Thay  
     ,  
,   trong   .
Kết luận nội suy láng riềng tự nhiên
     , 
      
    p       
   , 
        
 (2i, 2j)       (2i +1, 2j+1) 
FCBI    cho  khi     
       
  FCBI p   4  
 .      to .

15
  DEM , h  bao  
   ,   NNI 
 NNI DEM .
2.2 Nội suy tuyến tính (Linear interpolation)
  
 
      
 
. 



(linear interpolation).
2.2.1 Nội suy theo phương pháp lặp



2.2.2 Thuật toán nội suy tuyến tính


 

2.2.3 Nội suy tuyến tính hàm bậc nhất
      .
, (x[1], y[1](x[2], y[2])  x[1] < x[2], ta suy ra 
  .

2

1
(2.21)
2.2.4 Nội suy tuyến tính hàm bậc hai
  ng     
.      hai  5 .


16
K (x
1
[k]
,x
2

[k]
) y
[k]
1 (1,1) 2
2 (2,3) 2
3 (2,5) 5
4 (4,2) 1
5 (5,5) 6
5    .
   R
2


1
,x
2

6
x
1
x
2

5
x
2
1

4
x

2
2

3
x
1

2
x
2

1
(2.25)
(2.25)  
j
   (x
[k]
,x
[k]
)    
  6 .
2.2.5 Nội suy tuyến tính giữa hai đường
   y ( 
      quan   x . 
   :
Y(x,z) = a(z)x + b(z) (2.35)
Cho   a(zb(z),  
   "y   x.
Kết luận nội suy tuyến tính
   


c
 

2.3 Nội suy s dụng hàm cơ sở bn kính
RBF      
d   p  c.     tham
        . 
 RBF   t  ,  cho 
RBF  .

17
2.3.1 Khái quát về hàm cơ sở bán kính RBF
    
 ta      
 t.

s
 R      
  R 

)()( rX


(2.47)

xr 

V  R
s,

 Euclide

N
||X
1
|| = ||X
2
||  (X
1
) = (X
2
), X
1
, X
2
 R
S
(2.48)

2.3.2 Các thuộc tính của hàm cơ sở bán kính RBF
   Euclide  quay, 
).   RBF 
h  Euclide,     
khi  Euclide     do
 2  . theo     
 mong  .
2.3.3 Nội suy sử dụng hàm bán kính cơ sở RBF
     

       


 



N
k
kkf
xxCxP
1
2
)(

, x  R
S
(2.60)



18
   p

(x
i
) = f(x
i
), i= 1, . . ., N, 
 c

k

     
     
     











































)x(f
)x(f
)x(f
C
C
C
xxxxxx
xxxxxx
xxxxxx
N
2
1
N

2
1
2
NN
2
2N
2
1N
2
N2
2
22
2
12
2
N1
2
21
2
11





(2.61)
2.3.4 Phép nội suy thời gian và bù chuyển động





.
Kết luận nội suy sử dụng hàm cơ sở bán kính RBF
 






19
CHƢƠNG 3: CHƢƠNG TRÌNH TH NGHIỆM
3.1 Bài ton








 Đầu vào 

 Đầu ra

3.2 Phân tích bài ton

 

 


    




.







20
3.3 Chƣơng trình biểu diễn trạng thi cơ bản của khuôn mặt


Hình 3.1 Ca sổ ban đầu của phần mềm biểu diễn trạng thi khuôn mặt 3D

                


Hình 3.2 Khung hình khuôn mặt nhìn nghiêng

21


Hình 3.3 Trạng thi ngạc nhiên của khuôn mặt


:

Hình 3.4 Trạng thi mỉm cƣời của khuôn mặt

              
,l   


22



23

KẾT LUẬN








''Nghiên cứu một
số kỹ thuật nội suy ảnh'' 
.
V
 .
 .

 
.