DIP_review_2_3

DIP_review_2_3 - Color image processing & Morphological image processing

1. Color image processing

1.1 Standard color spaces

1.1.1 RGB

• Blue
• Red
• Green
• 主要用于自身发光

1.1.2 CMYK

$\left[\begin{matrix}C \\M \\Y\end{matrix}\right] = \left[\begin{matrix}1 \\1 \\1\end{matrix}\right] - \left[\begin{matrix}R \\G \\B\end{matrix}\right]$

• Cyan = White – Red
• Magenta = White – Green
• Yellow = White – Blue
• Black = White – Red - Green - Blue
• 主要用于自身不发光，在照明条件下，吸收之后，反射的光谱
• 

1.1.3 HSI/HSV

• HSI
  • 将RGB color model以对角线投影到2D平面，再将正六边形拉成圆形
    • 
  • Hue 色调 主要是哪种颜色(波长determine)
  • Saturation 饱和度 颜色的纯度，即混有多少白光
  • Intensity/Lightness $I = \frac{r+g+b}{3}$
  • 
• HSV
  • Hue 色调 主要是哪种颜色(波长determine)
  • Saturation 饱和度 颜色的纯度，即混有多少白光
  • Value $v = max(r+g+b)$
  • 

1.2 Transform between color spaces

1.2.1 RGB to gray scale

• 1. Maximum value: $g_R(x,y) = g_G(x,y) = g_B(x,y) = max[f_R,f_G,f_B]$
• 2. Average value: $g_R(x,y) = g_G(x,y) = g_B(x,y) = [f_R+f_G+f_B]/3$
• 3. Weighted value: $g_R(x,y) = g_G(x,y) = g_B(x,y) = 0.299f_R+0.587f_G+0.114f_B$

1.2.2 RGB to CMYK

$\left[\begin{matrix}g_R \\g_G \\g_B\end{matrix}\right] = \left[\begin{matrix}255 \\255 \\255\end{matrix}\right] - \left[\begin{matrix}f_R \\f_G \\f_B\end{matrix}\right]$

1.2.3 RGB to HSI

• 

1.2.4 HSI to RGB

• 

1.3 Color balance

1.3.1 White balance

• step 1 $I = 0.299f_R+0.587f_G+0.114f_B$
• step 2 $k_R = \frac{\overline{I}}{\overline{f_R}}$, $k_G = \frac{\overline{I}}{\overline{f_G}}$, $k_B = \frac{\overline{I}}{\overline{f_B}}$
• step 3

  $\left[\begin{matrix}g_R \\g_G \\g_B\end{matrix}\right] = \left[\begin{matrix}k_R& & \\ & k_G& \\ & &k_B\end{matrix}\right] \left[\begin{matrix}f_R \\f_G \\f_B\end{matrix}\right]$

1.3.2 Max value balance

• step 1 $S_{RGB} = min[R_{max},G_{max},B_{max}]$
• step 2 在每个channel中计算 $> S_{RGB}$ 的intensity的数目. $N_{max} = max[N_R,N_G,N_B]$
• step 3 在每个channel中从大往小找到$N_{max^{th}}$的intensity得到 $[T_R,T_G,T_B]$
• step 4 $k_R = \frac{S_{RGB}}{T_R}$, $k_G = \frac{S_{RGB}}{T_G}$, $k_B = \frac{S_{RGB}}{T_B}$
• step 5

  $\left[\begin{matrix}g_R \\g_G \\g_B\end{matrix}\right] = \left[\begin{matrix}k_R& & \\ & k_G& \\ & &k_B\end{matrix}\right] \left[\begin{matrix}f_R \\f_G \\f_B\end{matrix}\right]$

2. Morphological image processing

• key point: SE(Structuring element, 与kernel十分类似)
  • def: small sets or sub-images used to probe an image under study for properties of interest.
  • Selection
    • Simpler than the image
    • With boundary
    • Convex
  • Structures
    • Origin
    • Rectangular
      

2.1 Morphological Operation

2.1.1 Erosion 腐蚀

• $A⊖B = \{z| (B)_z \subseteq A\}$, 其中$B$表示结构元集合，$z$表示结构元的origin
• 结构元要全部与图像重合，否则不进行erosion操作！！！
  
  

2.1.2 Dilation 膨胀

• $A⨁B = \{z|\hat{B_z}\cap A \subseteq A\}$
• 结构元至少有一个element与图像重合，否则不进行Dilation操作
  

2.1.3 Opening

• $𝐴 ∘ 𝐵 = (𝐴 ⊖ 𝐵) ⊕ 𝐵$
• Effect:
  • Smooth the contour of an object
  • Break narrow bridges
  • Eliminate thin structures
    

2.1.4 Closing

• $𝐴 • 𝐵 = (𝐴 ⊕ 𝐵) ⊖ 𝐵$
• Effect:
  • Smooth the contour of an object
  • Fuse narrow breaks and long thin gulfs
  • Eliminate small holes
  • Fill gaps in the contour
    
    
  • step 1 首先利用erode来消除背景的小的噪声点
  • step 2 再利用dilation来恢复变细的指纹纹路(此步骤也会恢复一部分背景噪声点)
  • step 3 此时指纹纹路中会有孔洞，做dilation来填充孔洞
  • step 4 恢复纹路大小，做erode

2.2.5 Hit - or - Miss Transform

2.2.6 Boundary extraction

• 𝛽 (𝐴) = 𝐴 − (𝐴 ⊖ 𝐵) 提取内边界 Inner border
• 𝛽 (𝐴) = (𝐴 ⊕ 𝐵) -A 提取外边界 Outer border

2.2.7 Hole filling