[CV] 1. Image Processing

Week 1-2. Image Processing 1

1. Image formation

• Pinhole camera
• Digital transformation: Sampling, Quantizing
  function f: R$^2$ -> R
• RGB color model
• HSV color model: Hue, Saturation, Value/brightness V

2. Image Processing

f -> g = T(f)
Point Operation
depends on only the corresponding input pixel value

• Linear operations

• Gamma correction

• Scene dissolve
  (e.g., k=2)

• Histogram
  how often each (grayscale) value in the range [0, L-1] appears in the image
  understand contrast, brightness, intensity distribution

• Histogram equalization
  flattens the histogram
  Enhances image quality by expanding the dynamic range of intensities
  intensity: 강도
  use cumulative histogram as the mapping function
  $\displaystyle l_{out} = T(l_{in}) = round(c(l_{in}) \times (L-1))\ where\ c(l_{in}) = \sum^{l_{in}}_{l=0}\hat{h}(l)$
  수식 외우기
  ex) 원래 gray level의 빈도수(히스토그램 값)의 누적합(앞 픽셀 값 다 더함) 구함, 누적합 최종 결과 360, gray level 총 갯수 15개
  누적합 x 15/360, 정규화하고 반올림
  원래 빈도수와 비교하면 균등하게 분포됨

• Binarization (Thresholding)

• Otsu's algorithm
  binarization is better when higher homogeneity <- lower variance

• Otsu's algorithm (efficient version)

• operations

Week 2-1. Image Processing 2

Neighborhood Operations

1. Convolution
Integral of the product of the two functions after one is reversed and shifted
dummy variable $\tau$
$\displaystyle h(t) = \int^{\infin}_{-\infin}f(\tau)g(t - \tau)d\tau,\ h = f * g$
convolution of f and g:
reflect one of the function g -> g(t - $\tau$)
slide t from $-\infin to \infin$
two function intersect, find the integral of their product

• Properties of Convolution
  f(x) -> g(x) 이면 f(x-a) -> g(x-a)임

• Convolution: Impulse Response
  f, delta($\delta$) 곱한 적분은 f(0)
  g(x)는 $f(\tau), \delta(x-\tau)$ 곱한거 적분이자 f(x)

• Discrete Convolution
  Images are discrete and finite 불연속
  kernel/filter/mask 수평, 수직 방향으로 flip
  kernel value 각각 곱하기
  f(x,y) -> h(x,y) -> g(x,y)
  $\displaystyle g(x,y) = \sum^m_{i=-m}\sum^n_{j=-n}f(x-i, y-j)h(i,j)$
• Border problem
  Pad with constant values, reflection

2. Cross-Correlation
locate the template 본뜬 판 두기
(f - t)$^2$ 합 E 최소화
t*f 합 R 최대화

• Normalized Correlation

+Convolution, Cross-Correlation 구분 안해도 됨

• Convolution is a Generic Function
  Separable linear filter: $K = vh^T$
  O(k$^2$) -> O(2k) 1차원 수평, 1차원 수직 convolution

3. Gaussian Smoothing
Gaussian kernel
$\displaystyle h(i,j) = \frac{1}{2\pi\sigma^2}e^{-\frac{1}{2}(\frac{i^2 + j^2}{\sigma^2})}$
$\displaystyle g(i,j) = \frac{1}{2\pi\sigma^2}\sum_{m=1}\sum_{n=1}e^{-\frac{1}{2}(\frac{m^2 + n^2}{\sigma^2})}f(i-m,j-n)$
$\displaystyle =\frac{1}{2\pi\sigma^2}\sum_{m=1}e^{-\frac{1m^2 }{2\sigma^2}}\sum_{n=1}e^{-\frac{1n^2 }{2\sigma^2}}f(i-m,j-n)$
-> Use two 1D Gaussian filters, horizontally and then vertically
Repeated averaging, Gaussian smoothing 비슷함

4. Median Filter
Smoothing is averaging: Blurs edges, sensitive to oufliers
-> Median filtering: 해결책
Sort k$^2$ values around the pixel
Select middle value(median)
Non-linear(no convolution)

Salt and pepper noise- median filter
Gaussian noise- Gaussian filter