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5. Homogeneous Point Processing. 3 가지 image processing operations * in A simplified approach to image processing , by Randy Crane. Point processing Modifies a pixel’s value based on that pixel’s original value or position Chapter 4 Area processing

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5 homogeneous point processing
5. Homogeneous Point Processing
  • 3가지 image processing operations

* in A simplified approach to image processing, by Randy Crane.

    • Point processing
      • Modifies a pixel’s value based on that pixel’s original value or position
      • Chapter 4
    • Area processing
      • Modifies a pixel’s value based on its original value and the values of neighboring pixels
      • Chapters 8-11
    • Geometric processing
      • Changes the position or arrangement of the pixels
      • Chapters 14
    • Frame processing
      • Generates pixle values based on operations on two or more images
h omogeneous point processing
Homogeneous point processing
  • Image quality (qualitative) 용어들
    • washed out (smeared, blurred)
    • brighter
    • Contrast
    • ….
  • Processing 목적
    • Noise suppression
    • Enhancement 등
histograms
Histograms
  • Histogram
    • Color image matching & retrieval 응용
    • Pixel value reduction 등의 많은 응용
    • PMF(Probability Mass Function)
      • 식 4.1 ~ 4.3
    • 예) 0~255사이 값을 갖는 64개 pixel
      • 0값 32개, 128값 16개, 255값 16개 pixels
      • Histogram in Figure 4-1

ValuePMF

0 32/64

128 16/64

255 16/64

histograms1
Histograms
  • Histogram
    • CMF (Cumulative Mass Function)
      • 식 4.6
    • 예)
      • Histogram in Figure 4-2

ValuePMFCMF

0 32/64 0.5

128 16/64 0.75

255 16/64 1.0

  • Histogram modification
    • CMF를 lookup table로 사용하여 PMF 변경
    • Image enhancement 응용
histogram class
Histogram class
  • Histogram class
    • In gui package
    • RGB (24 bits/pixel) image
      • 총 224 16 million color values
      • PMF is too sparse
      • 그래서 RGB 각각에 대한 histogram (each with 256 equal bins)
      • 예) figure 4.3

// histogram computation

histArray = new double[256];

for(int i=0; i<width; i++)

for(int j=0; j<height; j++)

histArray[plane[i][j] & 0xFF]++;

homogeneous point processing functions
Homogeneous point processing functions
  • Point operation
    • vij’ = fij(vij)
  • Homogeneous point operation
    • vij’ = f(vij)
    • Independent of pixel location
  • Linear map
    • f(vij) = vij
    • No change
    • Figure 4-4
  • Negative image
    • f(vij) = 255 – vij
    • Figure 4-5
using the pow function to brighten or darken
Using the pow function to brighten or darken
  • Power function
    • f(vij) = 255 * ( vij/255)pow
    • For pow<1.0, brightening but loss of contrast
      • 예) pow=0.9
        • Figure 4-6
        • 7번 적용 후 bright but washed out
    • For pow>1.0, darkening
      • 예) pow=1.5
        • Figure 4-7 & 4-8
        • Darkened
        • Histogram shifted to the left and narrowed: Figure 4-9
using linear transforms to alter brightness and contrast
Using linear transforms to alter brightness and contrast
  • Linear transform
    • Linear brightness and contrast adjustment
    • vij’ = c*vij + b
      • c=contrast
      • b=brightness
    • 예) c=2, b=-90
      • Figure 4-10
      • 범위 넘는 값은 0과 255로 clipping
using linear transforms to alter brightness and contrast1
Using linear transforms to alter brightness and contrast
  • Display의 dynamic range에 따른 조정
    • D = Dmax – Dmin
      • Dmax=maximum value that can be displayed
      • Dmin=minimum value that can be displayed
    • V = Vmax – Vmin
      • Vmax=maximum value in the image
      • Vmin=minimum value in the image
    • Linear transform 수식
      • vij’ = c*vij + b
        • c= D / V
        • b=(Dmin*Vmax – Dmax*Vmin) / V
using linear transforms to alter brightness and contrast2
Using linear transforms to alter brightness and contrast
  • Display의 dynamic range에 따른 조정
      • Dmin=0, Dmax=255
      • Vmin=10, Vmax=90
      • vij’ = (255/80)*vij – 2550/80

= 3.19*vij – 31.9

      • Figure 4-11
      • Applying결과: Figure 4-13
        • Histogram being spread out
        • Contrast enhancement
      • lut (lookup table) 사용한 구현
        • public short linearMap(short v, double c, double c)
        • public void linearTransform(double c, double br)
histogram modification
Histogram Modification
  • Histogram stretch
  • Histogram shrink
  • Histogram slide
  • Histogram equalization
  • …..

shrunk

original

stretched

shifted

4 2 3 the uniform non adaptive histogram equalization unahe
4.2.3 The Uniform Non-adaptive Histogram Equalization (UNAHE)
  • Clustering of pixel values  low-contrast images, so image details 잘 보이지 않음
  • Histogram equalization
    • Histogram modification에서 가장 보편적인 기법
    • Image contrast 개선 목적
the uniform non adaptive histogram equalization
The Uniform Non-adaptive Histogram Equalization
  • UNAHE
    • Create a uniform PMF from an image that has a non-uniform PMF
    • Using a scaled version of the CMF as a lookup table
    • CMF given by

Pv(a) = i=0,a pv(i) =p(V<=i)

a  [0..K-1]

    • The goal
      • Finding a function vij’ = f(vij) having a uniform PMF
  • UNAHE algorithm
    • vij’ = f(vij) = V*Pv(vij)
    • Pv(vij) : CMF
    • V = Vmax - Vmin
      • Vmax=maximum value in the image
      • Vmin=minimum value in the image
the uniform non adaptive histogram equalization1
The Uniform Non-adaptive Histogram Equalization
  • UNAHE 적용 예
    • 3 bits/pixel (Vmax=7, Vmin=0, V=7)
    • 4*4 image

3324

3566

2356

2366

    • vij PMF Pv(vij)

0 0 0

1 0 0

2 3/16 3/16

3 5/16 8/16

4 1/16 9/16

5 2/16 11/16

6 5/16 16/16

7 0 16/16

the uniform non adaptive histogram equalization2
The Uniform Non-adaptive Histogram Equalization
  • UNAHE 적용 예
    • f(vij) = 7*Pv(vij)

f(0) = 7*0 = 0  0

f(1) = 7*0 = 0  0

f(2) = 7*(3/16) = 1.31  1

f(3) = 7*(8/16) = 3.5  4

f(4) = 7*(9/16) = 3.93  4

f(5) = 7*(11/16) = 4.81  5

f(6) = 7*(16/16) = 7  7

f(7) = 7*(16/16) = 7  7

    • 영상에 적용

4414

4577

1457

1477

the uniform non adaptive histogram equalization3
The Uniform Non-adaptive Histogram Equalization
  • Effect of UNAHE
    • Figure 4.14: original & UNAHE 적용
    • Figure 4.15: histograms of original and UNAHE
    • Figure 4.16: UNAHE and linear transform
      • UNAHE 적용 영상이 much higher contrast
      • Higher quality ??
    • Low-contrast detail enhancement, but increase the contrast of noise
4 2 5 adaptive histogram equalization
4.2.5 Adaptive Histogram Equalization
  • 지역별로 다른 특성을 갖는 영상
    • 특히, document 영상
  • AUHE (Adaptive Uniform Histogram Equalization)
    • 영상을 여러 개의 부 영상으로 분할
    • 각각 부 영상에 대해 uniform histogram equalization 적용
    • Fine-grained vs. coarse-grained subdivision
  • 적용 예
    • Figure 4.22 & 4.23
  • Artifact 발생
    • Figure 4.24
    • How to solve this problem ??
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