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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

Homogeneous point processing

- Image quality (qualitative) 용어들
- washed out (smeared, blurred)
- brighter
- Contrast
- ….
- Processing 목적
- Noise suppression
- Enhancement 등

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

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
- 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

- 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

- 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

- 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 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 contrast

- Display의 dynamic range에 따른 조정
- 예
- 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 stretch
- Histogram shrink
- Histogram slide
- Histogram equalization
- …..

shrunk

original

stretched

shifted

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

- 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 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 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 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

- 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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