# 5. Homogeneous Point Processing - PowerPoint PPT Presentation

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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

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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

• 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

• 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

• Skip !!

• 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 ??