5. Homogeneous Point Processing

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5. Homogeneous Point Processing - PowerPoint PPT Presentation

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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Presentation Transcript
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

• Clustering of pixel values  low-contrast images, so image details 잘 보이지 않음
• Histogram equalization
• Histogram modification에서 가장 보편적인 기법
• Image contrast 개선 목적
• 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
• 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

• 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

• 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