5 homogeneous point processing
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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

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


Exponential non adaptive histogram equalization

Exponential Non-adaptive Histogram Equalization

  • Skip !!


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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