Binary Image Processing

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Binary image

• Binary image:
  • 0: black
  • 1: white (255)

advantages
* less memory
* easy to process
* can sometimes be applied on grayscale image
* more cheap

disadvantage
* application field is limited
* cannot be applied on D data
* less expressive force, fial to express the color and gray level of the image

Acquisiton of binary image

• Thresholding:
  \(I(x,y)=0 if I(x,y)<Threshold\)
  \(I(x,y)=255 if I(x,y)>=Threshold\)

How to find a good threshold?

大津算法

    img=imread('INPUT_FILE.bmp'); 

    gray_img=rgb2gray(img);  
    binary_img=imbinarize(gray_img); 
    subplot(1,2,1); 
    imshow(gray_img);
    title('Grayscale Image');
    subplot(1,2,2);
    imshow(binary_img);
    title('Binarized Image');

Try to find a suitable threshold to minimize the variances within the foreground and background, while maximize the variance between them.
\(N_{Fgrd}\): the number of pixels in the foreground
\(N_{Bgrd}\): the number of pixels in the background
\(\sigma_{Fgrd}^2\): the variance of the foreground
\(\sigma_{Bgrd}^2\): the variance of the background
\(\sigma_{within}^2\): the variance within the foreground and background
\(\mu_{Fgrd}\): the mean of the foreground
\(\mu_{Bgrd}\): the mean of the background
Simplified formula:

\(\sigma_{between}=w_b*w_f*(\mu_{Fgrd}-\mu_{Bgrd})^2\) (use findmax loop to find the maximum value of \(\sigma_{between}\))
Otsu's method: embedded in matlab

    threshold=graythresh(gray_img);
    binary_img=imbinarize(gray_img,threshold);

Tip

Numerical Analysis can bew imoplemented to find the optimal threshold

Generalization

Weber's law

• Weber's law:

  \(\frac{\Delta I}{I}=k\)
  \(\Delta I\): the smallest difference that can be perceived by human eyes
  \(I\): the intensity of the light
  \(k\): constant, between 0.01 and 0.02