Histogram equalization

HIstogram equalization

1) 개요

    - Transform color image to grayscale is the one of histogram equalization.

    - This is often a good way to normalize image intensity before further processing.

    - Effective way to increase image contrast.

 

2) 방법

    - Implement histogram of image by flattening.

 

Pixel values range : [0, 255]

    - Use cumulative distribution function (cdf) of the pixel values. (stack the frequency of pixels)

    - Normalize the cdf to range between [0, 1].

    - Use linear interpolation of cdf to find new pixel values.

A way of using histogram equalization equation
$$h(v) = \frac{cdf - cdf_{min}}{cdf_{max}-cdf_{min}}\times 255$$

 

3) Result

Code

# Using linear interpolation
def histeq(im,nbr_bins=256):
    """ Histogram equalization of a grayscale image. """
    # get image histogram
    imhist,bins = histogram(im.flatten(), nbr_bins, normed=True)
    
    # cumulative distribution function
    cdf = imhist.cumsum()
    cdf = 255 * cdf / cdf[-1] # normalize
    
    # use linear interpolation of cdf to find new pixel values
    im2 = interp(im.flatten(), bins[:-1], cdf)
    
    return im2.reshape(im.shape), cdf

# Using normalization equation
img = cv2.imread('images/hist_unequ.jpg');

hist, bins = np.histogram(img.flatten(), 256,[0,256])

cdf = hist.cumsum()

# cdf의 값이 0인 경우는 mask처리를 하여 계산에서 제외
# mask처리가 되면 Numpy 계산에서 제외가 됨
# 아래는 cdf array에서 값이 0인 부분을 mask처리함
cdf_m = np.ma.masked_equal(cdf,0)

#History Equalization 공식
cdf_m = (cdf_m - cdf_m.min())*255/(cdf_m.max()-cdf_m.min())

# Mask처리를 했던 부분을 다시 0으로 변환
cdf = np.ma.filled(cdf_m,0).astype('uint8')

img2 = cdf[img]

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참고

opencv-python.readthedocs.io/en/latest/doc/20.imageHistogramEqualization/imageHistogramEqualization.html

http://programmingcomputervision.com/