contrast stretching

In the previous blog, we discussed contrast stretching, a linear contrast enhancement method. In this blog, we will learn Histogram Equalization which automatically increase the dynamic range based on the information available in the histogram of the input image.

Histogram Equalization, as the name suggests, stretches the histogram to fill the dynamic range and at the same time tries to keep the histogram uniform as shown below

By doing this, the resultant image will have an appearance of high contrast and exhibits a large variety of grey tones.

Mostly we will not be able to perfectly equalize the histogram. This is only possible if we assume continuous intensity values.. But in reality, intensity values are discrete thus perfectly flat histograms are rare in practical applications of the histogram equalization.

The transformation function used in this is

where ‘s’ and ‘r’ are the output and input pixel intensities respectively. ‘L’ is the maximum intensity value(for n bit image L = 2ⁿ). The probability of occurrence of the intensity level r_j in the image is approximated by

Here, MN is the total number of pixels in the image and n_j is the number of pixels that have intensity r_j.

Now, let’s take an example to understand how to perform Histogram Equalisation using the above equations.

Suppose we have a 3-bit, 8×8 image whose pixel count and corresponding histogram is shown below

Now, using the above transformation function we calculate the equalized intensity values. For instance

Doing this for all values we get

Because the pixel values can only be integers so we round the last column(s_k) to the nearest integer as shown below

So, the round column is the output pixel intensity. The last step is to replace the pixel values in the original image( r_k column) with the round column values. For example, replace 0 with 0, 1 with 1, 2 with 1 and so on. This results in the histogram equalized image.

To plot the histogram, count the total pixels belonging to the rounded intensity values(See Round and n_k column). For example, 2 pixels belonging to 0, 8 pixels for 1, 6 pixels for 2 and so on.

The initial and equalized histogram is shown below

Sometimes rounding to nearest integer yield non-zero minimum value. If we want the output to range from say [0,255] for 8-bit, then we need to apply stretching (as we did in Min-Max stretching) after rounding.

Histogram Equalization often produces unrealistic effects in photographs and reduce color depth(no. of unique grey levels) as shown in the example above(See pixel value 5). It works best when applied to images with much higher color depth.

Let’s see OpenCV function for Histogram Equalization

equalized_img = cv2.equalizeHist(greyscale_img)

1	equalized_img = cv2.equalizeHist(greyscale_img)

Its input is grayscale image and output is our histogram equalized image.

Hope you enjoy reading.

If you have any doubt/suggestion please feel free to ask and I will do my best to help or improve myself. Good-bye until next time.

In the previous blog, we discussed the meaning of contrast in image processing, how to identify low and high contrast images and at last, we discussed the cause of low contrast in an image. In this blog, we will learn about the methods of contrast enhancement.

Below figure summarizes the Contrast Enhancement process pretty well.

Depending upon the transformation function used, Contrast Enhancement methods can be divided into Linear and Non-Linear.

The linear method includes Contrast-Stretching transformation that uses Piecewise Linear functions while Non-linear method includes Histogram Equilisation, Gaussian Stretch etc. which uses Non-Linear transformation functions that are obtained automatically from the histogram of the input image.

In this blog, we will discuss only the Linear methods. Rest we will discuss in the next blogs.

Contrast stretching as the name suggests is an image enhancement technique that tries to improve the contrast by stretching the intensity values of an image to fill the entire dynamic range. The transformation function used is always linear and monotonically increasing.

Below figure shows a typical transformation function used for Contrast Stretching.

By changing the location of points (r1, s1) and (r2, s2), we can control the shape of the transformation function. For example,

When r1 =s1 and r2=s2, transformation becomes a Linear function.
When r1=r2, s1=0 and s2=L-1, transformation becomes a thresholding function.
When (r1, s1) = (r_min, 0) and (r2, s2) = (r_max, L-1), this is known as Min-Max Stretching.
When (r1, s1) = (r_min + c, 0) and (r2, s2) = (r_max – c, L-1), this is known as Percentile Stretching.

Let’s understand Min-Max and Percentile Stretching in detail.

In Min-Max Stretching, the lower and upper values of the input image are made to span the full dynamic range. In other words, Lower value of the input image is mapped to 0 and the upper value is mapped to 255. All other intermediate values are reassigned new intensity values according to the following formulae

Sometimes, when Min-Max is performed, the tail ends of the histogram becomes long resulting in no improvement in the image quality. So, it is better to clip a certain percentage like 1%, 2% of the data from the tail ends of the input image histogram. This is known as Percentile Stretching. The formulae is same as Min-Max but now the X_max and X_min are the clipped values.

Let’s understand Min-Max and Percentile Stretching with an example. Suppose we have an image whose histogram looks like this

Clearly, this histogram has a left tail with few values(around 70 to 120). So, when we apply Min-max Stretching, the result looks like this

Clearly, Min-Max stretching doesn’t improve the results much. Now, let’s apply Percentile Stretching

As we clipped the long tail of input histogram, Percentile stretching produces much superior results than the Min-max stretching.

Let’s see how to perform Min-Max Stretching using OpenCV-Python

import cv2
import numpy as np

# Read the image
img1 = cv2.imread('D:/downloads/contrast.PNG',0)

# Create zeros array to store the stretched image
minmax_img = np.zeros((img1.shape[0],img1.shape[1]),dtype = 'uint8')

# Loop over the image and apply Min-Max formulae
for i in range(img1.shape[0]):
    for j in range(img1.shape[1]):
        minmax_img[i,j] = 255*(img1[i,j]-np.min(img1))/(np.max(img1)-np.min(img1))

# Displat the stretched image
cv2.imshow('Minmax',minmax_img)
cv2.waitKey(0)

import cv2

import numpy as np

# Read the image

img1 = cv2.imread('D:/downloads/contrast.PNG',0)

# Create zeros array to store the stretched image

minmax_img = np.zeros((img1.shape[0],img1.shape[1]),dtype = 'uint8')

# Loop over the image and apply Min-Max formulae

for i in range(img1.shape[0]):

for j in range(img1.shape[1]):

minmax_img[i,j] = 255*(img1[i,j]-np.min(img1))/(np.max(img1)-np.min(img1))

# Displat the stretched image

cv2.imshow('Minmax',minmax_img)

cv2.waitKey(0)

For a color image, either change it into greyscale and then apply contrast stretching or change it into another color model like HSV and then apply contrast stretching on V. For percentile stretching, just change the min and max values with the clipped value. Rest all the code is the same.

So, always plot histogram and then decide which method to follow. Hope you enjoy reading.

If you have any doubt/suggestion please feel free to ask and I will do my best to help or improve myself. Good-bye until next time.

TheAILearner

Mastering Artificial Intelligence

Tag Archives: contrast stretching

Histogram Equalization