Tag Archives: Image histogram

Histogram Matching (Specification)

In the previous blog, we discussed Histogram Equalization that tries to produce an output image that has a uniform histogram. This approach is good but for some cases, this does not work well. One such case is when we have skewed image histogram i.e. large concentration of pixels at either end of greyscale.

One reasonable approach is to manually specify the transformation function that preserves the general shape of the original histogram but has a smoother transition of intensity levels in the skewed areas.

So, in this blog, we will learn how to transform an image so that its histogram matches a specified histogram. Also known as histogram matching or histogram Specification.

Histogram Equalization is a special case of histogram matching where the specified histogram is uniformly distributed.

First let’s understand the main idea behind histogram matching.

We will first equalize both original and specified histogram using the Histogram Equalization method. As we know that the transformation function is invertible, so by inverting we can get the mapping from original to specified histogram. The whole operation is shown in the below image

For example, suppose the pixel value 10 in the original image gets mapped to 20 in the equalized image. Then we will see what value in Specified image gets mapped to 20 in the equalized image and let’s say that this value is 28. So, we can say that 10 in the original image gets mapped to 28 in the specified image.

Most of you might be thinking why both original and specified histogram on equalization converges to same uniform histogram.

This is true only if we assume continuous intensity values. But in reality, the intensity values are discrete thus both original and specified histograms may not map to the same histogram on equalization. That’s why Histogram matching is not able to perfectly match the specified histogram.

Let’s take an example where we want to match the original image with the specified image, both histograms are shown below.

Here, I am taking the original image from the histogram equalization blog. All the steps of equalization are explained in this blog. Here, I will only show the final table

Original Image Histogram Equalization

Specified Image Histogram Equalization

After equalizing both the images, we need to perform a mapping from original to equalized to the specified image. For that, we need only the round columns of the original and specified image as shown below.

Pick one by one the values from the round column of the original image, find it in the round column of the specified image and note down the index. For example for 3 in the round original, we have 3 in the round specified column (with index 1) so we map it to 1.

If the value doesn’t exist then find the index of its nearest one. For example for 0 in round original, 1 is the nearest in round specified column (with index 0) so we map it to 0.

If multiple nearest values exist then pick the one which is greater than the value. For example for 2 in the round original, there are 2 closest values in round specified i.e. 1 and 3 so we pick 3 (with index 1) so we map it to 1.

After obtaining the Map column, replace the values in the original image with the map values. This is the final result.

The matched histogram(shown on left) approximately matches with the specified histogram(shown on right) as shown below

Now, let’s see how to perform Histogram matching using OpenCV-Python

Code

def find_nearest_above(my_array, target):
    diff = my_array - target
    mask = np.ma.less_equal(diff, -1)
    # We need to mask the negative differences
    # since we are looking for values above
    if np.all(mask):
        c = np.abs(diff).argmin()
        return c # returns min index of the nearest if target is greater than any value
    masked_diff = np.ma.masked_array(diff, mask)
    return masked_diff.argmin()

def find_nearest_above(my_array, target):

diff = my_array - target

mask = np.ma.less_equal(diff, -1)

# We need to mask the negative differences

# since we are looking for values above

if np.all(mask):

c = np.abs(diff).argmin()

return c # returns min index of the nearest if target is greater than any value

masked_diff = np.ma.masked_array(diff, mask)

return masked_diff.argmin()

def hist_match(original, specified):

    oldshape = original.shape
    original = original.ravel()
    specified = specified.ravel()

    # get the set of unique pixel values and their corresponding indices and counts
    s_values, bin_idx, s_counts = np.unique(original, return_inverse=True,return_counts=True)
    t_values, t_counts = np.unique(specified, return_counts=True)

    # Calculate s_k for original image
    s_quantiles = np.cumsum(s_counts).astype(np.float64)
    s_quantiles /= s_quantiles[-1]
    
    # Calculate s_k for specified image
    t_quantiles = np.cumsum(t_counts).astype(np.float64)
    t_quantiles /= t_quantiles[-1]

    # Round the values
    sour = np.around(s_quantiles*255)
    temp = np.around(t_quantiles*255)
    
    # Map the rounded values
    b=[]
    for data in sour[:]:
        b.append(find_nearest_above(temp,data))
    b= np.array(b,dtype='uint8')

    return b[bin_idx].reshape(oldshape)

def hist_match(original, specified):

oldshape = original.shape

original = original.ravel()

specified = specified.ravel()

# get the set of unique pixel values and their corresponding indices and counts

s_values, bin_idx, s_counts = np.unique(original, return_inverse=True,return_counts=True)

t_values, t_counts = np.unique(specified, return_counts=True)

# Calculate s_k for original image

s_quantiles = np.cumsum(s_counts).astype(np.float64)

s_quantiles /= s_quantiles[-1]

# Calculate s_k for specified image

t_quantiles = np.cumsum(t_counts).astype(np.float64)

t_quantiles /= t_quantiles[-1]

# Round the values

sour = np.around(s_quantiles*255)

temp = np.around(t_quantiles*255)

# Map the rounded values

b=[]

for data in sour[:]:

b.append(find_nearest_above(temp,data))

b= np.array(b,dtype='uint8')

return b[bin_idx].reshape(oldshape)

import cv2
import numpy as np

# Load the images in greyscale
original = cv2.imread('D:/downloads/opencv_logo1.PNG',0)
specified = cv2.imread('D:/downloads/dat.jpg',0)

# perform Histogram Matching
a = hist_match(original, specified)

# Display the image
cv2.imshow('a',np.array(a,dtype='uint8'))
cv2.imshow('a1',original)
cv2.imshow('a2',specified)
cv2.waitKey(0)
cv2.destroyAllWindows()

import cv2

import numpy as np

# Load the images in greyscale

original = cv2.imread('D:/downloads/opencv_logo1.PNG',0)

specified = cv2.imread('D:/downloads/dat.jpg',0)

# perform Histogram Matching

a = hist_match(original, specified)

# Display the image

cv2.imshow('a',np.array(a,dtype='uint8'))

cv2.imshow('a1',original)

cv2.imshow('a2',specified)

cv2.waitKey(0)

cv2.destroyAllWindows()

Note: Specified image can have different dimensions as compared to the original image.

The output looks like this

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.

Understanding Image Histograms

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In this blog, we will discuss image histogram which is a must-have tool in your pocket. This will help in contrast enhancement, image segmentation, image compression, thresholding etc. Let’s see what is an image histogram and how to plot histogram using OpenCV and matplotlib.

What is an Image Histogram?

An image histogram tells us how the intensity values are distributed in an image. In this we plot the intensity values on the x-axis and the no. of pixels corresponding to intensity values on the y-axis. See the figure below.

This is called 1D histogram because we are taking only one feature into our consideration, i.e. greyscale intensity value of the pixel. In the next blog, we will discuss 2D histograms.

Now, let’s understand some terminologies associated with histogram

Tonal range refers to the region where most of the intensity values are present (See above figure). The left side represents the black and dark areas known as shadows, the middle represents medium grey or midtones and the right side represents light and pure white areas known as Highlights.

So, for a dark image the histogram will cover mostly the left side and center of the graph. While for a bright image, the histogram mostly rests on the right side and center of the graph as shown in the figure below

Now, let’s see how to plot the histogram for an image using OpenCV and matplotlib.

OpenCV: To calculate the image histogram, OpenCV provides the following function

cv2.calcHist(image, channel, mask, bins, range)

image : input image, should be passed in a list. e.g. [image]
channel : index of the channel. for greyscale pass as [0], and for color image pass the desired channel as [0], [1], [2].
mask : provide if you want to calculate histogram for specific region otherwise pass None.
bins : No. of bins to use for each channel, should be passed as [256]
range : range of intensity values. For 8-bit pass as [0,256]

This returns a numpy.ndarray with shape (n_bins,1) which can then be plotted using matplotlib. Below is the code for this

import cv2
import matplotlib.pyplot as plt

# Load the image
image = cv2.imread('hist.jpg',0)

# Calculate histogram using cv2.calcHist()
hist = cv2.calcHist([image], [0], None, [256], [0,256])
# Display the histogram
plt.plot(hist)

import cv2

import matplotlib.pyplot as plt

# Load the image

image = cv2.imread('hist.jpg',0)

# Calculate histogram using cv2.calcHist()

hist = cv2.calcHist([image], [0], None, [256], [0,256])

# Display the histogram

plt.plot(hist)

Matplotlib: Unlike OpenCV, matplotlib directly finds the histogram and plots it using plt.hist()

plt.hist(image.flatten(), 256, [0,256])
plt.show()

1 2	plt.hist(image.flatten(), 256, [0,256]) plt.show()

For a color image, we can show each channel individually or we can first convert it into greyscale and then calculate the histogram. So, a color histogram can be expressed as “Three Intensity(Greyscale) Histograms”, each of which shows the brightness distribution of each individual Red/Green/Blue color channel. Below figure summarizes this.

So, always see the histogram of the image before doing any other pre-processing operation. 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.

What is Contrast in Image Processing?

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According to Wikipedia, Contrast is the difference in luminance or color that makes an object distinguishable from other objects within the same field of view.

Take a look at the images shown below

Clearly, the left image has a low contrast because it is difficult to identify the details present in the image as compared to the right image.

A real life example can be of a sunny and a foggy day. On a sunny day, everything looks clear to us, thus has a high contrast, as compared to a foggy day, where everything looks nearly of the same intensity (dull, washed-out grey look).

A more valid way to check whether an image has a low or high contrast is to plot the image histogram. Let’s plot the histogram for the above images

Clearly, from the left image histogram, we can see that the image intensity values are located in a narrow range. Because it’s hard to distinguish nearly the same intensity values (See below figure, 150 and 148 are hard to distinguish as compared to 50 and 200), thus the left image has low contrast.

The right histogram increases this gap between the intensity values and Whoo! the details in the image are now much more perceivable to us and thus yields a high contrast image.

So, for the high contrast, the image histogram should span the entire dynamic range as shown above by the right histogram. In the next blogs, we will learn different methods to do this.

There is another naive approach where we subtract the max and min intensity values and based on this difference we judge the image contrast. I will not recommend following this as this may get affected by the outliers (we will discuss in the next blogs). So, always plot the histogram to check.

Till now, we discussed contrast but we didn’t discuss the cause of low contrast images.

Low contrast images can result from Poor illumination, lack of dynamic range in the imaging sensor or even wrong setting of lens aperture during image acquisition etc.

When performing Contrast enhancement, you must first decide whether you want to do global or local contrast enhancement. Global means increasing the contrast of the whole image, While in local we divide the image into small regions and perform contrast enhancement on these regions independently. Don’t Worry, we will discuss these in detail in the next blogs.

This concept has been beautifully illustrated by the figure shown below( Taken from OpenCV Documentation)

Clearly, on global enhancement, the details present on the face of the statue are lost. While these are preserved in the local enhancement. So you need to be careful when selecting these methods.

In the next blog, we will discuss the methods used to transform a low contrast image into a high contrast 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.

TheAILearner

Mastering Artificial Intelligence

Tag Archives: Image histogram

Histogram Matching (Specification)

Original Image Histogram Equalization

Specified Image Histogram Equalization

Code

Understanding Image Histograms

What is Contrast in Image Processing?