Histograms - 2: Histogram Equalization {#tutorial_py_histogram_equalization}
======================================

Goal
----

In this section,

-   We will learn the concepts of histogram equalization and use it to improve the contrast of our
    images.

Theory
------

Consider an image whose pixel values are confined to some specific range of values only. For eg,
brighter image will have all pixels confined to high values. But a good image will have pixels from
all regions of the image. So you need to stretch this histogram to either ends (as given in below
image, from wikipedia) and that is what Histogram Equalization does (in simple words). This normally
improves the contrast of the image.

![image](images/histogram_equalization.png)

I would recommend you to read the wikipedia page on [Histogram
Equalization](http://en.wikipedia.org/wiki/Histogram_equalization) for more details about it. It has
a very good explanation with worked out examples, so that you would understand almost everything
after reading that. Instead, here we will see its Numpy implementation. After that, we will see
OpenCV function.
@code{.py}
import numpy as np
import cv2 as cv
from matplotlib import pyplot as plt

img = cv.imread('wiki.jpg',0)

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

cdf = hist.cumsum()
cdf_normalized = cdf * float(hist.max()) / cdf.max()

plt.plot(cdf_normalized, color = 'b')
plt.hist(img.flatten(),256,[0,256], color = 'r')
plt.xlim([0,256])
plt.legend(('cdf','histogram'), loc = 'upper left')
plt.show()
@endcode
![image](images/histeq_numpy1.jpg)

You can see histogram lies in brighter region. We need the full spectrum. For that, we need a
transformation function which maps the input pixels in brighter region to output pixels in full
region. That is what histogram equalization does.

Now we find the minimum histogram value (excluding 0) and apply the histogram equalization equation
as given in wiki page. But I have used here, the masked array concept array from Numpy. For masked
array, all operations are performed on non-masked elements. You can read more about it from Numpy
docs on masked arrays.
@code{.py}
cdf_m = np.ma.masked_equal(cdf,0)
cdf_m = (cdf_m - cdf_m.min())*255/(cdf_m.max()-cdf_m.min())
cdf = np.ma.filled(cdf_m,0).astype('uint8')
@endcode
Now we have the look-up table that gives us the information on what is the output pixel value for
every input pixel value. So we just apply the transform.
@code{.py}
img2 = cdf[img]
@endcode
Now we calculate its histogram and cdf as before ( you do it) and result looks like below :

![image](images/histeq_numpy2.jpg)

Another important feature is that, even if the image was a darker image (instead of a brighter one
we used), after equalization we will get almost the same image as we got. As a result, this is used
as a "reference tool" to make all images with same lighting conditions. This is useful in many
cases. For example, in face recognition, before training the face data, the images of faces are
histogram equalized to make them all with same lighting conditions.

Histograms Equalization in OpenCV
---------------------------------

OpenCV has a function to do this, **cv.equalizeHist()**. Its input is just grayscale image and
output is our histogram equalized image.

Below is a simple code snippet showing its usage for same image we used :
@code{.py}
img = cv.imread('wiki.jpg',0)
equ = cv.equalizeHist(img)
res = np.hstack((img,equ)) #stacking images side-by-side
cv.imwrite('res.png',res)
@endcode
![image](images/equalization_opencv.jpg)

So now you can take different images with different light conditions, equalize it and check the
results.

Histogram equalization is good when histogram of the image is confined to a particular region. It
won't work good in places where there is large intensity variations where histogram covers a large
region, ie both bright and dark pixels are present. Please check the SOF links in Additional
Resources.

CLAHE (Contrast Limited Adaptive Histogram Equalization)
--------------------------------------------------------

The first histogram equalization we just saw, considers the global contrast of the image. In many
cases, it is not a good idea. For example, below image shows an input image and its result after
global histogram equalization.

![image](images/clahe_1.jpg)

It is true that the background contrast has improved after histogram equalization. But compare the
face of statue in both images. We lost most of the information there due to over-brightness. It is
because its histogram is not confined to a particular region as we saw in previous cases (Try to
plot histogram of input image, you will get more intuition).

So to solve this problem, **adaptive histogram equalization** is used. In this, image is divided
into small blocks called "tiles" (tileSize is 8x8 by default in OpenCV). Then each of these blocks
are histogram equalized as usual. So in a small area, histogram would confine to a small region
(unless there is noise). If noise is there, it will be amplified. To avoid this, **contrast
limiting** is applied. If any histogram bin is above the specified contrast limit (by default 40 in
OpenCV), those pixels are clipped and distributed uniformly to other bins before applying histogram
equalization. After equalization, to remove artifacts in tile borders, bilinear interpolation is
applied.

Below code snippet shows how to apply CLAHE in OpenCV:
@code{.py}
import numpy as np
import cv2 as cv

img = cv.imread('tsukuba_l.png',0)

# create a CLAHE object (Arguments are optional).
clahe = cv.createCLAHE(clipLimit=2.0, tileGridSize=(8,8))
cl1 = clahe.apply(img)

cv.imwrite('clahe_2.jpg',cl1)
@endcode
See the result below and compare it with results above, especially the statue region:

![image](images/clahe_2.jpg)

Additional Resources
--------------------

-#  Wikipedia page on [Histogram Equalization](http://en.wikipedia.org/wiki/Histogram_equalization)
2.  [Masked Arrays in Numpy](http://docs.scipy.org/doc/numpy/reference/maskedarray.html)

Also check these SOF questions regarding contrast adjustment:

-#  [How can I adjust contrast in OpenCV in
    C?](http://stackoverflow.com/questions/10549245/how-can-i-adjust-contrast-in-opencv-in-c)
4.  [How do I equalize contrast & brightness of images using
    opencv?](http://stackoverflow.com/questions/10561222/how-do-i-equalize-contrast-brightness-of-images-using-opencv)

Exercises
---------
