Function histogram

Synopse

Image histogram.

h = histogram(f)
- f: Input image. Pixel data type must be integer.
- h: Output, integer vector.

Description

This function computes the number of occurrence of each pixel value. The function histogram_eq is implemented to show an implementation based on the equation of the histogram.

Function Code



In [12]:

    
import numpy as np

def histogram(f):

    return np.bincount(f.ravel())

Function Code for brute force implementation



In [13]:

    
def histogram_eq(f):

    from numpy import amax, zeros, arange, sum

    n = amax(f) + 1
    h = zeros((n,),int)
    for i in arange(n):
        h[i] = sum(i == f)
    return h

Function code for bidimensional matrix implementation



In [14]:

    
def histogram_eq1(f):

    import numpy as np
    n = f.size
    m = f.max() + 1
    haux = np.zeros((m,n),int)
    fi = f.ravel()
    i = np.arange(n)
    haux[fi,i] = 1
    h = np.add.reduce(haux,axis=1)
    return h

Examples



In [1]:

    
testing = (__name__ == "__main__")

if testing:
    ! jupyter nbconvert --to python histogram.ipynb
    import numpy as np
    import sys,os
    import matplotlib.image as mpimg
    ia898path = os.path.abspath('../../')
    if ia898path not in sys.path:
        sys.path.append(ia898path)
    import ia898.src as ia









    



[NbConvertApp] Converting notebook histogram.ipynb to python
[NbConvertApp] Writing 2706 bytes to histogram.py

Numerical examples



In [2]:

    
if testing:

    f = np.array([[0,1,2,3,4],
                  [4,3,2,1,1]], 'uint8')

    h = ia.histogram(f)
    print(h.dtype)
    print(h)









    



int64
[1 3 2 2 2]



In [3]:

    
if testing:
    h1 = ia.histogram_eq(f)
    print(h1.dtype)
    print(h1)









    



int64
[1 3 2 2 2]



In [4]:

    
if testing: 
    h1 = ia.histogram_eq1(f)
    print(h1.dtype)
    print(h1)









    



int64
[1 3 2 2 2]

Example 1



In [5]:

    
if testing:
    %matplotlib inline
    import matplotlib.pyplot as plt
    import matplotlib.image as mpimg
    f = mpimg.imread('../data/woodlog.tif')
    plt.imshow(f,cmap='gray')



In [6]:

    
if testing:
    h = ia.histogram(f)
    plt.plot(h)

Speed performance



In [7]:

    
if testing:
    import numpy as np
    from numpy.random import rand, seed
   
    seed([10])
    f = (255 * rand(1000,1000)).astype('uint8')
    %timeit h = ia.histogram(f)
    %timeit h1 = ia.histogram_eq(f)
    %timeit h2 = ia.histogram_eq1(f)









    



100 loops, best of 3: 3.86 ms per loop
1 loop, best of 3: 358 ms per loop
1 loop, best of 3: 1.54 s per loop

Equation

$$ h(i) = card\{p | f(p)=i\} \\ \text{or} \\ h(i) = \sum_p \left\{ \begin{array}{l l} 1 & \quad \text{if} \ f(p) = i\\ 0 & \quad \text{otherwise}\\ \end{array} \right. $$



In [9]:

    
if testing: 
    print(ia.histogram(np.array([3,7,0,0,3,0,10,7,0,7])) == \
          np.array([4, 0, 0, 2, 0, 0, 0, 3, 0, 0, 1]))









    



[ True  True  True  True  True  True  True  True  True  True  True]



In [ ]: