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2 Dimensional Array Manipulations and Equalization for Clarity images





In [2]:



    


#insert your own parth here
import os
os.chdir('/Users/albertlee/NeuroCV/Module1/PCV/2Dhisteq')



    











In [3]:



    


### Run below if necessary

##import sys

##sys.path.append('/usr/local/lib/python2.7/site-packages')

import math
import csv,gc
import matplotlib
import numpy as np
import cv2

#%matplotlib
BINS = 32



    











In [4]:



    


import matplotlib.pyplot as plt
%matplotlib inline



    











In [5]:



    


from skimage import data, img_as_float
from skimage import exposure



    











In [6]:



    


import cv2



    











In [7]:



    


from PCV import tools
from PIL import Image
from numpy import *

def histeq(im,nbr_bins=256):
    """    Histogram equalization of a grayscale image. """
    
    # get image histogram
    imhist,bins = histogram(im.flatten(),nbr_bins,normed=True)
    cdf = imhist.cumsum() # cumulative distribution function
    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



    











In [8]:



    


im = array(Image.open('Fear199.png'))
plt.imshow(np.asarray(im))



    


















    
Out[8]:








<matplotlib.image.AxesImage at 0x10e692950>










    
























In [9]:



    


im = array(Image.open('Fear199.png').convert('L'))
im2,cdf = histeq(im)
plt.imshow(np.asarray(im))



    


















    
Out[9]:








<matplotlib.image.AxesImage at 0x10fc402d0>










    
























In [11]:



    


histeqimage = Image.fromarray(im2)
histeqimage = histeqimage.convert('RGB')
plt.imshow(np.asarray(histeqimage))



    


















    
Out[11]:








<matplotlib.image.AxesImage at 0x11536a310>










    
























In [12]:



    


import math

## Import image

im = np.asarray(im)

print im
z = im

# Number of pixels
pixels = len(z) * len(z[0])
print "The number of pixels is {}".format(pixels)
## The output should be 4 since there are 4 numbers in this array

##Flatten method doesn't work because of tuple conversion later on
'''# Now we flatten Z
zz = z.reshape(-1)'''


# Initialize histogram and CDF
hist = {}
cdf = {}
norm_cdf = {}
## The range value should be be adjusted to the bin number
### In our case the range and bin number is obviously 10 
### since we generated numbers 1-10
BINS = 255

for i in range(BINS):
    hist[i] = 0
    cdf[i] = 0
    norm_cdf[i] = 0

# Create histogram


for row in z:
    for val in row:
        hist[val] += 1

'''
for val in zz:
    hist[val] += 1
'''    


# Create cdf
for i in range(BINS):
    for j in range(i+1):
        cdf[i] += hist[j]
    norm_cdf[i] = int(math.floor(float(cdf[i]-1)/63*BINS))
    
print "The histogram values are {}".format(hist)
print "The cdf values are {}".format(cdf)
print "The normalized cdf values are {}".format(norm_cdf)



    


















    






[[0 0 0 ..., 0 0 0]
 [0 0 0 ..., 0 0 0]
 [0 0 0 ..., 0 0 0]
 ..., 
 [0 0 0 ..., 0 0 0]
 [0 0 0 ..., 0 0 0]
 [0 0 0 ..., 0 0 0]]
The number of pixels is 1046864
The histogram values are {0: 793273, 1: 32538, 2: 90886, 3: 0, 4: 38341, 5: 37845, 6: 0, 7: 10750, 8: 10592, 9: 0, 10: 5950, 11: 2231, 12: 2092, 13: 1921, 14: 1681, 15: 1600, 16: 1510, 17: 2776, 18: 0, 19: 1163, 20: 2038, 21: 0, 22: 883, 23: 1517, 24: 0, 25: 1333, 26: 600, 27: 0, 28: 944, 29: 447, 30: 366, 31: 326, 32: 329, 33: 274, 34: 246, 35: 407, 36: 0, 37: 198, 38: 312, 39: 0, 40: 137, 41: 221, 42: 0, 43: 178, 44: 76, 45: 0, 46: 123, 47: 53, 48: 52, 49: 43, 50: 33, 51: 28, 52: 34, 53: 53, 54: 0, 55: 22, 56: 59, 57: 0, 58: 35, 59: 16, 60: 0, 61: 27, 62: 13, 63: 0, 64: 28, 65: 8, 66: 12, 67: 9, 68: 5, 69: 8, 70: 9, 71: 12, 72: 0, 73: 11, 74: 10, 75: 0, 76: 11, 77: 3, 78: 0, 79: 8, 80: 4, 81: 0, 82: 7, 83: 3, 84: 2, 85: 3, 86: 4, 87: 6, 88: 0, 89: 2, 90: 0, 91: 2, 92: 125, 93: 0, 94: 0, 95: 0, 96: 0, 97: 0, 98: 0, 99: 0, 100: 0, 101: 0, 102: 0, 103: 0, 104: 0, 105: 0, 106: 0, 107: 0, 108: 0, 109: 0, 110: 0, 111: 0, 112: 0, 113: 0, 114: 0, 115: 0, 116: 0, 117: 0, 118: 0, 119: 0, 120: 0, 121: 0, 122: 0, 123: 0, 124: 0, 125: 0, 126: 0, 127: 0, 128: 0, 129: 0, 130: 0, 131: 0, 132: 0, 133: 0, 134: 0, 135: 0, 136: 0, 137: 0, 138: 0, 139: 0, 140: 0, 141: 0, 142: 0, 143: 0, 144: 0, 145: 0, 146: 0, 147: 0, 148: 0, 149: 0, 150: 0, 151: 0, 152: 0, 153: 0, 154: 0, 155: 0, 156: 0, 157: 0, 158: 0, 159: 0, 160: 0, 161: 0, 162: 0, 163: 0, 164: 0, 165: 0, 166: 0, 167: 0, 168: 0, 169: 0, 170: 0, 171: 0, 172: 0, 173: 0, 174: 0, 175: 0, 176: 0, 177: 0, 178: 0, 179: 0, 180: 0, 181: 0, 182: 0, 183: 0, 184: 0, 185: 0, 186: 0, 187: 0, 188: 0, 189: 0, 190: 0, 191: 0, 192: 0, 193: 0, 194: 0, 195: 0, 196: 0, 197: 0, 198: 0, 199: 0, 200: 0, 201: 0, 202: 0, 203: 0, 204: 0, 205: 0, 206: 0, 207: 0, 208: 0, 209: 0, 210: 0, 211: 0, 212: 0, 213: 0, 214: 0, 215: 0, 216: 0, 217: 0, 218: 0, 219: 0, 220: 0, 221: 0, 222: 0, 223: 0, 224: 0, 225: 0, 226: 0, 227: 0, 228: 0, 229: 0, 230: 0, 231: 0, 232: 0, 233: 0, 234: 0, 235: 0, 236: 0, 237: 0, 238: 0, 239: 0, 240: 0, 241: 0, 242: 0, 243: 0, 244: 0, 245: 0, 246: 0, 247: 0, 248: 0, 249: 0, 250: 0, 251: 0, 252: 0, 253: 0, 254: 0}
The cdf values are {0: 793273, 1: 825811, 2: 916697, 3: 916697, 4: 955038, 5: 992883, 6: 992883, 7: 1003633, 8: 1014225, 9: 1014225, 10: 1020175, 11: 1022406, 12: 1024498, 13: 1026419, 14: 1028100, 15: 1029700, 16: 1031210, 17: 1033986, 18: 1033986, 19: 1035149, 20: 1037187, 21: 1037187, 22: 1038070, 23: 1039587, 24: 1039587, 25: 1040920, 26: 1041520, 27: 1041520, 28: 1042464, 29: 1042911, 30: 1043277, 31: 1043603, 32: 1043932, 33: 1044206, 34: 1044452, 35: 1044859, 36: 1044859, 37: 1045057, 38: 1045369, 39: 1045369, 40: 1045506, 41: 1045727, 42: 1045727, 43: 1045905, 44: 1045981, 45: 1045981, 46: 1046104, 47: 1046157, 48: 1046209, 49: 1046252, 50: 1046285, 51: 1046313, 52: 1046347, 53: 1046400, 54: 1046400, 55: 1046422, 56: 1046481, 57: 1046481, 58: 1046516, 59: 1046532, 60: 1046532, 61: 1046559, 62: 1046572, 63: 1046572, 64: 1046600, 65: 1046608, 66: 1046620, 67: 1046629, 68: 1046634, 69: 1046642, 70: 1046651, 71: 1046663, 72: 1046663, 73: 1046674, 74: 1046684, 75: 1046684, 76: 1046695, 77: 1046698, 78: 1046698, 79: 1046706, 80: 1046710, 81: 1046710, 82: 1046717, 83: 1046720, 84: 1046722, 85: 1046725, 86: 1046729, 87: 1046735, 88: 1046735, 89: 1046737, 90: 1046737, 91: 1046739, 92: 1046864, 93: 1046864, 94: 1046864, 95: 1046864, 96: 1046864, 97: 1046864, 98: 1046864, 99: 1046864, 100: 1046864, 101: 1046864, 102: 1046864, 103: 1046864, 104: 1046864, 105: 1046864, 106: 1046864, 107: 1046864, 108: 1046864, 109: 1046864, 110: 1046864, 111: 1046864, 112: 1046864, 113: 1046864, 114: 1046864, 115: 1046864, 116: 1046864, 117: 1046864, 118: 1046864, 119: 1046864, 120: 1046864, 121: 1046864, 122: 1046864, 123: 1046864, 124: 1046864, 125: 1046864, 126: 1046864, 127: 1046864, 128: 1046864, 129: 1046864, 130: 1046864, 131: 1046864, 132: 1046864, 133: 1046864, 134: 1046864, 135: 1046864, 136: 1046864, 137: 1046864, 138: 1046864, 139: 1046864, 140: 1046864, 141: 1046864, 142: 1046864, 143: 1046864, 144: 1046864, 145: 1046864, 146: 1046864, 147: 1046864, 148: 1046864, 149: 1046864, 150: 1046864, 151: 1046864, 152: 1046864, 153: 1046864, 154: 1046864, 155: 1046864, 156: 1046864, 157: 1046864, 158: 1046864, 159: 1046864, 160: 1046864, 161: 1046864, 162: 1046864, 163: 1046864, 164: 1046864, 165: 1046864, 166: 1046864, 167: 1046864, 168: 1046864, 169: 1046864, 170: 1046864, 171: 1046864, 172: 1046864, 173: 1046864, 174: 1046864, 175: 1046864, 176: 1046864, 177: 1046864, 178: 1046864, 179: 1046864, 180: 1046864, 181: 1046864, 182: 1046864, 183: 1046864, 184: 1046864, 185: 1046864, 186: 1046864, 187: 1046864, 188: 1046864, 189: 1046864, 190: 1046864, 191: 1046864, 192: 1046864, 193: 1046864, 194: 1046864, 195: 1046864, 196: 1046864, 197: 1046864, 198: 1046864, 199: 1046864, 200: 1046864, 201: 1046864, 202: 1046864, 203: 1046864, 204: 1046864, 205: 1046864, 206: 1046864, 207: 1046864, 208: 1046864, 209: 1046864, 210: 1046864, 211: 1046864, 212: 1046864, 213: 1046864, 214: 1046864, 215: 1046864, 216: 1046864, 217: 1046864, 218: 1046864, 219: 1046864, 220: 1046864, 221: 1046864, 222: 1046864, 223: 1046864, 224: 1046864, 225: 1046864, 226: 1046864, 227: 1046864, 228: 1046864, 229: 1046864, 230: 1046864, 231: 1046864, 232: 1046864, 233: 1046864, 234: 1046864, 235: 1046864, 236: 1046864, 237: 1046864, 238: 1046864, 239: 1046864, 240: 1046864, 241: 1046864, 242: 1046864, 243: 1046864, 244: 1046864, 245: 1046864, 246: 1046864, 247: 1046864, 248: 1046864, 249: 1046864, 250: 1046864, 251: 1046864, 252: 1046864, 253: 1046864, 254: 1046864}
The normalized cdf values are {0: 3210862, 1: 3342564, 2: 3710436, 3: 3710436, 4: 3865625, 5: 4018808, 6: 4018808, 7: 4062320, 8: 4105192, 9: 4105192, 10: 4129275, 11: 4138305, 12: 4146773, 13: 4154549, 14: 4161353, 15: 4167829, 16: 4173941, 17: 4185177, 18: 4185177, 19: 4189884, 20: 4198133, 21: 4198133, 22: 4201707, 23: 4207848, 24: 4207848, 25: 4213243, 26: 4215672, 27: 4215672, 28: 4219493, 29: 4221302, 30: 4222783, 31: 4224103, 32: 4225435, 33: 4226544, 34: 4227539, 35: 4229187, 36: 4229187, 37: 4229988, 38: 4231251, 39: 4231251, 40: 4231805, 41: 4232700, 42: 4232700, 43: 4233420, 44: 4233728, 45: 4233728, 46: 4234226, 47: 4234440, 48: 4234651, 49: 4234825, 50: 4234959, 51: 4235072, 52: 4235210, 53: 4235424, 54: 4235424, 55: 4235513, 56: 4235752, 57: 4235752, 58: 4235894, 59: 4235958, 60: 4235958, 61: 4236068, 62: 4236120, 63: 4236120, 64: 4236234, 65: 4236266, 66: 4236315, 67: 4236351, 68: 4236371, 69: 4236404, 70: 4236440, 71: 4236489, 72: 4236489, 73: 4236533, 74: 4236574, 75: 4236574, 76: 4236618, 77: 4236630, 78: 4236630, 79: 4236663, 80: 4236679, 81: 4236679, 82: 4236707, 83: 4236719, 84: 4236727, 85: 4236740, 86: 4236756, 87: 4236780, 88: 4236780, 89: 4236788, 90: 4236788, 91: 4236796, 92: 4237302, 93: 4237302, 94: 4237302, 95: 4237302, 96: 4237302, 97: 4237302, 98: 4237302, 99: 4237302, 100: 4237302, 101: 4237302, 102: 4237302, 103: 4237302, 104: 4237302, 105: 4237302, 106: 4237302, 107: 4237302, 108: 4237302, 109: 4237302, 110: 4237302, 111: 4237302, 112: 4237302, 113: 4237302, 114: 4237302, 115: 4237302, 116: 4237302, 117: 4237302, 118: 4237302, 119: 4237302, 120: 4237302, 121: 4237302, 122: 4237302, 123: 4237302, 124: 4237302, 125: 4237302, 126: 4237302, 127: 4237302, 128: 4237302, 129: 4237302, 130: 4237302, 131: 4237302, 132: 4237302, 133: 4237302, 134: 4237302, 135: 4237302, 136: 4237302, 137: 4237302, 138: 4237302, 139: 4237302, 140: 4237302, 141: 4237302, 142: 4237302, 143: 4237302, 144: 4237302, 145: 4237302, 146: 4237302, 147: 4237302, 148: 4237302, 149: 4237302, 150: 4237302, 151: 4237302, 152: 4237302, 153: 4237302, 154: 4237302, 155: 4237302, 156: 4237302, 157: 4237302, 158: 4237302, 159: 4237302, 160: 4237302, 161: 4237302, 162: 4237302, 163: 4237302, 164: 4237302, 165: 4237302, 166: 4237302, 167: 4237302, 168: 4237302, 169: 4237302, 170: 4237302, 171: 4237302, 172: 4237302, 173: 4237302, 174: 4237302, 175: 4237302, 176: 4237302, 177: 4237302, 178: 4237302, 179: 4237302, 180: 4237302, 181: 4237302, 182: 4237302, 183: 4237302, 184: 4237302, 185: 4237302, 186: 4237302, 187: 4237302, 188: 4237302, 189: 4237302, 190: 4237302, 191: 4237302, 192: 4237302, 193: 4237302, 194: 4237302, 195: 4237302, 196: 4237302, 197: 4237302, 198: 4237302, 199: 4237302, 200: 4237302, 201: 4237302, 202: 4237302, 203: 4237302, 204: 4237302, 205: 4237302, 206: 4237302, 207: 4237302, 208: 4237302, 209: 4237302, 210: 4237302, 211: 4237302, 212: 4237302, 213: 4237302, 214: 4237302, 215: 4237302, 216: 4237302, 217: 4237302, 218: 4237302, 219: 4237302, 220: 4237302, 221: 4237302, 222: 4237302, 223: 4237302, 224: 4237302, 225: 4237302, 226: 4237302, 227: 4237302, 228: 4237302, 229: 4237302, 230: 4237302, 231: 4237302, 232: 4237302, 233: 4237302, 234: 4237302, 235: 4237302, 236: 4237302, 237: 4237302, 238: 4237302, 239: 4237302, 240: 4237302, 241: 4237302, 242: 4237302, 243: 4237302, 244: 4237302, 245: 4237302, 246: 4237302, 247: 4237302, 248: 4237302, 249: 4237302, 250: 4237302, 251: 4237302, 252: 4237302, 253: 4237302, 254: 4237302}

















In [13]:



    


np.set_printoptions(threshold='nan')

imgflat = im.reshape(-1)
print imgflat
print imgflat.sum()

print " "
fig = plt.hist(imgflat, bins='auto')
plt.title('Histogram')
plt.show()



    


















    






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 11  4  0  2  4  8  2  0  1 10  4  2  2  2  5 10  0 15  5  5  5 25  8  5 12
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 10  5  7  8  7 16  5 15  8 17 11 10  2 20 14 23  8 12 25 17  0 25 13 35 28
 25 31 41 23 28 25 40 34 11 12 11 13 12  5 17  5  5  5  8  8 10  5  2  2  2
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 10  8  8  5 11  5 13 10 13 17  7 20 17 17 16 17 19 17 12  8 14 20 25 12 28
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 16  2  2  2  1  5  1 10  7  4  2  0  0  1  2  0  5  1  5  2 12  0  4 13  8
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 15 17 20 92 13 11 30 10 17  5 38 16 25 17 20 10 38 16 33 26 10 16 30 16 22
 20 17 14  8 11  4  2  2  8  5  1  0  5  5 11  0  1  1  2  2  0  4  2  2  0
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 28 16 35  5 16 41 32 13 17  4  2 14  5  5 23 25 46 22 25 10 37 15 10 13 10
 25 19 10 16 22 19 17 10 35 11 44 19 16 32 20  7 20 19 16 12  5 31 17 43 25
 31 30 13 14 12 10 20  7  7  0  4  4  4  4  1  5  4  8  2  4  1  2  1  4  1
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 19 13 31 15 33 13 15 30 13  2 11  2 20  5  2  1  2  8  2  2  2  2  2  5  2
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  2  8  5  0  0 15  4  0  0  1  5  0  4  8 14  5 22  7 17  2  5  7  8 10  0
 10  7 25 17 80 37  5 20 14 10 25 25 11 12 15 22 12 41 32 40 10  8 20 41 31
 23 10 16 32 31 23 22 51 32 17  7 43 41 23 23 17 20  5 28 34 10 25  4  2  0
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 20 11 16 26 13 25 14 12 17 23 13 25 19 37 12 20 28 40 26 25 28 28 35 12 11
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 10 19 11 17 15  8 12 10 13 11  5 12  7  7  8  8  0 16  7  5  7  2  1 10  7
 16 16 14 23 26 17  7  5  7  5  1  2  0  1  5  8  4  5  1  4  0  5  1  2  4
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  7  7  7  4  4  2  5  5  4  5  2  7  2  2  0  4  5  2  2  7  0  1  1  2  8
  1  0  0  2  0  1  0  0  0  0  0  0  5  0  4  0  1  5  5 12 14  7 17 20 14
 31 25 22  7 34 14 14 17 17 12  8 17 11 16 19 15  4 10 20  7 10  8 19 14 19
 23 35 33 32 34 16 23 25 32 14 22 11 14 14 22 16 17  7 17 38 10 11 17  5 10
 30 20 28 29 23  5 12  7 10  5  1  8  5  2  0  5  0  0  0  2  1  0  1  1  2
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  2  2  2  4 11  1  5  0  5  2  0  1  0  2  0  5  2  4  0  0  2  4  2  0 10
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  2  5  0  4  4  4  2  0  7  0  2  0  0  7  2  0  4  2  2  2  2  2  2  2  0
  0  1  1  2  2  0  2  0  5  0  0  1  2  5  2  2  4  1  2  7  4  1  0  2  2
  0  0  5  7  5  5  4  0  0  4  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
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  0  2  0  2  4  0  1  2  5  4  0  2  2  1  5  0  5  2  4  1  0  4  5  2  0
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 10 19 15 15 22  7  2  4 25  0 17 14 13 10  5 32 23 11 10 11  8  7 25 13 12
 34  1 14  2  8 10  7 12  0  8 25 15 28 10 17 29  8 17  7  8  5  5  0  7  4
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  2  2  2  1  4  2  2  0  7  0  0  0  2  0  0  4  4  0  4  0  4  4  4  0  0
  2  2  1  0  4  4  0  0  5  5  0  4  7  5  8  2  0  0  0  5  8  2  0  2  2
  0  0  2  2  0 14  4  8 16 11 40 25 29  5 20 15 19 19 17 13 17 14 12  8 17
 92 19 20 10 14 20  8 15 11 11 44  2  5 28 23 20 28 20 14  2 22 17 92 20 12
 20 23 20 10 11 17 17 23 19 23 10 19 25 17 23 14 20 19 14  8  5 13 10  7  2
  2  5  2  8  0  2  1  5  0  2  4  2  4  0  1  0  0 12  0  1  1  0  5  0  1
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  0  5  4  2  0  2  0  0  2  2  0  4  5 17  2  2  4  1  0  5  0  0  5  0  1
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  1 10  0  1  0  2  5  0  1  0  4 11  4  2  2  5  4  0  0  8 14  4  5  1  8
 10  4 22 17 23 16 17 15 25 19 22 12 23 26  8 35 35 20  4 17  7 10 12 10 10
 12 15  8 23 35 23 16 22  2  8 11 14  8 10 14  7 12 11  2 17 29  8  8 26 23
 43  5 17  8 14 64  4  2 17  5  8  7  8  0  4  5  2  0  0  0  2  2  5  2  1
  4  2  0  4  4  0  4  4  2  5  0  0  2  0  0  4  5  7  2  0  0  5  0  2  2
  1  7  0  2  0  5  0  0  0  0  1  0  0  0  0  4  0  2  1  2  2  0  0  0  0
  2  2  5  2  7 10 10  5  4  0  5  2  2  8  2  8  0  0  0 14  5  2 14 23 33
  8 11 17 23 17  8 12 20 31  4  5 13  5 14 16 12 10 10  5 16 11 13 16 25 17
 52 20 23 17 16 17 17  7 10 12 17 32 17 23 10 25 17  4 17 25 15 12 23 10 19
 15 23 31 20 13 41  8 13 15 13 14  8  5  5  4  2  5  5  5  5  2  0  1  1  4
  1  0  0  0  2  0  0  2  2  0  2  2  4  0  0  0  0  0  5 10  5  0  0  0  0
  2  0  2  0  5  2  5  0  0  2  2  0  5  1  5  2  0  0  0  2  1  2  2  5  1
  4  0  2  1  2  0  4  1  0  2  0  2  5  4  4  0  1  4  0  0  0  0  1  5  1
  0  4  2  4  0  0  1 10  7  4  4  0  2  7  2  5  2  0  2  1  5  1  2  2  2
  1  8  2  0  0  2  4  2  0  0  2  2  2  5  0  0  2  2  0  2 10  2  0  0  0
  0  7  2  1  0  2  2  0  0  4  4  1  0  2  0  2  7  0  0  0  0  2  0  0  2
  0  4  2  1  2  0 10  0  0  0  0  0  4  0  0  1  0  1  0  4  0  0  4  5  2
  4  2  0  2  0  0  2  0  1  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0
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 31 25 33 29 29 20 20 16 12  8  8  8  8 25 17 17 11  0  8 12 22 23 12 15 12
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 28 17 35 25 15 20  8 11 14 11 12 17 28 13 38 43 16 32 15  2 14 28 35 23 10
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 11  7  7  2  5 19 19 17 15 29 20 13 23 23 15  7 16 38 12 15 28 13 32 17 10
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 28 23 28 26 29 20 23 23 20 19 16 23 19 20  5 20 15 12 22 10 31 16 22 14 13
 31 20 46 44 20 13 82 17 23 43 20 30  8 15 17  7 20 14 13 10 20 33 17 34 25
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 28 50 23 33 25 25 29 20 23 20 12 17 28 22 92 17 22 82 14 20 26 30 25 23 23
 20 23 76 13 14 17 10 15 10 13 10 15 19 23 19 22 10 12 48 25 22 17 15 25  8
 15 38 37 17  5  7 17  5 16 14  8  7  7  8  4  7  2  2  2 10  2  8  2  2  5
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 15 17  8 29 20 23 23 22 32 23 17 23 14 11 17 14 11 19 19 12 20 12 12 13 31
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 17 20 15 17 28 25 34 12 15 41 16 28 20 25 35 43 17 30 20 23 15 26 35 22 22
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 17  8 25 14 29 30 26 26 25 32 23 31 28  5 15 17 17 14 22 23 14 26 16 25 87
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 41 29 38 31 23 14 25 59 12 10 16 11 33 25 33 17 23 31 22 28 38 41 15 10 10
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 14 17  8 29 55 23 26 17 28 13 15 29 16 23 17 12 17 15 16 26  8 19  8 23 25
 33 25 11 29 17 28 25 33  7 14 17 15 25 13 12 17 10 17 23 22 29 13 17 29 15
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 12  4 26  8 23 15 20 15  1 38 20 23 16 20 25 38 28 11 20 17 17 17 15  5 17
 23 17 22 20 16 30  5 46 28  8 16 13 17 28 26 22 10 10  8 10 25 15 12  8 17
 25 20  8 17 20 11 12 22 32 26 23 34  8 28 28 29 20 19 17 20 23 16 10  7 17
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  4  2  5 11 10  5  8 20  8 20 25 17 20 26  7 19 35 30 52 14 20 17 35 20  0
 25 13 10 10 20 19 13 23 16 29 13 25 19 23 20 17 34 34 20 30 23 12 17 26 23
 20 32 16 25 43 10 23  8 33 25 15 22 33 20 31 28 17 20 13 22 28 26 17 12 23
 19 19 17 19 33 25 37 41 17 23 17 16 31 29 33 15 15 11 13 19 23 13  2 10 12
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 30 13 25 38 16 22 23 25 28 17 28 23 17 20 22 15 23 14 32 41 20 19 28 37  4
 16 10 20  7 17 35 22 25 25 43 20 11 12  8 20 10 25 28 17 14 19 13 37 41 35
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 29 16 14 10 28 15 25 46 23 28 25 33 44 35 12 23 28 29 20 23 37 20 17 17  8
 16 20 22 23 17 37 17 17 16 56 23 31 12 31 19  8 47 23 25 16 22 17 23  8 29
 20 25 15 11 22 17 14 23 10 10  4 13 12 17  4  0 11 11 17  2  4  1  0  5  5
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 30 13 16 10  8 15  8 19 20 15 16 22 13 26 34 11 15 26 33 23 30 19 11 26 26
 10 14  5 17 23 22 17 25 17 16 37 34 12 23 12 14 19 16 10 12  8  1 28 10 16
 14 40 16  5 17 32 53 25 16 37 92  0 13 26 23 23 12  8 19 25 17  5 17  4 11
 13 17  4 11  5  4 10  7  4  0  5  8  4  1  2  8  0  2  2  2  4 10 11  2  4
  7  1  8  5  0  5  4  5  5  0  7  2 40  8  5  7  5  2  4  2  8  5  5  2 10
  5 15  8 15  8 10  7  2  7 20 20 15 17 30 11  8 20 35 23 34 34 43 13 26 32
 22 17 13 10 11 16 22 17 16 17 20 16 23 16 28 17 26  8  4 19 25 30  0 17 31
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 13 20 23 25 30 35 32 37 20 17 17 12 35 28 19 23 13 10 10 15 10 25 25 16 11
  8 15 14  8  5  8  8  4  2  8  5  5  2  1  2  2  7  2  2  5  2  2  8  5  5
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 28 32 38 38 26 31 29 25 28 20 23 28 16 22 20 25 92 20 22 15 11 29  8 17 17
 20 31 92 29 20 16 16 31 20 10 23 13 28 12 15  7 28 23 10 15 12 46 10 26 34
 17 14 22 35 20 25 23 19 17 33 12 19 12 11 17 15  7 23  8 13 10 10  5  2 11
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 11 20 19 16 19 12 28 20 15 25 13 14  8 12 17  8 16 20  8 14 31 22 34 22 46
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 10 13 28 17 23 14 11 16 11 20 33 20 33 25 22  4 17 16 34 29 14 22 25 20  5
 13 23 20 10 19 14  8 10  8  0  0  7  2  2  1  2  7  0 10  0  2  5  2  4  4
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 17 28 19 26 28  8 20 11 13 26 23 19 19 12 25 15  7 17 16 30 38 79 11 19 11
 17 17 37 32 28 25 10 20 34 20 23 17 30  5 20 17 17 38 20 15 26 35 23 22 26
 29 32 19 33 67 33 26 28 23 31 33 17 20 17 15 25 29 22 14  8  7 10 14 19  8
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 31 41 41 34 25 30 32 66 28 23  8 15 23 14 10 28  5 26 15 30 30 20 20 17 19
 10 17  8 19 61 22 28 32 23 11 23 14 26 11 17 19 17 16 16 17 20 29 20 17 16
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  5  7 10  5  2  7  4  0  8  2  1  1  2  0  0  2  0  4  2  2  2  4  8  2  4
  0  4  5  2  0  5  2  0  5  7  0  5  4  2  4  5 10  2  2  2  4  4  8  7  2
 14 16 14 25 22 25 22 25 20 32 32  5 29 64 38 23 29 59 16 17 15 19 35 23 25
 12 13 14 23  5 26 41 28 53 29 16 22  8 10 15 22 92 43 31 13 35 10 17 17 10
 15 25 12 25 49 19 23 14 19 11 12 17 17 23  8 12 11 19 26 10  8 11 17 15 11
 11 22 20 10 17 16 20 14 17  7 20 11 12 14 17 10  5  4  7 15  5  2  4  8  0
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 25 23 37 30 14 62 17 35 23 17 16 25 17 11 16 23 16 10 17 35 28 34 17  7 25
 28 28 30 22 25 20 15 22 29 23 23 20 33 23 20 17 20 25 20 15 16 14 22 20 15
 14 17  1 15 29 14 26 23 10 14 17 20 16 22 32 14 20 19 10 14 12 10 19 17  8
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 16 26  5 20 20  8 34 48 25 29 35 35 28 20 41 41 29 22 38 37 17 23 43 12 30
 13 29 22 23 19 23 29 28 23 12 28 25 35 26 22 41 34 28 34 16 20 22 25 23 61
 17 23 22 22 30 20 17 25 23 11 20 23 19 22  0  8 10  2 16 13 23 15  8  5 12
 19 20 17 20 29 10 13  8 26 16 17  2 19  1 16  8  2 16 12  5  1  0  8  1  0
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 26 25  5 10 46 20 22 23 31 22 37 15 23 26 22 22 31 92 37 19 15 26 29 25 23
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 25 30 38 30 16 23 26 20 28 31 31 34 47 29 47  5 23 23 34 22 26 11  7 13  8
  4 17  8 14 11 11  5  0  5  5  2  7  5  7 10  4  0  5  8  5  1  5  0  1  5
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 31 37 34 37 28 12 17 23 28 28  8 14 26 17 23 17 19 19 41 31 17 20 29 47 26
 30 25 20 28 22 25 20 43 31 33  4 28 11 17 46 22 22 13 17 23 19 16 23  7 12
 13 25 22 17 19 17 17  8 30 10 28 23 14 22 30 23 13 17 15 14  2 19 12 26 10
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 34 92 19 14 19 12 23 19 10 12 16 41 13 17  7 15 55 14 40 30 19 22 16 20 30
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 12 23 16  7  5 10  2 10 11 11  8 10 11  5 12  0  0 10  4  2  0  2  8  5  2
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 19 23  8 15 43 11 30  8 15 17 20 43 25 19 28 23 25 28 40 25 16 17 12 19 29
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 19 15  0 17 11 16 17 14 26 20 15 10 20 15 20 20 15 59 49 20 16 19 12 28 32
 15 17 17 20 13 15 16 10 19 25 12 15 30 23 12 20 13 13 16 17 20 28 25 12 13
 31 25 35 50 29 25 23 20 23 25 17 17 11 15  8  7 11 15 13 14 10 13  8 13  8
  7  7 10  7  7 11 10  8  2  0  5  2  1  0  2  0  0  4  4  5  0  4 10 11  8
  8 10 13 19 19 10 22 16 11 14 17 17 30 26 23 34 20 37 31 23 22 26 43 35 26
 15 16 20 13 13 19 16 23 19 13 20 25 25 10 25 25 16 17 23 20 26 16 17 17 23
 13 16 19 20 28 19 15 14 32 20 22 17 19 10 11 19 43 38 16 26 10 13 17 20 10
 17 15 17 12 10 10 12 19 14  7  8 10 10 14  5 10  5  4  5  5  2  2  7  2 11
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  2  2  2  5  2  5  0  4  0  2  2  1  2  2  1  1  0  1  0  4  2  0  1  0  2
  4  0  0  4  0  1  5  0  2  0  2  0  0  1  2  1  1  2  0  0 17  5  2  4  5
  2  1  5 12  5  2  5  7  7  5 10 11 15 10  8 11  4 14 10 10 11  8  8 12 13
 13 20 28 17 28 23 17 20 20 20 25 22 25 20 12 10 10 23 11 37 28 33 25 12 23
 26 20 19 35 20 15 10 23 12 17 10 17 22 17 20 14 12 14 20 15 17 14 19 32 12
 19 17 16 17 17 25 38 23 28 10 26 20 17 17 23 32 29 28 26 23 15 31 23 23 10
 15 23  7 14 14 14 17 19 11 15 17 10 17 10  8  8  8  5  7  5  7  5  2 11  1
  5  4  1  5  4  2  7 12 16 10  8  5 14  8 20 25 17 20  7 20 17 15 17 16 25
 23 22 33 29 34 34 30 34 25 43 70 41 14 28 20 15 14 20 15 25 16 15 10 17 23
 28 26 20 19 23 19 19 17 15 10 17 23  8 12 15 13  8 15 25 15 17 13 17 23 10
  7 10 16 17 16 17 20 14 20 15 22 15 14 19  4 11 13  4  5  5 11 10 10  7 11
  7  4  7  2  5  4  7  2  2  2  5  0  1  2  2  1  0  0  5  5  0  2  0  2  0
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  2  2  2  0  1  2  1  5 11  2  1  0  2  2  2  5  5  2  2  1  0  4  2  2  0
  2  2  2  2  4  2  4  0  0  0  2  1  1  5  2  2  2  0  2  2  0  1  2  2  5
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 23 13 20 17 16 17 17 28 17  5 19 19 20 13 25 23 16 32 22 19 23 11 19 16 10
 12 29 17 23 23 37 28 25 28 31 92 67 13 11 22 17 11 20 28 17 20 16 19 26 26
 10 15 23 37 38 32 35 20 38 17 19 22 11 14 11  8 14 14 17 20  8 16 12 15 17
 17  5 13 10  8  8  4  2  5  5  4 10  5  8  8  1  2  2  2  0  8 11 11  8 10
  5 17 14 20 12 12 13 15  8 12 17 20 11 16 23 35 35 35 28 23 17 31 43 31 25
 25 34 14 20 25 14 25 12 20 20 32 17 17 19 19 17 19 14 19 28 28 17 23 34 14
 23 10  7 23 14 19 15 16 23 23 23  5 13 22 10  4 14 32 17  8  8 11 17 20 12
 15 26 12 10 15  8 12  8  8  8  5  2  8  4 10  8  5  0  2  0  1  0  2  1  4
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 11  8 35 23 17 31 20 17 16 23  8 25 20 20 17 34 14 38 20 19 11 20  8 19 17
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 20 34 32 19 23 29 28 25 25 47 33 31 29 28 25 48 28 32 38 38 23 20 20 19 19
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 10 10 15 13 23 23 16 20 17 31 92 16 29 38 25 25 13 10 20  8 34 26 25 44 43
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 26 22 28 25 30 20 51 31 28 30 23 25 31 26 17 20 38 30 17 25 17 29 20 23 58
 19 17 28 19 38 20 15 26 23 29 28 20 32 26 32 20 25 15 37 33 92 23 14 14 28
 32 31 10 38 20 17 19 17 35 29 16 10 22 12 12  4 20 11  4 17  5  2  5  8  2
  0  5  4  2  0  0  2  1  0  2  5  7  2  4  0  5  1  5 10  4  5  0  2  0  0
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 13  2 11  2 31 12 25 25 25 32 14 16 19  5 25 10  4  8 17 23 26 26 13  7 17
 23 17 13  5 23 30 15 61 26 13 20 10 71 22 12 23 14 20 26 43 10 15 31 16 35
 23 23 40 29 38 23 22 35 37 26 34 38 92 64 51 41 22 30 23 28 23 28 23 28 28
 23 22 22 22 20 19 20  8 10  8 16 10 10 14  8  8 23 13  5 13 10 15  2  2  2
  1 10 14 19 25 20 20 20  8 20 17 37 13 20 29 28 29 35 35 46 40 41 35 25 32
 20 25 32 44 33 31 33 32 17 19 20 25 20 23 25 23 25 33 25 20 23 33 17 17 11
 20 28 23 22 17 31 26 34 35 10 79 17 23 32 34 14 17 33 12 23 23 25 23 10 11
 20 10 12  8 23 17 17  8  7  4  2  2  8 11  2  8  5  0  2  1  2  5  2  2  4
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  0  0  2  2  4  2  4  0  1  7  2  1  0  0  2  5  0  0  0  2  5  2  5  5  2
  0  4  0  5  2  4  5  8  2 17 23 29  5 23 23 25 38 16 20 25 65 14 20 30 20
 34 13 13 20 26  7 19 13 25 25 13 23  8 17 11 20 10 15 15 12 13  7 13 14 15
 16 16 20 14 25 10 38 23 23 12 26 29 20 43 25 38 32 22 40 44 26 46 37 26 33
 46 34 32 56 29 28 28 41 40 41 23 41 16  8 28 25 14 13 19 16 10 17  8 12 12
 16 15 14 19 14  5 14  2  8  7 11  8  5 10  8  5 11 14  5 37 28 28 28 17 25
 23 10 15 35 17 20 28 50 35 35 28 25 17 23 17 23 25 25 16 30 15 20 23 76 20
 30 23 14 56 17 19 19 28 17 29 25 28 31 26 25 28 64 20 22 23 33 26 32 37 26
 26 33 92 31  8 20 20 19 23 28 17 17 17 13  7 12  2 10  8 10 10  2  5  0 13
  1  0  5  5  5  1  2  2  8  1  5  2 17  4  5  2  0  0  0  0  4 14  0  2  0
  2  2  0  2  0  4  0  0  0  4  4  1  1  4  2  5  0  0  2  0  0  5  0  2  2
  4  7  2 11  8  7  2  2  0  2  4  5  0  0  8  4  0  1 15  1  0  2  0  0  0
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  0  7  4  5  2 10  2  2  0  0  2  5  8  2  1  2  2  2  2  5  2  8  2  4  0
  2  4  0  4  1  4  2  2  0  4  5  2  0  2  0  4  4  0  7 10  0  2 10 16 12
  8 25  4 14 20 23 11 25 23 10 20 22 17 40 25 17 16 23 17 16 34  0 22 28 41
 23 12  8 12 17 12 70 14 22 11 25 40 25 15  8 19 16 23 25 40 28 37  8 35 34
 23 16 23 38 33 22 23 28 53 34 33 43 35 35 53 48 25 46 52 35 23 19 38 12 25
 15 17 17 22 15 15 28 32 17 12 22 12 15 12 10 10 13 13  2  4 15 15 10  2  2
  5  0  8 11 16 28 14 20 14 20 33 30 20 17 14 20 38 56 40 37 44 50 58 31 26
 49 46 25 22 12 44 25 32 17 20 15 16 40 25 16 22 29 26 25 23 22 33 26 20 25
 35 23 20 26 48 10 23 14 12 33 28 23 17 28 17 13 22 20 10 19 14 22 19 22 12
 17 20 14  5 10  5  5  5  2  7  7  5  2  5  5  5  4  7  5  0  5  1  2  2  5
  0  2  5  0  1  2  4  0  4  4  0  5  0  4  5  2  1  5  5  4  7  2  5 17  4
  2  0  5  2  0  2  4  4  4  5  8  0  2  4  0  1  2  0  1  4  0 10  1  5  2
  4  4  2  0  0  0  5  5 15  0  2  5  0  1  5  8  1  2  0 22  2  2  1  0  2
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  0  2  5  4  0  0  5  2  0  2  0  1  0  0  0  4  4  1  2  0  2 20  2  7  4
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 25 29 20 33 11  8 25 16 23 16 15 12 16 13 10  8 15 10 23  5 17 11 20 20 19
 17 25  5  8 13 20 46 79 20 43 17 28 50 28 37 26 16 51 29 74 40 38 33 30 84
 33 29 43 32 41 67 43 70 29 53 43 26 23 23 19 33 22 28 23 17 25  8 16 12 12
  8 13 16  8 20 23 12  5  5  2  0  1  2  4  5 17 10 14 25 17 17 20 17 20 17
 12 31 31 14 25 40 38 40 28 43 38 51 32 30 43 26 35 31 56 40 23 56 14 25 29
 17 20 17 25 23 19 17 25 10 20 23 40 25 55 44 34 26 29 20 19 17 28 19 35 33
 37 20 33 20 25 29 20 32 17 25 13 10  4  8  8 10  4  2  5  4  2  5  5  7  2
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  2  2  5  4  2  4  4  2  0  0  2  2  0  5  0  2  0 17  2  4  2 12  2  7  4
 16 10 25  4  2  4 15 20 20 10 14 31  7 14 23 20 17 25  8 30 13 19 20 23 20
 16 29 16  1 14  8 13  8 10 12  8 53 25 16 11 15 17 23 15 19 16 33 16 26 11
 22 22 11 41 28 32 23 32 17 50 31 44 25 29 31 44 31 44 48 41 35 25 22 53 35
 25 25 13 37 35 17 17 20 13 25 10 10 17 14 10 10 19 10 22 10 20 20 10  4 11
  4  2  4  5 17 28 32 23 16 17 25 35 13 30 25 33 23 37 23 34 58 41 53 43 47
 56 38 38 33 48 20 32 34 35 25 23 29 35 12 30  2 29 16 23 13 15 20 48 19 26
 23 10 47  8 29 25 23 23 29 28 17 56 13 28 26 38 50 28 33 16 23 20 17 13 10
  7 12 14  7  5  5 10 12  2  8  0  7  8  0  0  5  5  2  5  0  4  4  2  4  0
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 20 22 17 25 23 28 26 16 23 20 28 32 25 25 13 17 25 35 25 19 32 37 35 34 52
 23 28 28 43 35 41 43 62 46 46 64 20 55 38 13 25 30 26 33 29 19 12 17 17 16
 12  5 11 15 13 11 14 19 22 10  2  5  8  8  7  5 14 13 11 12 17 10 20 20 14
 19 22 19 25 25 32 43 28 28 38 38 52 46 46 41 29 38 16 29 37 29 33 38 30 26
 23 13 19 19 19 25 30 23 17 29 26 14 31 19 19 19 11 35 10 17 28 17 30 19 35
 17 23  0 43 43 35 25 17 17 16 13 16 13 25  0  4  5  5  2  5  5  2  2  0  2
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 48 23 28 14 35 19 12 17 13 13 10  7  8  8 13  0  2  4 10  4  5  5  5  2  2
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 13 17 20 16 25 11 16  1 17 10 11  1  7  8 10 10 26 20 20 13 16 65 17 28 25
 25 23 43 25 35 28 25 35 26 22 34 28 25 51 38 20 33 35 23 43 26 28 29 38 65
 44 48 46 46 31 10 35 20 23 17 17 11 16 22 15 10 17 19 15 14 20 20 12 20 25
 17  7  0  8 15  2  2  4  5 20 31 13 22 16 16 52 16 16 17 23 25 41 31 61 64
 51 49 49 53 92 44 74 41 26 25 28 20 58 41 43 12 28 29 23 25 25 12 25 17 28
 34 30 15 30 35 17 12 28 43 25 20 22 31 38 10 38 32 17  8 10 11 26 14 15 10
 13  2 10  5  5  4  7  0  5  5  8  8  5  2  1  0  5  4  8  2 10  5  2  2  4
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 11  4  8 10 12  2  8 14 17 19 12 10  8 17 25 26 22 28 16 15  2 32 25  2  8
  8 20  8 11 12 13 22  5  8 41 25 16 26 23 22 28 34 14 20 28 32 20  8 32 25
 48 37 33 33 35 17 50 28 20  2 47 56 40 28 28 35 92 43 11 35 17 25 20 20 17
 15 29 17 25 32 10 16 17 12 23 30 17  5 15  4  7 10  8  5 15  0 12 10 29 23
 17 10 31 25 20 56 37 34 23 23 37 33 37 49 30 35 53 62 43 38 25 38 23 30 26
 23 20 17 35 29 26 20 40 17 19 19 23 41 28 31 22 31 16 20 17 34 12 25 35 41
 26 35 22 30 17 16 10 17 14 10 10  2 10 13 10  5  7  2  8  4  5  5  8  5 14
  5  7  4  2  5  2  4  5  5  2  5  7  0  2  8  7  2  0  2  0  2  7  1  4  1
  0  4  5  2  2  2  4  5  2  0  2  2  0  2 17  5  1  4  2  2  8  2  0  5  4
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 29 38 29 59 25 30 38 47 43 20 58 52 56 70 43 44 35 41 29 43 29 22 32 23 34
 17 11 28 11  8 16 14 15 14 19 20 23 22 35 17 20 20 23  8 12 16  7  0 10  7
 10 22 11 13 28 17 38 43 19 20 29 35 38 61 22 38 46 56 32 43 30 53 48 34 31
 35 67 48 40 35 30 35 37 29 23 22 28 37 25 25 32 33 56 17 34 34 38 38 22 23
 14 23 17 32 10 15 19 16  2 20 17 13  0  4  0  7  7 10 10 11  2  2  4  0  2
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 53 22 11 26 20 35 38 23 28 16 20 16 26 17 31 23 35 16 20 25 28 17 15 19 28
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 14 16 13 10 20 15 10 10 15  8  2 10  7 16 10 19  8  4 26 26 25 20 20 17 25
 38 31 59 41 25 40 23 17 40 32 35 28 22 25 49 14 38 13 17 13 20 43 30 25 17
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 26 32 46 22 43  0 17 25 41 26 17 43 31 13 20 17 33 35 23 22 23 29 29 31 37
 38 28 25 16 16 20  5 17 13  8  2  8  4  1 14  7  2  0 13  2  4  2  2  4 10
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 34 38 32 31 28 20 25 17 26 28 34 74 22 20 25  8 34 29 16 20 15  5 33 28 25
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  0  4  2  4 10  4  1  5  4  0  7  7  2  0  0  0  8  1  2  2  4  2  2  5  0
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 15 28  5 11 23 15 13 17  5  7 13 22 23 10  2  8 10  5 12 16 16 12  5  8 10
 12  5 15 10 15  8  8  8  5 13 14 25  4  0  0  1  0  2  0  0  2  4  7  2  0
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 10  7  4  0  5  2  5  5  0  0  2  2  0  0  2  0  2  5  2  0  4  7  7  0  4
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 56 51 22 29 25 32 17 35 28 25 34 35 20 37 25 28 25 23 20 22 20 13 20 19 17
 19 15 12 22 10 13 26 13 13 13 23 17 17 17 38 22  8 12 10 15 17 15 26 20  5
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  8  2  5  0  0  5  2  0  2  2  2  0  2  2  0 13  5  0  0  2  7  0  1  4  0
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 10 20 22 13 17 23  2  7 20  7 23 38 19 35 22 10 25 28 26 23 44 51 67 69 26
 12 23  4 14 13 11 20 17 20 20 17 23 38 20 17 17 11 15 23 23  0  8 17 25  8
 20 16 20 17 31 33 10 15 23 14 10 11 10 12  7 11  8  7  2  0  7  4  0 15  2
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  4  1  0  4  2  5  2  0  0  0  4  0  4  4  5  0  0  2  0  2  0  2  0  4  0
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  2  2  1  0  2  0  5  0  4  2  2 12  2 10  5 10 12 11  8 16  5 20 20  1 17
 14 19 19 17 23 26 26 44 35 55 68 31 26 17 29 25 22 11  8 13 25 25 46 38 56
 22 13 14 19 17 37 12 10 16 22 19  8 10 14 17 14 25 11 17 13 17 17 19 14 12
 10 12  5 14  7  2  2  5  5  7  5  2  0  0  1  2  2  4  2  2  2  5  2  2  0
  2  0  0  7  4  2  2  0  0  1  0  2  1  5  0  2  0  0  2  4  2  0  5  0  0
  1  0  2  2  2  1  2  0  2  0  2  2  0  0  0  5  0  2  0  0  0 30  2  5  0
  4  4  0  0  2  4  4  0  5  2  0  0  5  0  2  8 15  4  2  2  0  0  2  2  4
  0  4  0  0  0  2  1  4  0  2  1  2  7  0  7  2  2  2  2  2  1  1  2  1  1
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 22 17 31 17 25 17 23 17  4 12 10 12 20 15 15 14 17 17 20 17 19 20 23 28 19
 23 28 22 28 15 14 23 22 16 44 14 25 16 25 32 14 25 11 12 12 25  2  5 11 13
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  2  2  0  4  2  5  2 17  2  0  2  0  0  0  0  2  0  4  0  0  8  5  5  0  2
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  0  4  2  2  0  2  2  2  0 10  5  5  0 10  5  1  0  5  0  0  2  1  0 12  2
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  0 11  0  2  1  2  2  4  2  7  4  2  5  1  1  0  2  5  0 28  4 14 22  0  7
 13 17 25 10 25  7 15 22  4  5  7  5 23 13 15 14 16 12 12 16 19 13 11  2  0
 16  4 23 12  7 19 22 15 20 20 12 23 23 26 25 28 12 11 20 16 20 23 28 29 22
 28 35 33 25 10 19 17 10  8  8 10  5 13  8 15  8  8 13  7 11  5  8  8  7  2
  7 10  2  4  7  8  4  5  0  2  1  0  5  0  0  4  0  2  2  4  2  2  4  0  0
  0  4  2  4  0  2  2  2  2  2  0 10  0  2  0  0  0  4  2  1  1  5  2  1  0
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  2 10  2  0  2  4  4  2  2  2  4  7  2  1  0  0 14  2  2  4  0  0  5  5  7
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  4  0  5  2  1  1  5  2  0  5  4  4  1  4  2  0  0  5  1  2  2  1  4  2 10
  0  1  2  2  2  2 15  4  0  0  0  0  5  2  0  5  2  0  0  4  0  0  2  5  8
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  4  2  4  4  0  4  2  0  4  4  5  1  5  0  0  4  7  2  2  1  0  8  0  2  5
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  8  5  4  7  0  5  1  5  1  5  2  5  2  7  0  0  0  0  1  4  2  0  0  1  1
  4  0  2  4  2  7  0  0  2  5  0  0  7  1  1  1  2  0  1  8  2  8  0  4  8
  4  7  1  8  4  2  4  0  4  8  2  7 13 12 13 17 11 10 15 26 22 10  5 17 13
 17  1 16 10  8 17 11  8 10  8  5 13 19 15 22 12 12  8 26 13 22 17 11 19 12
 29 28 23 17 17 29 20 30 15 19 25 29 17 30 20 22 30 11 25 17 10  2 10  7  5
  5 17 10  0  2 14  5  4  8  8  5  5  7  4  2  2  4  7  2  4  5  2  5  2  5
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 14  2  1  2  4  2  0  2  2  4  0  0  0  0  2  2  0  2  2  5  0  0 10  0  0
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 11  8  2  0  5  1  4  2  5  4  2  0  0  2  4  0  2  0  0  1  0  2  4  4  4
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 10  0  0  2  1  4  5  4  0  2  5  0  5  0  1  2  1  0  1  2  2  2  0  1  2
 12  5  0  0  1  4  4  0  4  5  0  1  5  5  4  2  1  0  1  4 10  2  2  0  2
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  4  5  0  2  4  1  2  2  1  4  5  5  0  4  1  4  2  1  2  2  0 15  2  5  0
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  0  0  2  4  1  0  0  4  5  4  8  0  0  0  4  2  2  2  8  2  2  0  4  1  0
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 10  8  0  0  0  0  0  2  8  0  5  0  1 12  2  2  0  0  0  2  1  5  4  4  2
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1337332
 










    
























In [14]:



    


print " "
imgnorm = imgflat*1.0/sum(imgflat)

fig = plt.hist(imgnorm, bins = 'auto')
plt.title('Normalized Histogram')
plt.show



    


















    






 










    
Out[14]:








<function matplotlib.pyplot.show>










    
























In [15]:



    


newimg = np.empty(im.shape)
## This should be the same exact dimensions as the original array
print im.shape

## set x_length to the first number, y_length to the second
x_length = im.shape[0]
y_length = im.shape[1]

print x_length, y_length

for i in range(x_length):
    for j in range(y_length):
        newimg[i][j] = norm_cdf[ im[i][j] ]

print newimg



    


















    






(728, 1438)
728 1438
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   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
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   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
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   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.]]

















In [26]:



    


fig = plt.hist(im, bins = 'auto')
plt.title('Normal Histogram')
plt.show



    


















    
Out[26]:








<function matplotlib.pyplot.show>










    
























In [16]:



    


fig = plt.hist(newimg, bins = 'auto')
plt.title('Equalized Histogram')
plt.show



    


















    






/usr/local/lib/python2.7/site-packages/matplotlib/axes/_axes.py:5907: UserWarning: 2D hist input should be nsamples x nvariables;
 this looks transposed (shape is 728 x 1438)
  '(shape is %d x %d)' % inp.shape[::-1])










    
Out[16]:








<function matplotlib.pyplot.show>










    
























In [17]:



    


#728 1438
for i in range(728):
    for j in range(1438):
        newimg[i][j] = norm_cdf[ im[i][j] ]

print '+-------+-----------+-----+----------------+'
print '| %5s | %9s | %3s | %14s |' % ('Value', 'Histogram', 'cdf', 'Normalized cdf')
print '+-------+-----------+-----+----------------+'
for i in range(255):
    if hist[i] == 0: continue
    print '| %5s | %9s | %3s | %14s |' % (i, hist[i], cdf[i], norm_cdf[i])
print '+-------+-----------+-----+----------------+'



    


















    






+-------+-----------+-----+----------------+
| Value | Histogram | cdf | Normalized cdf |
+-------+-----------+-----+----------------+
|     0 |    793273 | 793273 |        3210862 |
|     1 |     32538 | 825811 |        3342564 |
|     2 |     90886 | 916697 |        3710436 |
|     4 |     38341 | 955038 |        3865625 |
|     5 |     37845 | 992883 |        4018808 |
|     7 |     10750 | 1003633 |        4062320 |
|     8 |     10592 | 1014225 |        4105192 |
|    10 |      5950 | 1020175 |        4129275 |
|    11 |      2231 | 1022406 |        4138305 |
|    12 |      2092 | 1024498 |        4146773 |
|    13 |      1921 | 1026419 |        4154549 |
|    14 |      1681 | 1028100 |        4161353 |
|    15 |      1600 | 1029700 |        4167829 |
|    16 |      1510 | 1031210 |        4173941 |
|    17 |      2776 | 1033986 |        4185177 |
|    19 |      1163 | 1035149 |        4189884 |
|    20 |      2038 | 1037187 |        4198133 |
|    22 |       883 | 1038070 |        4201707 |
|    23 |      1517 | 1039587 |        4207848 |
|    25 |      1333 | 1040920 |        4213243 |
|    26 |       600 | 1041520 |        4215672 |
|    28 |       944 | 1042464 |        4219493 |
|    29 |       447 | 1042911 |        4221302 |
|    30 |       366 | 1043277 |        4222783 |
|    31 |       326 | 1043603 |        4224103 |
|    32 |       329 | 1043932 |        4225435 |
|    33 |       274 | 1044206 |        4226544 |
|    34 |       246 | 1044452 |        4227539 |
|    35 |       407 | 1044859 |        4229187 |
|    37 |       198 | 1045057 |        4229988 |
|    38 |       312 | 1045369 |        4231251 |
|    40 |       137 | 1045506 |        4231805 |
|    41 |       221 | 1045727 |        4232700 |
|    43 |       178 | 1045905 |        4233420 |
|    44 |        76 | 1045981 |        4233728 |
|    46 |       123 | 1046104 |        4234226 |
|    47 |        53 | 1046157 |        4234440 |
|    48 |        52 | 1046209 |        4234651 |
|    49 |        43 | 1046252 |        4234825 |
|    50 |        33 | 1046285 |        4234959 |
|    51 |        28 | 1046313 |        4235072 |
|    52 |        34 | 1046347 |        4235210 |
|    53 |        53 | 1046400 |        4235424 |
|    55 |        22 | 1046422 |        4235513 |
|    56 |        59 | 1046481 |        4235752 |
|    58 |        35 | 1046516 |        4235894 |
|    59 |        16 | 1046532 |        4235958 |
|    61 |        27 | 1046559 |        4236068 |
|    62 |        13 | 1046572 |        4236120 |
|    64 |        28 | 1046600 |        4236234 |
|    65 |         8 | 1046608 |        4236266 |
|    66 |        12 | 1046620 |        4236315 |
|    67 |         9 | 1046629 |        4236351 |
|    68 |         5 | 1046634 |        4236371 |
|    69 |         8 | 1046642 |        4236404 |
|    70 |         9 | 1046651 |        4236440 |
|    71 |        12 | 1046663 |        4236489 |
|    73 |        11 | 1046674 |        4236533 |
|    74 |        10 | 1046684 |        4236574 |
|    76 |        11 | 1046695 |        4236618 |
|    77 |         3 | 1046698 |        4236630 |
|    79 |         8 | 1046706 |        4236663 |
|    80 |         4 | 1046710 |        4236679 |
|    82 |         7 | 1046717 |        4236707 |
|    83 |         3 | 1046720 |        4236719 |
|    84 |         2 | 1046722 |        4236727 |
|    85 |         3 | 1046725 |        4236740 |
|    86 |         4 | 1046729 |        4236756 |
|    87 |         6 | 1046735 |        4236780 |
|    89 |         2 | 1046737 |        4236788 |
|    91 |         2 | 1046739 |        4236796 |
|    92 |       125 | 1046864 |        4237302 |
+-------+-----------+-----+----------------+

















In [18]:



    


print newimg



    


















    






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   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.  3210862.  3210862.  3210862.  3210862.
   3210862.  3210862.  3210862.]]

















In [19]:



    


print ''
print 'Original subimage:'
print ''
for i in range(728):
    print ('%4d'*8) % tuple(im[i])



    


















    






Original subimage:











    






---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-19-131bd9fc2c29> in <module>()
      3 print ''
      4 for i in range(728):
----> 5     print ('%4d'*8) % tuple(im[i])
      6 

TypeError: not all arguments converted during string formatting
















In [20]:



    


print ''
print ''
print 'Equalized subimage:'
print ''

for i in range(728):
    print ('%4d'*8) % tuple(newimg[i])



    


















    







Equalized subimage:











    






---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-20-7b2503e252d1> in <module>()
      5 
      6 for i in range(728):
----> 7     print ('%4d'*8) % tuple(newimg[i])

TypeError: not all arguments converted during string formatting
















In [21]:



    


imgflat = im.reshape(-1)

print " "
fig = plt.hist(imgflat, bins='auto')
plt.title('Original Histogram')
plt.show()



    


















    






 










    
























In [22]:



    


print 'Equalized subimage:'
print ''

fig = plt.hist(newimg, bins = 'auto')
plt.title('Equalized Histogram')
plt.show



    


















    






Equalized subimage:











    
Out[22]:








<function matplotlib.pyplot.show>










    
























In [24]:



    


newimgflat = newimg.reshape(-1)

print 'Equalized subimage:'
print ''

fig = plt.hist(newimgflat, bins = 'auto')
plt.title('Equalized Histogram')
plt.show



    


















    






Equalized subimage:











    
Out[24]:








<function matplotlib.pyplot.show>










    
























In [27]:



    


fig = plt.hist(imgflat, bins=255)
plt.title('Original Histogram')
plt.show()



    


















    
























In [28]:



    


newimgflat = newimg.reshape(-1)
fig = plt.hist(newimgflat, bins = 255)
plt.title('Equalized Histogram')
plt.show



    


















    
Out[28]:








<function matplotlib.pyplot.show>

Content source: alee156/NeuroCV

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