In [1]:

    

from __future__ import division, print_function
%matplotlib inline
import math,sys,os,numpy as np
from numpy.linalg import norm
from PIL import Image
from matplotlib import pyplot as plt, rcParams, rc
from scipy.ndimage import imread
from skimage.measure import block_reduce
import pickle
from scipy.ndimage.filters import correlate, convolve
from ipywidgets import interact, interactive, fixed
from ipywidgets.widgets import *
rc('animation', html='html5')
rcParams['figure.figsize'] = 3, 6
%precision 4
np.set_printoptions(precision=4, linewidth=100)


    

In [2]:

    

"""
"""
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("data/MNIST_data/")
images, labels = mnist.train.images, mnist.train.labels
images = images.reshape((55000,28,28))
np.savez_compressed("data/MNIST_data/train", images=images, labels=labels)


    

    




Extracting data/MNIST_data/train-images-idx3-ubyte.gz
Extracting data/MNIST_data/train-labels-idx1-ubyte.gz
Extracting data/MNIST_data/t10k-images-idx3-ubyte.gz
Extracting data/MNIST_data/t10k-labels-idx1-ubyte.gz

In [3]:

    

def plots(ims, interp=False, titles=None):
    ims=np.array(ims)
    mn,mx=ims.min(),ims.max()
    f = plt.figure(figsize=(12,24))
    for i in range(len(ims)):
        sp=f.add_subplot(1, len(ims), i+1)
        if not titles is None: sp.set_title(titles[i], fontsize=18)
        plt.imshow(ims[i], interpolation=None if interp else 'none', vmin=mn,vmax=mx)

def plot(im, interp=False):
    f = plt.figure(figsize=(3,6), frameon=True)
    plt.imshow(im, interpolation=None if interp else 'none')

plt.gray()
plt.close()


    

In [4]:

    

data = np.load("data/MNIST_data/train.npz")
images=data['images']
labels=data['labels']
n=len(images)
images.shape


    

    
Out[4]:





(55000, 28, 28)

In [5]:

    

plot(images[0])


    

In [6]:

    

labels[0]


    

    
Out[6]:





7

In [7]:

    

plots(images[:5], titles=labels[:5])


    

In [8]:

    

top=[[-1,-1,-1],
     [ 1, 1, 1],
     [ 0, 0, 0]]

plot(top)


    

In [9]:

    

r=(0,28)
def zoomim(x1=0,x2=28,y1=0,y2=28):
    plot(images[0,y1:y2,x1:x2])
w=interactive(zoomim, x1=r,x2=r,y1=r,y2=r)
w


    

In [10]:

    

k=w.kwargs
dims = np.index_exp[k['y1']:k['y2']:1,k['x1']:k['x2']]
images[0][dims]


    

    
Out[10]:





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In [11]:

    

corrtop = correlate(images[0], top)


    

In [12]:

    

corrtop[dims]


    

    
Out[12]:





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        -0.098 , -0.098 , -0.098 ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.4431,  1.1569,  1.4196,  0.9333,  0.1137,
        -0.6941, -1.298 , -1.9451, -2.2078, -2.3686, -1.9098, -1.3686, -0.6196, -0.3255, -0.1098,
        -0.349 , -0.349 , -0.298 ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.2196,  0.3569,  0.051 , -0.8745, -1.902 ,
        -2.0471, -1.6902, -0.9216, -0.4706, -0.1216,  0.    ,  0.1882,  0.3098,  0.3098,  0.0941,
        -0.1882, -0.1882, -0.1608,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    , -0.5922, -1.102 , -1.7922, -1.4431, -0.9333,
        -0.2431,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.1412,  0.2314,  0.2314, -0.1765,
        -0.2667, -0.2667,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    , -0.0706, -0.5569, -0.5569, -0.4863,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.2157,  0.2157,  0.1529, -0.4902,
        -0.4902, -0.4275,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.8235,  1.2588,  1.2588,  0.1608, -0.498 ,
        -0.498 , -0.2235,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.1255,  0.1412,  0.0824, -0.4784, -0.4941,
        -0.4353,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.349 ,  0.3843,  0.3333, -0.6157, -0.8745, -0.8235,
        -0.2235,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    ,  0.0196,  0.4784,  0.4588,  0.1098, -0.6863, -0.6667, -0.3373,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    , -0.0039, -0.3529, -1.0471, -1.6588, -1.3098, -0.6157,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    , -0.0157, -0.4745, -0.7451, -0.7294, -0.2706,  0.    ,  0.    ,
         0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ]], dtype=float32)

In [13]:

    

plot(corrtop[dims])


    

In [14]:

    

plot(corrtop)


    

In [15]:

    

np.rot90(top, 1)


    

    
Out[15]:





array([[-1,  1,  0],
       [-1,  1,  0],
       [-1,  1,  0]])

In [16]:

    

convtop = convolve(images[0], np.rot90(top,2))
plot(convtop)
np.allclose(convtop, corrtop)


    

    
Out[16]:





True






    

In [17]:

    

straights=[np.rot90(top,i) for i in range(4)]
plots(straights)


    

In [18]:

    

br=[[ 0, 0, 1],
    [ 0, 1,-1.5],
    [ 1,-1.5, 0]]

diags = [np.rot90(br,i) for i in range(4)]
plots(diags)


    

In [19]:

    

rots = straights + diags
corrs = [correlate(images[0], rot) for rot in rots]
plots(corrs)


    

In [20]:

    

def pool(im): return block_reduce(im, (7,7), np.max)

plots([pool(im) for im in corrs])


    

In [21]:

    

eights=[images[i] for i in range(n) if labels[i]==8]
ones=[images[i] for i in range(n) if labels[i]==1]


    

In [22]:

    

plots(eights[:5])
plots(ones[:5])


    

In [23]:

    

pool8 = [np.array([pool(correlate(im, rot)) for im in eights]) for rot in rots]


    

In [24]:

    

len(pool8), pool8[0].shape


    

    
Out[24]:





(8, (5389, 4, 4))

In [25]:

    

plots(pool8[0][0:5])


    

In [26]:

    

def normalize(arr): return (arr-arr.mean())/arr.std()


    

In [27]:

    

filts8 = np.array([ims.mean(axis=0) for ims in pool8])
filts8 = normalize(filts8)


    

In [28]:

    

plots(filts8)


    

In [29]:

    

pool1 = [np.array([pool(correlate(im, rot)) for im in ones]) for rot in rots]
filts1 = np.array([ims.mean(axis=0) for ims in pool1])
filts1 = normalize(filts1)


    

In [30]:

    

plots(filts1)


    

In [31]:

    

def pool_corr(im): return np.array([pool(correlate(im, rot)) for rot in rots])


    

In [32]:

    

plots(pool_corr(eights[0]))


    

In [33]:

    

def sse(a,b): return ((a-b)**2).sum()
def is8_n2(im): return 1 if sse(pool_corr(im),filts1) > sse(pool_corr(im),filts8) else 0


    

In [34]:

    

sse(pool_corr(eights[0]), filts8), sse(pool_corr(eights[0]), filts1)


    

    
Out[34]:





(126.77776, 181.26105)

In [35]:

    

[np.array([is8_n2(im) for im in ims]).sum() for ims in [eights,ones]]


    

    
Out[35]:





[5223, 287]

In [36]:

    

[np.array([(1-is8_n2(im)) for im in ims]).sum() for ims in [eights,ones]]


    

    
Out[36]:





[166, 5892]

In [37]:

    

def n1(a,b): return (np.fabs(a-b)).sum()
def is8_n1(im): return 1 if n1(pool_corr(im),filts1) > n1(pool_corr(im),filts8) else 0


    

In [38]:

    

[np.array([is8_n1(im) for im in ims]).sum() for ims in [eights,ones]]


    

    
Out[38]:





[5129, 254]

In [39]:

    

[np.array([(1-is8_n1(im)) for im in ims]).sum() for ims in [eights,ones]]


    

    
Out[39]:





[260, 5925]