import numpy as np
from scipy import signal
from scipy import misc
import matplotlib.pyplot as plt# %matplotlib inlineimg = misc.ascent()
kernel = np.random.randn(5,5)
# kernel = np.array([[0,-10,0,10,0],[-10,-30,0,30,10],[0,-10,0,10,0]])img = img.astype(np.float32)/255
orig_in = imgoffsetx = offsety = 20
shift_in = np.zeros(orig_in.shape)
shift_in[offsetx:,offsety:] = img[:-offsetx,:-offsety]rot_in = misc.imrotate(img, 90)
scale_in = misc.imresize(orig_in, 1.5)output1 = signal.convolve2d(orig_in, kernel, mode='same')
output2 = signal.convolve2d(shift_in, kernel, mode='same')
output3 = signal.convolve2d(rot_in, kernel, mode='same')
output4 = signal.convolve2d(scale_in, kernel, mode='same')

fig, axes = plt.subplots(2, 4, figsize=(14, 7))
ax_orig = axes[0,0]
ax_shift = axes[0,1]
ax_rot = axes[0,2]
ax_scale = axes[0,3]diff_orig = axes[1,0]
diff_shift = axes[1,1]
diff_rot = axes[1,2]
diff_scale = axes[1,3]ax_orig.imshow(output1, cmap='gray')
ax_orig.set_title('Original')
ax_shift.imshow(output2, cmap='gray')
ax_shift.set_title('Shifted')
ax_rot.imshow(output3, cmap='gray')
ax_rot.set_title('Rotated')
ax_scale.imshow(output4, cmap='gray')
ax_scale.set_title('Scaled')def shift(arr, offset):
output = np.zeros(arr.shape)
output[offset:, offset:] = arr[:-offset,:-offset]
return outputdef rotate(arr, angle):
return misc.imrotate(arr, angle)def resize(arr, scale):
return misc.imresize(arr, scale)diff_orig.hist(np.ravel(output1),bins=100)
diff_orig.set_title('Output histogram')
diff_shift.hist(np.ravel(np.abs(output2-shift(output1, 20))),bins=100)
diff_shift.set_title('Shift histogram difference')
diff_rot.hist(np.ravel(np.abs(output3-rotate(output1, 10))),bins=100)
diff_rot.set_title('Rotate histogram difference')
diff_scale.hist(np.ravel(np.abs(output4-resize(output1, 1.5))),bins=100)
diff_scale.set_title('Scale histogram difference')ax_orig.set_xticks([])
ax_shift.set_xticks([])
ax_rot.set_xticks([])
ax_scale.set_xticks([])ax_orig.set_yticks([])
ax_shift.set_yticks([])
ax_rot.set_yticks([])
ax_scale.set_yticks([])plt.tight_layout()
# plt.show()
plt.savefig('images/conv_equivariance.png')

import numpy as np
np.random.seed(101)from scipy import signal
from scipy import misc
import matplotlib.pyplot as plt
%matplotlib inlineimg = misc.ascent()
img = img.astype(np.float32)/255# The image is more interesting here
orig_in = img[-200:,-300:-100]
offsetx = offsety = 15
shift_in = img[-200-offsetx:-offsetx,-300-offsety:-100-offsety]
kernel1 = np.random.randn(5,5)
kernel2 = np.random.randn(5,5)
kernel3 = np.random.randn(5,5)def sigmoid(arr):
# Lazy implementation of sigmoid activation
return 1./(1 + np.exp(-arr))def maxpool(arr, poolsize, stride):
# Lazy looping implementation of maxpool
output_shape = np.floor((np.array(arr.shape)-poolsize)/stride)+1
output_shape = output_shape.astype(np.int32)
output = np.zeros(output_shape)
for x in range(output_shape[0]):
for y in range(output_shape[1]):
output[x,y] = np.max(arr[x*stride:x*stride+poolsize,y*stride:y*stride+poolsize])
return outputoutput1_1 = signal.convolve2d(orig_in, kernel1, mode='valid')
pool1_1 = maxpool(output1_1, 2, 2)
actv1_1 = sigmoid(pool1_1)
output1_2 = signal.convolve2d(actv1_1, kernel2, mode='valid')
pool1_2 = maxpool(output1_2, 2, 2)
actv1_2 = sigmoid(pool1_2)
output1_3 = signal.convolve2d(actv1_2, kernel3, mode='valid')
pool1_3 = maxpool(output1_3, 2, 2)output2_1 = signal.convolve2d(shift_in, kernel1, mode='valid')
pool2_1 = maxpool(output2_1, 2, 2)
actv2_1 = sigmoid(pool2_1)
output2_2 = signal.convolve2d(actv2_1, kernel2, mode='valid')
pool2_2 = maxpool(output2_2, 2, 2)
actv2_2 = sigmoid(pool2_2)
output2_3 = signal.convolve2d(actv2_2, kernel3, mode='valid')
pool2_3 = maxpool(output2_3, 2, 2)fig, axes = plt.subplots(4, 3, figsize=(10, 10))k1, k2, k3 = axes[0,:]
p1_1, p1_2, p1_3 = axes[1,:]
p2_1, p2_2, p2_3 = axes[2,:]
h1, h2, h3 = axes[3,:]k1.imshow(kernel1, cmap='gray')
k1.set_title('kernel1')
k2.imshow(kernel2, cmap='gray')
k2.set_title('kernel2')
k3.imshow(kernel3, cmap='gray')
k3.set_title('kernel3')
k1.set_xticks([])
k2.set_xticks([])
k3.set_xticks([])
k1.set_yticks([])
k2.set_yticks([])
k3.set_yticks([])p1_1.imshow(pool1_1, cmap='gray')
p1_1.set_title('pool1_1')
p1_2.imshow(pool1_2, cmap='gray')
p1_2.set_title('pool1_2')
p1_3.imshow(pool1_3, cmap='gray')
p1_3.set_title('pool1_3')
p1_1.set_xticks([])
p1_2.set_xticks([])
p1_3.set_xticks([])
p1_1.set_yticks([])
p1_2.set_yticks([])
p1_3.set_yticks([])p2_1.imshow(pool2_1, cmap='gray')
p2_1.set_title('pool2_1')
p2_2.imshow(pool2_2, cmap='gray')
p2_2.set_title('pool2_2')
p2_3.imshow(pool2_3, cmap='gray')
p2_3.set_title('pool2_3')
p2_1.set_xticks([])
p2_2.set_xticks([])
p2_3.set_xticks([])
p2_1.set_yticks([])
p2_2.set_yticks([])
p2_3.set_yticks([])h1.hist(np.ravel(np.abs(pool1_1-pool2_1)),bins=100)
h1.set_title('Pool 1 diff')
h2.hist(np.ravel(np.abs(pool1_2-pool2_2)),bins=100)
h2.set_title('Pool 2 diff')
h3.hist(np.ravel(np.abs(pool1_3-pool2_3)),bins=100)
h3.set_title('Pool 3 diff')plt.tight_layout()
# plt.show()
plt.savefig('images/pool_invariance.png')