import numpy as np
import scipy.signal
import cv2
def generating_kernel(a):
'''Return a 5x5 generating kernel with parameter a.
'''
w_1d = np.array([0.25 - a/2.0, 0.25, a, 0.25, 0.25 - a/2.0])
return np.outer(w_1d, w_1d)
def reduce(image):
'''Reduce the image to half the size.
image - a float image of shape (r, c)
output - a float image of shape (ceil(r/2), ceil(c/2))
For instance, if the input is 5x7, the output will be 3x4.
You should filter the image with a generating kernel of a = 0.4, and then
sample every other point.
Please consult the lectures and tutorial videos for a more in-depth discussion
of the reduce function.
'''
out = None
# Insert your code here ------------------------------------------------------
kernel = generating_kernel(0.4)
import scipy.signal
smooth = scipy.signal.convolve(image, kernel, 'same')
size = image.shape
import math
width = int(math.ceil(size[0]/2.0))
height = int(math.ceil(size[1]/2.0))
out = np.zeros((width, height), dtype = np.float)
for i in range(width):
for j in range(height):
out[i, j] = smooth[2*i, 2*j]
# ----------------------------------------------------------------------------
return out
def expand(image):
'''Expand the image to double the size.
image - a float image of shape (r, c)
output - a float image of shape (2*r, 2*c)
You should upsample the image, and then filter it with a generating kernel of
a = 0.4. Finally, scale the output by the appropraite amount to make sure that
the net weight contributing to each output pixel is 1.
Please consult the lectures and tutorial videos for a more in-depth discussion
of the expand function.
'''
out = None
# Insert your code here ------------------------------------------------------
(width, height) = image.shape
out = np.zeros((2*width, 2*height), dtype = np.float)
for i in range(width):
for j in range(height):
out[2*i, 2*j] = image[i, j]
kernel = generating_kernel(0.4)
# ----------------------------------------------------------------------------
return out
def test():
'''This script will perform a unit test on your function, and provide useful
output.
'''
# Each subsequent layer is a reduction of the previous one
reduce1 =[np.array([[ 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 255., 255., 255., 255., 0., 0.],
[ 0., 0., 255., 255., 255., 255., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0.]]),
np.array([[ 0.64, 8.92, 12.11, 3.82],
[ 8.29, 116.03, 157.46, 49.73],
[ 3.82, 53.55, 72.67, 22.95]]),
np.array([[ 12.21, 31.85],
[ 17.62, 45.97]]),
np.array([[ 9.77]])]
reduce2 = [np.array([[ 255., 255., 255., 255., 255., 255., 255.],
[ 255., 255., 255., 255., 255., 255., 255.],
[ 255., 255., 125., 125., 125., 255., 255.],
[ 255., 255., 125., 125., 125., 255., 255.],
[ 0., 0., 0., 0., 0., 0., 0.]]),
np.array([[ 124.62, 173.95, 173.95, 124.62],
[ 165.35, 183.1 , 183.1 , 165.35],
[ 51.6 , 49.2 , 49.2 , 51.6 ]]),
np.array([[ 72.85, 104.71],
[ 49.53, 68.66]]),
np.array([[ 31.37]])]
if __name__ == "__main__":
print 'Evaluating reduce.'
for red_pyr in reduce1, reduce2:
for imgin, true_out in zip(red_pyr[0:-1], red_pyr[1:]):
if __name__ == "__main__":
print "input:\n{}\n".format(imgin)
usr_out = reduce(imgin)
if not type(usr_out) == type(true_out):
if __name__ == "__main__":
print "Error- reduce out has type {}. Expected type is {}.".format(
type(usr_out), type(true_out))
return False
if not usr_out.shape == true_out.shape:
if __name__ == "__main__":
print "Error- reduce out has shape {}. Expected shape is {}.".format(
usr_out.shape, true_out.shape)
return False
if not usr_out.dtype == true_out.dtype:
if __name__ == "__main__":
print "Error- reduce out has dtype {}. Expected dtype is {}.".format(
usr_out.dtype, true_out.dtype)
return False
if not np.all(np.abs(usr_out - true_out) < 1):
if __name__ == "__main__":
print "Error- reduce out has value:\n{}\nExpected value:\n{}".format(
usr_out, true_out)
return False
if __name__ == "__main__":
print "reduce passed.\n"
print "Evaluating expand."
expandin = [np.array([[255]]),
np.array([[125, 255],
[255, 0]]),
np.array([[ 255., 0., 125., 125., 125.],
[ 255., 0., 125., 125., 125.],
[ 50., 50., 50., 50., 50.]])]
expandout =[np.array([[ 163.2 , 102. ],
[ 102. , 63.75]]),
np.array([[ 120.8 , 164.75, 175.75, 102. ],
[ 164.75, 158.75, 121. , 63.75],
[ 175.75, 121. , 42.05, 12.75],
[ 102. , 63.75, 12.75, 0. ]]),
np.array([[ 183.6, 114.75, 34.2, 56.25, 101.25, 112.5, 112.5,112.5, 101.25, 56.25],
[ 204. , 127.5, 38., 62.5, 112.5, 125., 125., 125., 112.5, 62.5 ],
[ 188.1, 119.75, 39.2, 61.25, 106.25, 117.5, 117.5,117.5, 105.75, 58.75],
[ 124.5, 88.75, 44. , 56.25, 81.25, 87.5, 87.5, 87.5, 78.75, 43.75],
[ 56.4, 52.75, 43.8, 46.25, 51.25, 52.5, 52.5, 52.5, 47.25, 26.25],
[ 22.5, 25., 25., 25., 25., 25., 25., 25., 22.5, 12.5 ]])]
for imgin, true_out in zip(expandin, expandout):
if __name__ == "__main__":
print "input:\n{}\n".format(imgin)
usr_out = expand(imgin)
if not type(usr_out) == type(true_out):
if __name__ == "__main__":
print "Error- expand out has type {}. Expected type is {}.".format(
type(usr_out), type(true_out))
return False
if not usr_out.shape == true_out.shape:
if __name__ == "__main__":
print "Error- expand out has shape {}. Expected shape is {}.".format(
usr_out.shape, true_out.shape)
return False
if not usr_out.dtype == true_out.dtype:
if __name__ == "__main__":
print "Error- expand out has dtype {}. Expected dtype is {}.".format(
usr_out.dtype, true_out.dtype)
return False
if not np.all(np.abs(usr_out - true_out) < 1):
if __name__ == "__main__":
print "Error- expand out has value:\n{}\nExpected value:\n{}".format(
usr_out, true_out)
return False
if __name__ == "__main__":
print "expand passed."
if __name__ == "__main__":
print "All unit tests successful."
return True
if __name__ == "__main__":
print "Performing unit tests. Your functions will be accepted if your result is\
within 1 of the correct output."
np.set_printoptions(precision=1)
test()
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