06-spectrum.py

import numpy
import cv2

numpyImage = cv2.imread(filename='./samples/lenna.png', flags=cv2.IMREAD_GRAYSCALE).astype(numpy.float32) / 255.0

# creating a relief kernel that you are subsequently asked to apply in the frequency space

numpyKernel = numpy.array([ [ -2, -1, 0 ], [ -1, 1, 1 ], [ 0, 1, 2 ] ], numpy.float32)

# pad numpyKernel such that its resolution is equal to the resolution of numpyImage
# roll it one pixel to the left and one pixel to the top in order to adjust the phase
# convert numpyKernel into the frequency space by using the fourier transform
# similarly, convert numpyImage into the frequency space, no need to pad or roll it though
# perform the convolution in the frequency space by using the hadamard product
# convert the result back to the spacial domain by using the inverse fourier transform
# the result / numpyImage should look as if the convolution was done in the spatial domain









# plotting the frequency spectrum of the gaussian kernel while making sure that we only plot the real part
# the logarithmic scaling improves the visualization, the constant bias avoids log(0-1) which is undefined / negative
# the value range for the spectrum is outside of [ 0, 1 ] and a color mapping is applied before saving it

numpySpectrum = numpy.log(numpy.fft.fftshift(numpyKernel).__abs__() + 1.0)
numpySpectrum = numpySpectrum / numpySpectrum.max()

numpyImage = numpyImage.real

cv2.imwrite(filename='./06-spectrum-1.png', img=cv2.applyColorMap(src=(numpySpectrum * 255.0).clip(0.0, 255.0).astype(numpy.uint8), colormap=cv2.COLORMAP_WINTER))
cv2.imwrite(filename='./06-spectrum-2.png', img=(numpyImage * 255.0).clip(0.0, 255.0).astype(numpy.uint8))