12.1.10.2.1. Later shifted image

In this demo the lateral image shift is determined.

import numpy as np
import scipy
import scipy.misc
import scipy.ndimage
import matplotlib.pyplot as plt
from numpy.typing import ArrayLike


def plotImage(image: ArrayLike, cmap: str="gray"):
    plt.figure()
    plt.gray()
    plt.imshow(image, cmap=cmap)
    plt.show()


if scipy.__version__ <= "0.14.0":
    # removed due to licensing reasons
    image = scipy.misc.lena()
else:
    image = scipy.misc.face()
    # Convert the image
    R = image[:, :, 0]
    G = image[:, :, 1]
    B = image[:, :, 2]
    image = R * 299. / 1000 + G * 587. / 1000 + B * 114. / 1000

plotImage(image)

Amount of pixel shift in x- and y-direction

xPixelShift = 16
yPixelShift = -7

Determine the ROI size: relative (centered) size of original image (relativeSize=1: original size).

row, col = image.shape
relativeSize = np.floor(min(1 - abs(xPixelShift) / col, 1 - abs(yPixelShift) / row) * 10) / 10

x0 = int((col - col * relativeSize) / 2)
x1 = col - x0 + 1
y0 = int((row - row * relativeSize) / 2)
y1 = row - y0 + 1

not shifted ROI

image1 = image[y0:y1, x0:x1].copy()
plotImage(image1)

# Shifted ROI
image2 = image[y0 + yPixelShift : y1 + yPixelShift, x0 + xPixelShift : x1 + xPixelShift].copy()
plotImage(image2)

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Determine the pixel shift using discrete fast fourier transformation and complex conjugation of image2.

image1FFT = np.fft.fft2(image1)
image2FFT = np.conjugate(np.fft.fft2(image2))

# inverse fourier transformation of product -> equal to cross correlation
imageCCor = np.real(np.fft.ifft2((image1FFT * image2FFT)))

# Shift the zero-frequency component to the center of the spectrum
imageCCorShift = np.fft.fftshift(imageCCor)
plotImage(imageCCorShift, "hot")

Determine the distance of the maximum from the center

row, col = image1.shape

yShift, xShift = np.unravel_index(np.argmax(imageCCorShift), (row, col))

yShift -= int(row / 2)
xShift -= int(col / 2)

print("shift of image1 in x-direction [pixel]: " + str(xShift))
print("shift of image1 in y-direction [pixel]: " + str(yShift))

shift of image1 in x-direction [pixel]: 16
shift of image1 in y-direction [pixel]: -7