{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Later shifted image\n\nIn this demo the lateral image shift is determined. \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\nimport scipy\nimport scipy.misc\nimport scipy.ndimage\nimport matplotlib.pyplot as plt\nfrom numpy.typing import ArrayLike\n\n\ndef plotImage(image: ArrayLike, cmap: str=\"gray\"):\n    plt.figure()\n    plt.gray()\n    plt.imshow(image, cmap=cmap)\n    plt.show()\n\n\nif scipy.__version__ <= \"0.14.0\":\n    # removed due to licensing reasons\n    image = scipy.misc.lena()\nelse:\n    image = scipy.misc.face()\n    # Convert the image\n    R = image[:, :, 0]\n    G = image[:, :, 1]\n    B = image[:, :, 2]\n    image = R * 299. / 1000 + G * 587. / 1000 + B * 114. / 1000\n\nplotImage(image)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Amount of pixel shift in x- and y-direction\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "xPixelShift = 16\nyPixelShift = -7"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Determine the ROI size: relative (centered) size of original image (relativeSize=1: original size).\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "row, col = image.shape\nrelativeSize = np.floor(min(1 - abs(xPixelShift) / col, 1 - abs(yPixelShift) / row) * 10) / 10\n\nx0 = int((col - col * relativeSize) / 2)\nx1 = col - x0 + 1\ny0 = int((row - row * relativeSize) / 2)\ny1 = row - y0 + 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "not shifted ROI\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "image1 = image[y0:y1, x0:x1].copy()\nplotImage(image1)\n\n# Shifted ROI\nimage2 = image[y0 + yPixelShift : y1 + yPixelShift, x0 + xPixelShift : x1 + xPixelShift].copy()\nplotImage(image2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Determine the pixel shift using discrete fast fourier transformation and complex conjugation of ``image2``.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "image1FFT = np.fft.fft2(image1)\nimage2FFT = np.conjugate(np.fft.fft2(image2))\n\n# inverse fourier transformation of product -> equal to cross correlation\nimageCCor = np.real(np.fft.ifft2((image1FFT * image2FFT)))\n\n# Shift the zero-frequency component to the center of the spectrum\nimageCCorShift = np.fft.fftshift(imageCCor)\nplotImage(imageCCorShift, \"hot\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Determine the distance of the maximum from the center\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "row, col = image1.shape\n\nyShift, xShift = np.unravel_index(np.argmax(imageCCorShift), (row, col))\n\nyShift -= int(row / 2)\nxShift -= int(col / 2)\n\nprint(\"shift of image1 in x-direction [pixel]: \" + str(xShift))\nprint(\"shift of image1 in y-direction [pixel]: \" + str(yShift))"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.10"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}