{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Scipy\n\nOpens the ascent image from ``scipy.misc`` and shifts the image.\nFinally, the shift offsets are determined using cross-correlation.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import scipy.misc\nimport numpy\nfrom numpy.fft import fft2\nfrom numpy.fft import fftshift\nimport pylab"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Get the ascent image and calculate an offset shift.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "ascent = scipy.misc.ascent()\nprint(\"The ascent-image has a size of\", ascent.shape)\nprint(\"The maximum value of this image is \", ascent.max())\nprint(\"Its data type is \", ascent.dtype)\n\nF = fft2(ascent)\nF2 = fftshift(F)\n\npylab.figure()\npylab.gray()\npylab.subplot(221)\npylab.imshow(ascent)\npylab.title(\"ascent (Original)\")\n\npylab.subplot(222)\nimg = pylab.imshow(numpy.real(F))\nimg.set_clim(0, 100)\npylab.title(\"ascent (FFT)\")\n\npylab.subplot(223)\nimg = pylab.imshow(numpy.real(F2))\nimg.set_clim(0, 100)\npylab.title(\"ascent (FFT), fftshift\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Calculate the cross-correlation. \n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pylab.figure()\npylab.subplot(231)\npylab.imshow(ascent)\n\nascent_roll = numpy.roll(ascent, 50, 1)\nascent_roll = numpy.roll(ascent_roll, -150, 0)\n\npylab.subplot(232)\npylab.imshow(ascent_roll)\n\nF = fftshift(fft2(ascent))\nF2 = fftshift(fft2(ascent_roll))\n\nF3 = numpy.multiply(F, F2.conj())\n\nF4 = fftshift(numpy.fft.ifft2(F3))\n\npylab.subplot(233)\nimg = pylab.imshow(numpy.real(F))\nimg.set_clim(0, 100)\n\npylab.subplot(234)\nimg = pylab.imshow(numpy.real(F2))\nimg.set_clim(0, 100)\n\npylab.subplot(235)\nimg = pylab.imshow(numpy.real(F3))\nimg.set_clim(0, 100)\n\npylab.subplot(236)\nF5 = numpy.real(F4)\nimg = pylab.imshow(F5, vmin=0, vmax=0.001)\n\nmax_pos = numpy.argmax(F5)\n\noffset_x = max_pos % 512\noffset_y = (max_pos - offset_x) / 512\n\nprint(\"offset_x: \", offset_x - 256)\nprint(\"offset_y: \", offset_y - 256)\n\npylab.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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    "language_info": {
      "codemirror_mode": {
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      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.10"
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