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 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "# Automatic estimate the patch size\n",
    "\n",
    "**Patch size** is an important parameter to extract local image motifs, compute rotatioanl and reflectional symmetry maps. "
   ],
   "id": "87fdf9e240b6b0a4"
  },
  {
   "metadata": {},
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "%matplotlib qt\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#from mtflearn import ZPs"
   ],
   "id": "ff9ad3349388a903",
   "outputs": []
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:24:23.724787Z",
     "start_time": "2024-05-20T09:24:21.766098Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from mtflearn.features import autocorrelation, radial_profile, get_characteristic_length, get_characteristic_length_fft\n",
    "from mtflearn.utils import normalize_image"
   ],
   "id": "d79a45862f3e9b25",
   "execution_count": 2,
   "outputs": []
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:24:24.171778Z",
     "start_time": "2024-05-20T09:24:24.146778Z"
    }
   },
   "cell_type": "code",
   "source": "from skimage.transform import resize",
   "id": "891eeaa61d4ea31d",
   "execution_count": 3,
   "outputs": []
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:24:25.036208Z",
     "start_time": "2024-05-20T09:24:25.021204Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "ec091987a852ab42",
   "execution_count": 3,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## Load image",
   "id": "73114210167a2bd8"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:24:27.990143Z",
     "start_time": "2024-05-20T09:24:27.905144Z"
    }
   },
   "cell_type": "code",
   "source": [
    "filename = 'data\\\\monolayer_MoSe2_80K.npy'\n",
    "img = np.load(filename)[0:800, 0:800]\n",
    "img = resize(img, (512, 512))\n",
    "img = normalize_image(img, 0, 1)"
   ],
   "id": "1d05106aaec9fa98",
   "execution_count": 4,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## Method 1: Estimating the Lattice Constant from Fourier Space\n",
    "\n",
    "Given an image $I$, we follow these steps to estimate the characteristic length from the Fourier space:\n",
    "\n",
    "1. **Compute the Power Spectrum**:\n",
    "   - Calculate the power spectrum of the image $I$, denoted as $F$.\n",
    "\n",
    "2. **Radial Averaging**:\n",
    "   - Compute the radial average of $F$, denoted as $L$.\n",
    "\n",
    "3. **Baseline Correction**:\n",
    "   - Perform baseline correction on $L$, resulting in a corrected curve denoted as $L'$.\n",
    "\n",
    "4. **Peak Detection**:\n",
    "   - Identify the dominant peak in $L'$. The position of this peak is denoted as $k$.\n",
    "\n",
    "5. **Conversion to Real Space**:\n",
    "   - Convert the peak position $k$ to a real-space length $s$.\n",
    "\n",
    "This method allows us to estimate the lattice constant by analyzing the frequency domain representation of the image and extracting the most prominent spatial frequency, which is then translated into a characteristic length in real space."
   ],
   "id": "24f52a17c98ece6c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:25:27.506315Z",
     "start_time": "2024-05-20T09:25:27.426599Z"
    }
   },
   "cell_type": "code",
   "source": [
    "s = get_characteristic_length_fft(img)\n",
    "a1 = 2/np.sqrt(3) * s\n",
    "print('Lattice constant is {} pixels.'.format(a1))"
   ],
   "id": "764e2a9707c45179",
   "execution_count": 7,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## Method 2: Estimating the Lattice Constant from the Radial Distribution Function\n",
    "\n",
    "Given an image $I$, we follow these steps to estimate the characteristic length from the radial distribution function:\n",
    "\n",
    "1. **Compute the Autocorrelation**:\n",
    "   - Calculate the autocorrelation of the image $I$, denoted as $A$.\n",
    "\n",
    "2. **Radial Averaging**:\n",
    "   - Compute the radial average of $A$, denoted as $L$.\n",
    "\n",
    "3. **Peak Detection**:\n",
    "   - Locate the first peak in $L$. The position of this peak is denoted as $s$.\n",
    "\n",
    "This method enables us to estimate the lattice constant by analyzing the spatial correlations within the image, identifying the most prominent distance over which the image exhibits periodicity."
   ],
   "id": "b309b7af62b517ea"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-20T09:30:20.655291Z",
     "start_time": "2024-05-20T09:30:20.544293Z"
    }
   },
   "cell_type": "code",
   "source": [
    "a2 = get_characteristic_length(img)\n",
    "\n",
    "print('Lattice constant is {} pixels.'.format(a2))"
   ],
   "id": "68ea640dfa95e51",
   "execution_count": 8,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "code",
   "execution_count": null,
   "source": "",
   "id": "a8af242e8b0f38a5",
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "code",
   "execution_count": null,
   "source": "",
   "id": "9b5e564ae8bd23ac",
   "outputs": []
  }
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