Many_Gaussian_Image_Fit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### creating a fit many gaussians to an image function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seperately fit amplitudes, locations, etc. to create a good guess and then do a total fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maxima finding is based on the answer to this question:  \n",
    "https://stackoverflow.com/questions/9111711/get-coordinates-of-local-maxima-in-2d-array-above-certain-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "import scipy.ndimage as ndimage\n",
    "import scipy.ndimage.filters as filters\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fitters.Gaussian import arb_2d_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "from importlib import reload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'fitters.Gaussian.arb_2d_sum' from 'C:\\\\Users\\\\Regal-Lab\\\\Code\\\\Data-Analysis-Code\\\\fitters\\\\Gaussian\\\\arb_2d_sum.py'>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reload(arb_2d_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findImageMaxima(im, neighborhood_size=20, threshold=1):\n",
    "    data_max = filters.maximum_filter(im, neighborhood_size)\n",
    "    maxima = (im == data_max)\n",
    "    data_min = filters.minimum_filter(im, neighborhood_size)\n",
    "    diff = ((data_max - data_min) > threshold)\n",
    "    maxima[diff == 0] = 0\n",
    "    labeled, num_objects = ndimage.label(maxima)\n",
    "    slices = ndimage.find_objects(labeled)\n",
    "    x, y = [], []\n",
    "    for dy,dx in slices:\n",
    "        x_center = (dx.start + dx.stop - 1)/2\n",
    "        x.append(x_center)\n",
    "        y_center = (dy.start + dy.stop - 1)/2    \n",
    "        y.append(y_center)\n",
    "    print('Found ' + str(len(x)) + ' Maxima.')\n",
    "    return [p for p in zip([int(x_) for x_ in x],[int(y_) for y_ in y])]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitManyGaussianImage(im, numGauss, neighborhood_size=20, threshold=1, direct=True, widthGuess=1):\n",
    "    \"\"\"\n",
    "    Maxima finding is based on the answer to this question:\n",
    "    https://stackoverflow.com/questions/9111711/get-coordinates-of-local-maxima-in-2d-array-above-certain-value\n",
    "    \"\"\"\n",
    "    maximaLocs = findImageMaxima(im, neighborhood_size=neighborhood_size, threshold=threshold)\n",
    "    if len(maximaLocs) != numGauss:\n",
    "        raise ValueError(\"ERROR: didn't find the right number of maxima!\")\n",
    "    guess = [min(im.flatten())]\n",
    "    for loc in maximaLocs:\n",
    "        guess += [im[loc[1],loc[0]], loc[0], loc[1], widthGuess, widthGuess]\n",
    "    xpts = np.arange(len(im[0]))\n",
    "    ypts = np.arange(len(im))\n",
    "    X,Y = np.meshgrid(xpts,ypts)\n",
    "    zpts = arb_2d_sum.f((X,Y), *guess).reshape(X.shape)\n",
    "    f, ax = subplots(1,5,figsize=(20,10))\n",
    "    ax[0].imshow(im)\n",
    "    ax[0].set_title('Orig')\n",
    "    ax[1].imshow(zpts)\n",
    "    ax[1].set_title('Guess')\n",
    "    ax[2].imshow(im-zpts)\n",
    "    ax[2].set_title('Guess-Diff')\n",
    "    optParam, optCov = opt.curve_fit(arb_2d_sum.f, (X,Y), im.flatten(), p0=guess)\n",
    "    zpts_fit = arb_2d_sum.f((X,Y), *optParam).reshape(X.shape)\n",
    "    ax[3].imshow(zpts_fit)\n",
    "    ax[3].set_title('Fit')\n",
    "    ax[4].imshow(im-zpts_fit)\n",
    "    ax[4].set_title('Fit-Diff')\n",
    "    return optParam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found 9 Maxima.\n"
     ]
    },
    {
     "data": {
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+PGyH3MdI2BrhkwleVlC2AfCiMtrO/FJacrK3zZP9K/x7vTc4mzSshBxIGMWKtbjOkpW8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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fitManyGaussianImage(zpts,9, widthGuess=3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}