RichieSams/filter_with_negative_detection.ipynb

## filter_with_negative_detection.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ReconstructionFilter:\n",
    "    def __init__(self, filterType):\n",
    "        self.filterType = filterType\n",
    "        self.width = 0.0\n",
    "        self.binSize = 0.0\n",
    "        self.invBinSize = 0.0\n",
    "        self.filterResolution = 32\n",
    "        self.cdf = np.empty(self.filterResolution + 1)\n",
    "        self.negativeIndices = []\n",
    "        \n",
    "        self.precompute()\n",
    "    \n",
    "    # Public\n",
    "    \n",
    "    def sample(self, x):\n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return (0.0, False)\n",
    "        \n",
    "        negative = x < 0.5;\n",
    "        x = x * 2.0 if negative else (x - 0.5) * 2.0;\n",
    "        \n",
    "        index = self.filterResolution;\n",
    "        for i in range(1, self.filterResolution):\n",
    "            if (x < self.cdf[i]):\n",
    "                index = i - 1\n",
    "                break\n",
    "        \n",
    "        pdf = self.cdf[index + 1] - self.cdf[index]\n",
    "        u = self.binSize * ((index) + ((x - self.cdf[index]) / pdf))\n",
    "        \n",
    "        isNegative = index in self.negativeIndices\n",
    "        return (-u, isNegative) if negative else (u, isNegative)\n",
    "    \n",
    "    # Private    \n",
    "    \n",
    "    def precompute(self):\n",
    "        self.width = self.filterWidth()\n",
    "        \n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return\n",
    "        \n",
    "        self.binSize = self.width / (self.filterResolution - 1);\n",
    "        self.invBinSize = (self.filterResolution - 1) / self.width;\n",
    "\n",
    "        normalizationFactor = 0.0\n",
    "        pdf = np.empty(self.filterResolution)\n",
    "        for i in range(self.filterResolution - 1):\n",
    "            temp = self.eval(i * self.binSize)\n",
    "            if temp <= 0.0:\n",
    "                self.negativeIndices.append(i)\n",
    "                temp = -temp\n",
    "            pdf[i] = temp\n",
    "            normalizationFactor += temp\n",
    "        \n",
    "        pdf[self.filterResolution - 1] = 0.0\n",
    "        \n",
    "        # Normalize. Aka, we want the area under the curve to equal 1.0\n",
    "        for i in range(self.filterResolution - 1):\n",
    "            pdf[i] /= normalizationFactor\n",
    "        \n",
    "        self.cdf[0] = 0.0\n",
    "        for i in range(1, self.filterResolution):\n",
    "            self.cdf[i] = self.cdf[i - 1] + (pdf[i - 1])\n",
    "        self.cdf[self.filterResolution] = 1.0\n",
    "    \n",
    "    def eval(self, x):\n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return 0.0\n",
    "        elif (self.filterType == \"Box\"):\n",
    "            return 1.0 if (x >= -self.width and x <= self.width) else 0.0\n",
    "        elif (self.filterType == \"Tent\"):\n",
    "            return self.width - abs(x)\n",
    "        elif (self.filterType == \"Gaussian\"):\n",
    "            alpha = 2.0\n",
    "            return max(math.exp(-alpha * x * x) - math.exp(-alpha * 4.0), 0.0)\n",
    "        elif (self.filterType == \"MitchellNetravali\"):\n",
    "            return self.mitchellNetravali(abs(x))\n",
    "        elif (self.filterType == \"CatmullRom\"):\n",
    "            return self.catmullRom(abs(x))\n",
    "        elif (self.filterType == \"Lanczos\"):\n",
    "            return self.lanczos(abs(x))\n",
    "        else:\n",
    "            return 0.0\n",
    "    \n",
    "    def filterWidth(self):\n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return 0.0\n",
    "        elif (self.filterType == \"Box\"):\n",
    "            return 0.5\n",
    "        elif (self.filterType == \"Tent\"):\n",
    "            return 1.0\n",
    "        elif (self.filterType == \"Gaussian\" or \n",
    "              self.filterType == \"MitchellNetravali\" or\n",
    "              self.filterType == \"CatmullRom\" or \n",
    "              self.filterType == \"Lanczos\"):\n",
    "            return 2.0\n",
    "        else:\n",
    "            return 0.0\n",
    "    \n",
    "    def mitchellNetravali(self, x):\n",
    "        B = 1.0 / 3.0\n",
    "        C = 1.0 / 3.0\n",
    "        if (x < 1.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((12.0 - 9.0 * B - 6.0 * C) * x * x * x + \\\n",
    "                 (-18.0 + 12.0 * B + 6.0 * C) * x * x + \\\n",
    "                 (6.0 - 2.0 * B))\n",
    "        elif (x < 2.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((-B - 6.0 * C) * x * x * x + \\\n",
    "                 (6.0 * B + 30.0 * C) * x * x + \\\n",
    "                 (-12.0 * B - 48.0 * C) * x + \\\n",
    "                 (8.0 * B + 24.0 * C))\n",
    "        else:\n",
    "            return 0.0\n",
    "\n",
    "    def catmullRom(self, x):\n",
    "        if (x < 1.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((12.0 - 3.0) * x * x * x + \\\n",
    "                 (-18.0 + 3.0) * x * x + \\\n",
    "                 6.0)\n",
    "        elif (x < 2.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                (-3.0 * x * x * x + \\\n",
    "                 15.0 * x * x - \\\n",
    "                 24.0 * x + \\\n",
    "                 12.0)\n",
    "        else:\n",
    "            return 0.0;\n",
    "\n",
    "    def lanczos(self, x):\n",
    "        if (x == 0.0):\n",
    "            return 1.0;\n",
    "        elif (x < 2.0):\n",
    "            return math.sin(math.pi * x) * \\\n",
    "                   math.sin(math.pi * x * 0.5) / \\\n",
    "                   (math.pi * math.pi * x * x * 0.5);\n",
    "        else:\n",
    "            return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "randNumbers = np.random.rand(100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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DktTN8JAkdTM8JEndDA9JUjfDQ5LUzfCQJHUzPCRJ3QwPSVI3w0OS1M3wkCR1MzwkSd0M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\nJKmb4SFJ6mZ4SJK6GR6SpG7/H2lrdniVkMO1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x944b668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diracFilter = ReconstructionFilter(\"Dirac\")\n",
    "\n",
    "diracSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    diracSamples[i], isNegative = diracFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(diracSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cDuwGngOunNjPfknSopYcBFX1f4Gtfdr/EfjlRZa5DrhuqduUJI2fTxZLUuMMAklqnEEg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\nAh8fCngMVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80ba1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxFilter = ReconstructionFilter(\"Box\")\n",
    "\n",
    "boxSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    boxSamples[i], isNegative = boxFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(boxSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8015358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tentFilter = ReconstructionFilter(\"Tent\")\n",
    "\n",
    "tentSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    tentSamples[i], isNegative = tentFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(tentSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QVfVQU+8QsBc4c7FOU74LuKWq7pvl9RxZPIEcWTxJMYx6e44sXg2WemTx7wInLiaBxkHg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\ny5kIJKnlTASS1HImAklqOROBJLXc/wcqjkwotHBKwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e9c2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussianFilter = ReconstructionFilter(\"Gaussian\")\n",
    "\n",
    "gaussianSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    gaussianSamples[i], isNegative = gaussianFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(gaussianSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x919a828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x947b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mitchellNetravaliFilter = ReconstructionFilter(\"MitchellNetravali\")\n",
    "\n",
    "mitchellNetravaliSamplesPos = np.zeros(100000)\n",
    "mitchellNetravaliSamplesNeg = np.zeros(100000)\n",
    "\n",
    "for i in range(100000):\n",
    "    sample, isNegative = mitchellNetravaliFilter.sample(randNumbers[i])\n",
    "    if isNegative:\n",
    "        mitchellNetravaliSamplesNeg[i] = sample\n",
    "    else:\n",
    "        mitchellNetravaliSamplesPos[i] = sample\n",
    "\n",
    "mitchellNetravaliSamplesPos = mitchellNetravaliSamplesPos[mitchellNetravaliSamplesPos != 0.0]\n",
    "mitchellNetravaliSamplesNeg = mitchellNetravaliSamplesNeg[mitchellNetravaliSamplesNeg != 0.0]\n",
    "\n",
    "plt.hist(mitchellNetravaliSamplesPos, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 4000])\n",
    "plt.show()\n",
    "\n",
    "plt.hist(mitchellNetravaliSamplesNeg, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 4000])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e7ae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e7a898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "catmullRomFilter = ReconstructionFilter(\"CatmullRom\")\n",
    "\n",
    "catmullRomSamplesPos = np.zeros(100000)\n",
    "catmullRomSamplesNeg = np.zeros(100000)\n",
    "\n",
    "for i in range(100000):\n",
    "    sample, isNegative = catmullRomFilter.sample(randNumbers[i])\n",
    "    if isNegative:\n",
    "        catmullRomSamplesNeg[i] = sample\n",
    "    else:\n",
    "        catmullRomSamplesPos[i] = sample\n",
    "\n",
    "catmullRomSamplesPos = catmullRomSamplesPos[catmullRomSamplesPos != 0.0]\n",
    "catmullRomSamplesNeg = catmullRomSamplesNeg[catmullRomSamplesNeg != 0.0]\n",
    "\n",
    "plt.hist(catmullRomSamplesPos, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 3500])\n",
    "plt.show()\n",
    "\n",
    "plt.hist(catmullRomSamplesNeg, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 3500])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f932b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f93ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lanczosFilter = ReconstructionFilter(\"Lanczos\")\n",
    "\n",
    "lanczosSamplesPos = np.zeros(100000)\n",
    "lanczosSamplesNeg = np.zeros(100000)\n",
    "\n",
    "for i in range(100000):\n",
    "    sample, isNegative = lanczosFilter.sample(randNumbers[i])\n",
    "    if isNegative:\n",
    "        lanczosSamplesNeg[i] = sample\n",
    "    else:\n",
    "        lanczosSamplesPos[i] = sample\n",
    "\n",
    "lanczosSamplesPos = lanczosSamplesPos[lanczosSamplesPos != 0.0]\n",
    "lanczosSamplesNeg = lanczosSamplesNeg[lanczosSamplesNeg != 0.0]\n",
    "\n",
    "plt.hist(lanczosSamplesPos, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 3500])\n",
    "plt.show()\n",
    "\n",
    "plt.hist(lanczosSamplesNeg, 50)\n",
    "plt.axis([-2.0, 2.0, 0, 3500])\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}