kislayabhi · October 22, 2014 09:43
diff --git a/RANSAC.ipynb b/RANSAC.ipynb
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "RANSAC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy\n",
      "import scipy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The RANSAC algorithm is composed of two steps that are repeated in an iterative fashion.\n",
      "\n",
      "* Hypothesize :\n",
      "First minimal sample sets(MSS's) are randomly selected from the input dataset and the model parameters are computed using only the elements of the MSS.\n",
      "\n",
      "\n",
      "* Test-framework :\n",
      "In the second step RANSAC checks which elements of the entire dataset are consistent with the model instantiated with the parameters estimated in the first step. The set of such elements is called the Consensus Set(CS).\n",
      "\n",
      "RANSAC terminates when the probability of finding a better ranked CS drops below a certain threshold."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_samples=500\n",
      "n_inputs=1\n",
      "n_outputs=1\n",
      "A_exact = 20*numpy.random.random((n_samples,n_inputs) )\n",
      "perfect_fit = 60*numpy.random.normal(size=(n_inputs,n_outputs) ) \n",
      "B_exact = scipy.dot(A_exact,perfect_fit)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add a little gaussian noise (linear least squares alone should handle this well)\n",
      "A_noisy = A_exact + numpy.random.normal(size=A_exact.shape )\n",
      "B_noisy = B_exact + numpy.random.normal(size=B_exact.shape )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add some outliers\n",
      "n_outliers=100\n",
      "all_idxs=numpy.arange(A_noisy.shape[0])\n",
      "numpy.random.shuffle(all_idxs)\n",
      "outlier_idxs = all_idxs[:n_outliers]\n",
      "non_outlier_idxs = all_idxs[n_outliers:]\n",
      "A_noisy[outlier_idxs] =  20*numpy.random.random((n_outliers,n_inputs) )\n",
      "B_noisy[outlier_idxs] = 50*numpy.random.normal(size=(n_outliers,n_outputs) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# setup model\n",
      "\n",
      "all_data=numpy.hstack((A_noisy, B_noisy))\n",
      "input_columns=range(n_inputs) # the first columns of the array\n",
      "output_columns = [n_inputs+i for i in range(n_outputs)] # the last columns of the array\n",
      "debug=False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class LinearLeastSquaresModel:\n",
      "    \"\"\"linear system solved using linear least squares\n",
      " \n",
      "    This class serves as an example that fulfills the model interface\n",
      "    needed by the ransac() function.\n",
      "     \n",
      "    \"\"\"\n",
      "    def __init__(self,input_columns,output_columns,debug=False):\n",
      "        self.input_columns = input_columns\n",
      "        self.output_columns = output_columns\n",
      "        self.debug = debug\n",
      "    \n",
      "    def fit(self, data):\n",
      "        A = numpy.vstack([data[:,i] for i in self.input_columns]).T\n",
      "        B = numpy.vstack([data[:,i] for i in self.output_columns]).T\n",
      "        x,_,_,_ = numpy.linalg.lstsq(A,B)\n",
      "        return x\n",
      "    \n",
      "    def get_error( self, data, model):\n",
      "        A = numpy.vstack([data[:,i] for i in self.input_columns]).T\n",
      "        B = numpy.vstack([data[:,i] for i in self.output_columns]).T\n",
      "        B_fit = scipy.dot(A,model)\n",
      "        err_per_point = numpy.sum((B-B_fit)**2,axis=1) # sum squared error per row\n",
      "        return err_per_point"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model=LinearLeastSquaresModel(input_columns, output_columns, debug=debug)\n",
      "linear_fit,_,_,_=numpy.linalg.lstsq(all_data[:,input_columns], all_data[:,output_columns])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# takes out n number of data values randomly from n_data\n",
      "def random_partition(n,n_data):\n",
      "    \"\"\"return n random rows of data (and also the other len(data)-n rows)\"\"\"\n",
      "    all_idxs = numpy.arange( n_data )\n",
      "    numpy.random.shuffle(all_idxs)\n",
      "    idxs1 = all_idxs[:n]\n",
      "    idxs2 = all_idxs[n:]\n",
      "    return idxs1, idxs2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "all_data.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(500, 2)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "** Hypothesize**\n",
      "\n",
      "\n",
      "* Take 50 random elements from the input noisy dataset of 500.\n",
      "* Calculate the model parameters using only the elements of the selected MSS.\n",
      "\n",
      "\n",
      "** Test Framework**\n",
      "\n",
      "\n",
      "* **RANSAC** checks which elements in the dataset **D** are consistent with the model instantiated with the estimated parameters.\n",
      "* If the number of inliers are found to be greater than 300, we want the **RANSAC** to consider this as a good model.\n",
      "* If it is found as a good model, **RANSAC** updates the current best **Consensus Set**. The model is re-estimated taking into account the more than 300 datapoints that approve of the current model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iterations=0\n",
      "bestfit=None\n",
      "besterr=numpy.inf\n",
      "best_inlier_idxs=None\n",
      "\n",
      "k=1000\n",
      "# number of times you want to iterate\n",
      "while iterations<k:\n",
      "    \n",
      "    # select 50 random points from all the data\n",
      "    maybe_idxs, test_idxs=random_partition(50, all_data.shape[0])\n",
      "    \n",
      "    # call the 50 choosen points as maybeinliers\n",
      "    maybeinliers=all_data[maybe_idxs,:]\n",
      "    # call the other 450 points as test_points\n",
      "    test_points=all_data[test_idxs]\n",
      "    \n",
      "    # find the best fit according to the maybeinliers. Call it maybemodel.\n",
      "    maybemodel=model.fit(maybeinliers)\n",
      "    \n",
      "    #for every point in test_points {\n",
      "    #     if point fits maybemodel with an error smaller than 7e3\n",
      "    #          add point to alsoinliers\n",
      "    test_err = model.get_error( test_points, maybemodel)\n",
      "    also_idxs=test_idxs[test_err<7e3] #select indices of rows with accepted points\n",
      "    alsoinliers=all_data[also_idxs,:]\n",
      "    \n",
      "    if len(alsoinliers)>300:\n",
      "        #This means that we may have found a good model. \n",
      "        #Now we test how good it is. \n",
      "        \n",
      "        #Take all the points from maybeinliers and alsoinliers and fit the model.\n",
      "        #call it bettermodel and find its error. Call it thiserr.\n",
      "        #This one is a great fit if the value of thiserr is lesser than the besterr.\n",
      "        \n",
      "        betterdata=numpy.concatenate((maybeinliers, alsoinliers))\n",
      "        bettermodel=model.fit(betterdata)\n",
      "        better_errs=model.get_error(betterdata, bettermodel)\n",
      "        thiserr=numpy.mean(better_errs)\n",
      "        if thiserr<besterr:\n",
      "            bestfit=bettermodel\n",
      "            besterr=thiserr\n",
      "            best_inlier_idxs=numpy.concatenate((maybe_idxs, also_idxs))\n",
      "            print best_inlier_idxs.shape\n",
      "    iterations+=1\n",
      "ransac_fit=bestfit\n",
      "ransac_data=all_data[best_inlier_idxs]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(402,)\n",
        "(393,)\n",
        "(411,)\n",
        "(407,)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#print best_inlier_idxs.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pylab.rcParams['figure.figsize'] = 10, 10 \n",
      "sort_idxs=numpy.argsort(A_exact[:,0])\n",
      "A_col0_sorted=A_exact[sort_idxs] #maintain as rank-2 array\n",
      "pylab.plot(A_noisy[:,0], B_noisy[:,0], 'k.', label='data')\n",
      "pylab.plot(A_noisy[best_inlier_idxs,0],\n",
      "           B_noisy[best_inlier_idxs,0],'bx', label='RANSAC data')\n",
      "pylab.plot( A_col0_sorted[:,0],numpy.dot(A_col0_sorted,linear_fit)[:,0],label='linear fit' )\n",
      "pylab.plot( A_col0_sorted[:,0],\n",
      "            numpy.dot(A_col0_sorted,perfect_fit)[:,0],label='exact system' )\n",
      "pylab.plot( A_col0_sorted[:,0],\n",
      "            numpy.dot(A_col0_sorted,ransac_fit)[:,0], label='RANSAC fit' )\n",
      "\n",
      "\n",
      "_=pylab.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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hzJgxCAsLg7OzM+Li4kzKMWrUKERGRmLBggVwdXXF7t27TcrWtWtXAIBKpYKLiwsSEhLK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F1rpckdP+7tEYmUn7eXb0VEqjTXWmA9ez5TZHsh1/pcxVWYT81MNa1eaGWWpSxzXiQ11ZjWrY1Z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\neSJjYMwY/tiWyjlr4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       "text": [
        "<matplotlib.figure.Figure at 0x3a44c90>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
 }
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