04-Implementing-Walsh-Haar-Transform-Using-Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing Walsh and Haar Transforms Using Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "* [Walsh Transform](#Walsh)\n",
    "    * [Introduction](#WalshIntroduction)\n",
    "    * [Python Implementation](#WalshImplementation)\n",
    "    * [Testing](#WalshTesting)\n",
    "* [Haar Transform](#Haar)\n",
    "    * [Introduction](#HaarIntroduction)\n",
    "    * [Python Implementation](#HaarImplementation)\n",
    "    * [Testing](#HaarTesting)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"Walsh\"></a>\n",
    "## The Walsh Transform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a name=\"WalshIntroduction\"></a>\n",
    "### Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Walsh Transform is one way of transforming a signal/image from a space-domain to its corresponding frequency-domain. The DFT is a complex, sinusoidal transform while DCT is a transform where the imaginary values are eliminated and the real ones are retained. In the case of Walsh, it is a square waveform transform. In addition, the base/kernel functions in the Walsh tranformation are orthogonal, orthonormal and symmetric. Those in DFT are also symmetric. The forward walsh transform is as follows (Assume that N = $2^n$):\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "H(u,v) = \\frac{1}{N}\\sum_{x=0}^{N-1}\\sum_{y=0}^{N-1}f(x,y) (-1)^{ \\beta } \\;\\\\ where \\; u,v=0,1,2,...N-1 \\\\\n",
    "\\beta = \\sum_{i=0}^{n-1}b_i(x)b_i(u) + \\sum_{i=0}^{n-1}b_i(y)b_i(v)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "Since the kernels of the walsh transform are real and orthogonal, they are separable. The forward transform can be rewritten as:\n",
    "\n",
    "$H(u,v) = k.f(x,y).k $\n",
    "\n",
    "$ Where \\; u,v=0,1,2,...N-1 \\; and \\; k = \\sum_{i=0}^{n-1}b_i(x)b_i(u) $\n",
    "\n",
    "Similarly, the inverse walsh transform will look as follows:\n",
    "\n",
    "$f(x,y) = k.H(u,v).k $\n",
    "\n",
    "This is exactly the same as that of the forward transformation as the kernels are real and symmetric. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"WalshImplementation\"></a>\n",
    "### Python Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, let's import the necessary python libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "#import matplotlib.image as img\n",
    "import PIL.Image as Image \n",
    "\n",
    "import math\n",
    "import cmath\n",
    "\n",
    "import time\n",
    "\n",
    "import csv\n",
    "\n",
    "from numpy import binary_repr\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's start with creating common image functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generateImagesWithResizedWhite(imge):\n",
    "    \"\"\"\n",
    "    Generates images with the same size as the original but with a resized white part of them.\n",
    "    \"\"\"\n",
    "\n",
    "    N = imge.shape[0]\n",
    "\n",
    "    imges = []\n",
    "    i = N/2\n",
    "    while i >= 4:\n",
    "        j = (N - i)/2\n",
    "\n",
    "        #Starting and ending indices for the white part.\n",
    "        indx1 = j\n",
    "        indx2 = j+i\n",
    "\n",
    "        #Draw the image.\n",
    "        imgeNew = np.zeros([N, N],dtype=int)\n",
    "        imgeNew[indx1:indx2, indx1:indx2] = np.ones([i, i], dtype=int)*255\n",
    "\n",
    "        #Add the image to the list.\n",
    "        imges.append(imgeNew)\n",
    "\n",
    "        i = i/2\n",
    "\n",
    "    return imges\n",
    "\n",
    "def generateBlackAndWhiteSquareImage(imgSize):\n",
    "    \"\"\"\n",
    "    Generates a square-sized black and white image with a given input size.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    imgSize : int\n",
    "        Input number that stores the dimension of the square image to be generated.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    imge : ndarray\n",
    "        The generated black and white square image.\n",
    "    \"\"\"\n",
    "\n",
    "    #Creating a matrix with a given size where all the stored values are only zeros (for initialization)\n",
    "    imge = np.zeros([imgSize, imgSize], dtype=int)\n",
    "\n",
    "    #Starting and ending indices of the white part of the image.\n",
    "    ind1 = imgSize/4\n",
    "    ind2 = ind1 + (imgSize/2)\n",
    "\n",
    "    #Make a part of the image as white (255)\n",
    "    imge[ind1:ind2, ind1:ind2] = np.ones([imgSize/2, imgSize/2], dtype=int)*255\n",
    "\n",
    "    #return the resulting image\n",
    "    return imge\n",
    "\n",
    "def generateImages(imgSizes=[128, 64, 32, 16, 8]): \n",
    "    \"\"\"\n",
    "    Generates images of different sizes.\"\"\"\n",
    "    #Create an empty list of images to save the generated images with different sizes.\n",
    "    images = []\n",
    "\n",
    "    #Generate the first and biggest image\n",
    "    imge = generateBlackAndWhiteSquareImage(imgSizes[0])\n",
    "\n",
    "    #Add to the images list\n",
    "    images.append(imge)\n",
    "\n",
    "    #Generate the resized and smaller images with different sizes.\n",
    "    for i in range(1, len(imgSizes)):\n",
    "        size = imgSizes[i]\n",
    "        images.append(resizeImage(imge, size))\n",
    "        \n",
    "    return images\n",
    "\n",
    "def resizeImage(imge, newSize):        \n",
    "    \"\"\"\n",
    "    Reduces the size of the given image.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    imge : ndarray\n",
    "        Input array that stores the image to be resized.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    newSize : int\n",
    "        The size of the newly generated image.\n",
    "    \"\"\"\n",
    "\n",
    "    #Compute the size of the original image (in this case, only # of rows as it is square)\n",
    "    N = imge.shape[0]\n",
    "\n",
    "    #The ratio of the original image as compared to the new one.\n",
    "    stepSize = N/newSize\n",
    "\n",
    "    #Creating a new matrix (image) with a black color (values of zero)\n",
    "    newImge = np.zeros([N/stepSize, N/stepSize])\n",
    "\n",
    "    #Average the adjacent four pixel values to compute the new intensity value for the new image.\n",
    "    for i in xrange(0, N, stepSize):\n",
    "        for j in xrange(0, N, stepSize):\n",
    "            newImge[i/stepSize, j/stepSize] = np.mean(imge[i:i+stepSize, j:j+stepSize])\n",
    "\n",
    "    #Return the new image\n",
    "    return newImge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we are going to implement the walsh transform:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Walsh(object):\n",
    "    \"\"\"\n",
    "    This class Walsh implements all the procedures for transforming a given 2D digital image\n",
    "    into its corresponding frequency-domain image (Walsh Transform)\n",
    "    \"\"\"\n",
    "    \n",
    "    @classmethod\n",
    "    def __computeBeta(self, u, x, n):\n",
    "        uBin = binary_repr(u, width=n)\n",
    "        xBin = binary_repr(x, width=n)\n",
    "        beta = 0\n",
    "        for i in xrange(n):\n",
    "            beta += (int(xBin[i])*int(uBin[i]))\n",
    "        \n",
    "        return beta\n",
    "    \n",
    "    #Compute walsh kernel (there is only a single kernel for forward and inverse transform\n",
    "    #as it is both orthogonal and symmetric).\n",
    "    @classmethod\n",
    "    def computeKernel(self, N):\n",
    "        \"\"\"\n",
    "        Computes/generates the walsh kernel function.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        N : int\n",
    "            Size of the kernel to be generated.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        kernel : ndarray\n",
    "            The generated kernel as a matrix.\n",
    "        \"\"\"\n",
    "        \n",
    "        #Initialize the kernel\n",
    "        kernel = np.zeros([N, N])\n",
    "        #Compute each value of the kernel...\n",
    "        n = int(math.log(N, 2))        \n",
    "        for u in xrange(N):\n",
    "            for x in xrange(N):\n",
    "                beta = Walsh.__computeBeta(u, x, n)\n",
    "                kernel[u, x] = (-1)**beta\n",
    "        \n",
    "        #To make the kernel orthonormal, we can divide it by sqrt(N)\n",
    "        #kernel /= math.sqrt(N)\n",
    "        \n",
    "        #Return the resulting kernel\n",
    "        return kernel\n",
    "\n",
    "    @classmethod\n",
    "    def computeForward2DWalshTransform(self, imge):\n",
    "        \"\"\"\n",
    "        Computes/generates the 2D Walsh transform.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        imge : ndarray\n",
    "            The input image to be transformed.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        final2DWalsh : ndarray\n",
    "            The transformed image.\n",
    "        \"\"\"\n",
    "        \n",
    "        N = imge.shape[0]\n",
    "        kernel = Walsh.computeKernel(N)\n",
    "\n",
    "        imge1DWalsh = np.dot(kernel, imge)        \n",
    "        final2DWalsh = np.dot(imge1DWalsh, kernel)\n",
    "\n",
    "        return final2DWalsh/N\n",
    "    \n",
    "    @classmethod\n",
    "    def computeInverse2DWalshTransform(self, imgeWalsh):\n",
    "        \"\"\"\n",
    "        Computes/generates the inverse of 2D Walsh transform.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        imgeWalsh : ndarray\n",
    "            The Walsh transformed image.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        imgeInverse : ndarray\n",
    "            The inverse of the transformed image.\n",
    "        \"\"\"\n",
    "        \n",
    "        N = imgeWalsh.shape[0]\n",
    "        kernel = Walsh.computeKernel(N)\n",
    "\n",
    "        imge1DInverse = np.dot(kernel, imgeWalsh)        \n",
    "        imgeInverse = np.dot(imge1DInverse, kernel)\n",
    "\n",
    "        return imgeInverse/N\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"WalshTesting\"></a>\n",
    "### Testing the Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to compute the 4x4 walsh kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.],\n",
       "       [ 1., -1.,  1., -1.],\n",
       "       [ 1.,  1., -1., -1.],\n",
       "       [ 1., -1., -1.,  1.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Walsh.computeKernel(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: if we want to make the kernel orthonormal, we divide it by $\\sqrt N$. Now, we will compute the walsh transform of a given image.  First we will read an image from a file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Read an image file\n",
    "imgeCameraman = Image.open(\"Images/cameraman.tif\") # open an image\n",
    "\n",
    "#Convert the image file to a matrix\n",
    "imgeCameraman = np.array(imgeCameraman)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imgeWalsh = Walsh.computeForward2DWalshTransform(imgeCameraman)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inverse of the transformed image can also be computed as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imgeInverse = Walsh.computeInverse2DWalshTransform(imgeWalsh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The minimum and maximum values of the transformation are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 60576.76953125)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(np.absolute(imgeWalsh)), np.max(np.absolute(imgeWalsh))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the original, the transformed and inverse transformed images as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAloAAADTCAYAAABZe73TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nXbeGIQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6542174790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axarr = plt.subplots(1, 3, figsize=(10,7))\n",
    "\n",
    "axarr[0].imshow(imgeCameraman, cmap=plt.get_cmap('gray'))\n",
    "axarr[0].set_title('Original Image')\n",
    "\n",
    "axarr[1].imshow(np.absolute(imgeWalsh), cmap=plt.get_cmap('gray'))\n",
    "axarr[1].set_title('Forward Transformed Image')\n",
    "\n",
    "axarr[2].imshow(imgeInverse, cmap=plt.get_cmap('gray'))\n",
    "axarr[2].set_title(\"Inverse Transformed Image\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's compute the running time of Walsh tranform using images with different size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Generate images\n",
    "imgSizes = [128, 64, 32, 16, 8]\n",
    "images = generateImages(imgSizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing for  128 x 128 image...\n",
      "Computing for  64 x 64 image...\n",
      "Computing for  32 x 32 image...\n",
      "Computing for  16 x 16 image...\n",
      "Computing for  8 x 8 image...\n"
     ]
    }
   ],
   "source": [
    "# A list that stores the running time of the DCT algorithm for images with different size.\n",
    "runningTimeWalsh = []\n",
    "\n",
    "#For each image...\n",
    "for i, imge in enumerate(images):\n",
    "    \n",
    "    #Compute the image size\n",
    "    N = imge.shape[0]\n",
    "    \n",
    "    print \"Computing for \", N, \"x\", N, \"image...\"\n",
    "    \n",
    "    #Save the starting time.\n",
    "    startTime = time.time()\n",
    "\n",
    "    #Compute the DCT of the image.\n",
    "    walshImge = Walsh.computeForward2DWalshTransform(imge)\n",
    "    \n",
    "    #Save the running time\n",
    "    runningTimeWalsh.append((time.time() - startTime)/60.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = zip(imgSizes, runningTimeWalsh)\n",
    "np.savetxt(\"RunningTimes/runningTimeWalsh.csv\", np.array(result), delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The running time will be visualized and compared with the other transformation methods in the next section. As it will be shown, Walsh is faster than DFT as it is only a square waveform where DFT is a complex, sinusoidal transformation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Haar Transform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"HaarIntroduction\"></a>\n",
    "### Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The Haar transform is also one type of the transformation methods. In contrast to Walsh, the kernel functions in Haar are not symmetric. So we need to transpose the first kernel when finding the second one.\n",
    "\n",
    "The forward transform is computed as follows:\n",
    "\n",
    "$ H(0, 0, x) = \\frac{1}{N} $\n",
    "\n",
    "$\n",
    "H(r, m, x) = \\left\\{\n",
    "  \\begin{array}{l l}\n",
    "   \\frac{2^{r/2}}{\\sqrt N} & \\quad \\text{$ \\frac{m-1}{2^r} \\leq x \\leq \\frac{m-1/2}{2^r}$ } \\\\\n",
    "   -\\frac{2^{r/2}}{\\sqrt N} & \\quad \\text{$ \\frac{m-1/2}{2^r} \\leq x \\leq \\frac{m}{2^r}$ }\\\\\n",
    "   0 & \\quad \\text{otherwise}\n",
    "  \\end{array} \\right.\n",
    "$\n",
    "\n",
    "Where $0 \\leq x < 1$, $0 \\leq r < log_2 N $ and $1 \\leq m \\leq 2^r$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"HaarImplementation\"></a>\n",
    "### Python Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's implementation is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Haar(object):\n",
    "    \"\"\"\n",
    "    This class Haar implements all the procedures for transforming a given 2D digital image\n",
    "    into its corresponding frequency-domain image (Haar Transform)\n",
    "    \"\"\"\n",
    "        \n",
    "    #Compute the Haar kernel.\n",
    "    @classmethod\n",
    "    def computeKernel(self, N):\n",
    "        \"\"\"\n",
    "        Computes/generates the haar kernel function.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        N : int\n",
    "            Size of the kernel to be generated.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        kernel : ndarray\n",
    "            The generated kernel as a matrix.\n",
    "        \"\"\"\n",
    "        \n",
    "        i = 0\n",
    "        kernel = np.zeros([N, N])\n",
    "        n = int(math.log(N, 2))\n",
    "\n",
    "        #Fill for the first row of the kernel\n",
    "        for j in xrange(N):\n",
    "            kernel[i, j] = 1.0/math.sqrt(N)\n",
    "\n",
    "\n",
    "        # For the other rows of the kernel....\n",
    "        i += 1\n",
    "        for r in xrange(n):\n",
    "             for m in xrange(1, (2**r)+1):\n",
    "                j=0\n",
    "                for x in np.arange(0, 1, 1.0/N):\n",
    "                    if (x >= (m-1.0)/(2**r)) and (x < (m-0.5)/(2**r)):\n",
    "                        kernel[i, j] = (2.0**(r/2.0))/math.sqrt(N)\n",
    "                    elif (x >= (m-0.5)/(2**r)) and (x < m/(2.0**r)):\n",
    "                        kernel[i, j] = -(2.0**(r/2.0))/math.sqrt(N)\n",
    "                    else:\n",
    "                        kernel[i, j] = 0\n",
    "                    j += 1\n",
    "                i += 1\n",
    "        return kernel\n",
    "\n",
    "    @classmethod\n",
    "    def computeForward2DHaarTransform(self, imge):\n",
    "        \"\"\"\n",
    "        Computes/generates the 2D Haar transform.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        imge : ndarray\n",
    "            The input image to be transformed.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        final2DHaar : ndarray\n",
    "            The transformed image.\n",
    "        \"\"\"\n",
    "        \n",
    "        N = imge.shape[0]\n",
    "        kernel = Haar.computeKernel(N)\n",
    "\n",
    "        imge1DHaar = np.dot(kernel, imge) \n",
    "        \n",
    "        #Transpose the kernel as it is not symmetric\n",
    "        final2DHaar = np.dot(imge1DHaar, kernel.T)\n",
    "\n",
    "        return final2DHaar/N\n",
    "    \n",
    "    @classmethod\n",
    "    def computeInverse2DHaarTransform(self, imgeHaar):\n",
    "        \"\"\"\n",
    "        Computes/generates the inverse of 2D Haar transform.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        imgeHaar : ndarray\n",
    "            The Haar transformed image.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        imgeInverse : ndarray\n",
    "            The inverse of the transformed image.\n",
    "        \"\"\"\n",
    "        \n",
    "        N = imgeHaar.shape[0]\n",
    "        kernel = Haar.computeKernel(N)\n",
    "\n",
    "        imge1DInverse = np.dot(kernel.T, imgeHaar)        \n",
    "        imgeInverse = np.dot(imge1DInverse, kernel)\n",
    "\n",
    "        return imgeInverse/N\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"HaarTesting\"></a>\n",
    "### Testing the Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try the 4x4 haar kernel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5       ,  0.5       ,  0.5       ,  0.5       ],\n",
       "       [ 0.5       ,  0.5       , -0.5       , -0.5       ],\n",
       "       [ 0.70710678, -0.70710678,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.70710678, -0.70710678]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xKernel = Haar.computeKernel(4)\n",
    "xKernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will compute the haar transform of a given image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imgeHaar = Haar.computeForward2DHaarTransform(imgeCameraman)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's return back to its original form by using the inverse Haar transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imgeHaarInverse = Haar.computeInverse2DHaarTransform(imgeHaar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The range of the results of the Haar transform is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 118.31400299072266)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(np.absolute(imgeHaar)), np.max(np.absolute(imgeHaar))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now visualize the original, forward and inverse transformed images as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAloAAADTCAYAAABZe73TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJMxCy2AwGAwGg+El8f8Bb/98qdOmUrIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6542174090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axarr = plt.subplots(1, 3, figsize=(10,7))\n",
    "\n",
    "axarr[0].imshow(imgeCameraman, cmap=plt.get_cmap('gray'))\n",
    "axarr[0].set_title('Original Image')\n",
    "\n",
    "axarr[1].imshow(np.absolute(imgeHaar), cmap=plt.get_cmap('gray'))\n",
    "axarr[1].set_title('Forward Transformed Image')\n",
    "\n",
    "axarr[2].imshow(imgeHaarInverse, cmap=plt.get_cmap('gray'))\n",
    "axarr[2].set_title(\"Inverse Transformed Image\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will compute the running time of Haar Transform using images with different sizes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing for  128 x 128 image...\n",
      "Computing for  64 x 64 image...\n",
      "Computing for  32 x 32 image...\n",
      "Computing for  16 x 16 image...\n",
      "Computing for  8 x 8 image...\n"
     ]
    }
   ],
   "source": [
    "#Generate images\n",
    "imgSizes = [128, 64, 32, 16, 8]\n",
    "images = generateImages(imgSizes)\n",
    "\n",
    "# A list that stores the running time of the DCT algorithm for images with different size.\n",
    "runningTimeHaar = []\n",
    "\n",
    "#For each image...\n",
    "for i, imge in enumerate(images):\n",
    "    \n",
    "    #Compute the image size\n",
    "    N = imge.shape[0]\n",
    "    \n",
    "    print \"Computing for \", N, \"x\", N, \"image...\"\n",
    "    \n",
    "    #Save the starting time.\n",
    "    startTime = time.time()\n",
    "\n",
    "    #Compute the Haar of the image.\n",
    "    haarImge = Haar.computeForward2DHaarTransform(imge)\n",
    "    \n",
    "    #Save the running time\n",
    "    runningTimeHaar.append((time.time() - startTime)/60.0)\n",
    "    \n",
    "result = zip(imgSizes, runningTimeHaar)\n",
    "np.savetxt(\"RunningTimes/runningTimeHaar.csv\", np.array(result), delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Load the running time for DFT, Walsh, Haar Transforms\n",
    "runningTimeDFT = np.loadtxt(\"RunningTimes/runningTimeDFT.csv\", delimiter =',')\n",
    "runningTimeWalsh = np.loadtxt(\"RunningTimes/runningTimeWalsh.csv\", delimiter =',')\n",
    "runningTimeHaar = np.loadtxt(\"RunningTimes/runningTimeHaar.csv\", delimiter =',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['128x128', '64x64', '32x32', '16x16', '8x8']\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8VeW18PHfyjwTAklkCEEECsoQ5gAWUVBpa0VbZ0Jb\nb+3wXu3bOtS22luxt7Zq1c6377WDE6jlatE6XMeKQ2UKyGgQUAkhQBLClBAynvX+sXdCCJlzTvbJ\nOev7+ZwP++yzh3Ue9sna+3n2fh5RVYwxxoSvCK8DMMYY4y1LBMYYE+YsERhjTJizRGCMMWHOEoEx\nxoQ5SwTGGBPmLBEYY0yYs0RgjDFhzhKBMcaEuSivA+iMgQMH6vDhw70Owxhj+pT169cfVNX0jpbr\nE4lg+PDh5Ofnex2GMcb0KSJS2JnlrGrIGGPCnCUCY4wJc5YIjDEmzPWJNgJjjGlNXV0de/fupbq6\n2utQPBUXF8fQoUOJjo7u1vohnQh2lFRw05Mb+P11kxmdmex1OMYYP9u7dy/JyckMHz4cEfE6HE+o\nKuXl5ezdu5czzzyzW9sI2aqhqtp6rn9kLTtLK7n+kXVU1dZ7HZIxxs+qq6sZMGBA2CYBABFhwIAB\nPboqCtlE8P1nNnOwshZVOFhZw+3PbPY6JGNMAIRzEmjU0zIIyUSwfF0R/ywopabeB0BNvY83C0pZ\nvq7I48iMMSb4hGQiuO+V7Zyoazhl3om6Bu57ZbtHERljgsWOkgou+tXb7Cip8Mv2IiMjycnJ4Zxz\nzmHixIk8+OCD+HzOSejKlSvp168fOTk55OTkMH/+fO65556m943r5uTk8Nvf/tYv8XRHSDYW/2DB\nGO76x7ZTkkF8dCQ//NwYD6Myxnitse1w39Fqrn9kHa/fMoeEmJ79GYyPj2fjxo0AlJaWct1113Hs\n2DHuvvtuAD772c/y4osvnrLOnXfeCUBSUlLTul4KySuCq6ZlccHYDGKjTn6988ekc+XULA+jMsZ4\nLdBthxkZGTz88MP8/ve/R1X9uu1ACskrAoBfXjGBCx96m+IjTkv6xedkehyRMSaQ7n5hGx/uO9bm\n56XHqik8VIXP/ftcU+/j5S37Of+Xb5GREtfqOmcPTuGuL57TpThGjBhBQ0MDpaWlALz77rvk5OQA\ncOWVVzZdDQSTkE0ECTFRPHL9dG5ctoGjJ+pYnr+XhTlDvQ7LGOORosMnmpJAI58689tKBP7QWtVQ\nsAnZRAAwOjOZ1285jz+8tYtfvvoRH5dVclZ6ktdhGWMCoKMz9+XrilptO/zpwnP8Wm38ySefEBkZ\nSUZGBgUFBX7bbiCFZBtBS1dNzSI6Uli2eo/XoRhjPNKy7TA2KoJ5YzP8mgTKysr49re/zU033dSn\nnm8Ii0SQnhzLgnGDeGZ9ESdqGzpewRgTkn55xQQGJsUgwMCkWO6/YkKPt3nixImm20fnz5/PRRdd\nxF133dXzYHtRSFcNNbc4N5sXNu3jhU37uGqa3T1kTDhqbDts7IOsp7eOAjQ0tH1yOXfuXObOndvm\n55WVlT3evz+ExRUBwLTh/RmdmcTjq3f3qdu6jDH+NTozmdduPs86omwmbBKBiLA4N5utxcfYtPeo\n1+EYY0zQCJtEAHDZpCEkxkSydHWnhvE0xpiwEFaJIDkumssmDeGFTfs4fLzW63CMMSYoBCwRiEiW\niLwlIh+KyDYR+a47P01EXheRne6//QMVQ2vycrOpqffxzPq9vblbY4wJWoG8IqgHblXVs4Fc4EYR\nORv4IfCmqo4C3nTf95qxg1KYNrw/y9YU4mv5mKExxoShgCUCVd2vqhvc6QqgABgCLAQecxd7DLgs\nUDG0JS83m93lVby362Bv79oY47XSAvhDrvOvH9x88838+te/bnp/8cUXc8MNNzS9v/XWW3nooYfa\nXD8pqf3eDjr63B96pY1ARIYDk4A1QKaq7nc/OgD0em9wC8adwYDEGJ6wRmNjwkvtcVh2JZRtd/6t\nPd7jTc6ePZv3338fAJ/Px8GDB9m2bVvT5++//z6zZs3q8X4CKeCJQESSgGeB76nqKV0DqnNDf6v1\nMyLyTRHJF5H8srIyv8YUGxXJ1dOyeLOghH1HTvh128aYIPb8jXC8DFDn3+dv6vEmZ82axapVqwDY\ntm0b48aNIzk5mcOHD1NTU0NBQQFnn3028+bNY/LkyYwfP57nn3/+tO3s37+fOXPmkJOTw7hx43j3\n3XebPrvzzjuZOHEiubm5lJSU9DjmlgL6ZLGIROMkgWWq+nd3domIDFLV/SIyCChtbV1VfRh4GGDq\n1Kl+r8y/dvow/vj2xzy1dg+3XvQZf2/eGNPb/veHcGBL259XHIDDn4A6o4dRXw0fPge/3QzJZ7S+\nzhnj4XP3trvbwYMHExUVxZ49e3j//feZOXMmxcXFrFq1in79+jF+/HgSEhJYsWIFKSkpHDx4kNzc\nXC699NJT+iN68sknufjii7nzzjtpaGigqqoKgOPHj5Obm8s999zD7bffzp/+9Cd+/OMfd6loOhLI\nu4YE+AtQoKrNK8j+AXzVnf4qcHpq7AVZaQlc8JkMnl5XRK07trExJoQdKTyZBBqpz5nfQ7NmzeL9\n999vSgQzZ85sej979mxUlTvuuIMJEyYwf/58iouLTzuznzZtGo888ghLlixhy5YtJCc7Tz7HxMRw\nySWXADBlyhR2797d43hbCuQVwWxgMbBFRBrHYrsDuBdYLiJfBwqBqwIYQ7vyZmZz/SPreO3DA1wy\nYbBXYRhj/KGDM3c2LIX//T7UVZ2cF50An38AJi3q0a4b2wm2bNnCuHHjyMrK4sEHHyQlJYXrr7+e\nZcuWUVZWxvr164mOjmb48OFUV1efso05c+bwzjvv8NJLL/G1r32NW265ha985StER0c3XTlERkZS\nX1/fo1hbE8i7ht5TVVHVCaqa475eVtVyVZ2nqqNUdb6qHgpUDB05b1Q6WWnxPLHKGo2NCXmT82D0\nxRDlDkITFQejF/Q4CYBzRfDiiy+SlpZGZGQkaWlpHDlyhFWrVjFr1iyOHj1KRkYG0dHRvPXWWxQW\nnv43p7CwkMzMTL7xjW9www03sGHDhh7H1Vlh9WRxSxERwqIZ2az59BA7Syq8DscYE2gL/wCJ6YA4\n/y78vV82O378+Ka6/+bz+vXrx8CBA1m0aBH5+fmMHz+exx9/nDFjxpy2jZUrVzJx4kQmTZrE3/72\nN7773e/6JbbOkL7QE+fUqVM1Pz8/INsur6xh5i/+ybXTs7h74biA7MMYExgFBQWMHTu2ayuVFsD/\nXA9XPgIZXVw3iLVWFiKyXlWndrRuWF8RAAxIiuULEwbx7IZijtf4v+7NGBNkMsbCjatDKgn0VNgn\nAnCeNK6sqef5jfu8DsUYY3qdJQJg8rBUxg5K4fFVNmiNMSb8WCLg5KA12w9UsGHPYa/DMcaYXmWJ\nwLUwZzDJsVEsXb3H61CMMaZXWSJwJcZG8aXJQ3hp837KK2u8DscYY3qNJYJm8nKzqW3wsTzfBq0x\nJlTtOryLy56/jF2Hd/lley27iX700Ue56aaed2bXmywRNDMqM5ncEWk8ubaQBhu0xpiQU1VXxb+/\n+e98cuQTbnzzRqqadzcRZALRlURbLBG0kJebTdGhE7yzw79dXxtjvPeT93/CoepDKEr5iXLuev+u\ngO7vhRdeYMaMGUyaNIn58+c3dTS3du1aZs6cyaRJk5g1axYfffQR4FxNXHrppVxwwQXMmzcvoLE1\nF9BuqPuii84+g/TkWJ5YXcj5YzK8DscY00n3rb2P7Ye2t/l5WVUZRZVF+NweSGt8Nby2+zUKygtI\nT0hvdZ0xaWP4wfQftLvfEydOkJOT0/T+0KFDXHrppQCce+65rF69GhHhz3/+M/fffz8PPvggY8aM\n4d133yUqKoo33niDO+64g2effRaADRs2sHnzZtLS0rr0/XvCEkELMVERXDsti9+9tYuiQ1VkpSV4\nHZIxxg+KK4ubkkAjHz6KK4vbTASdER8fz8aNG5veP/roozR2ibN3716uvvpq9u/fT21tLWeeeSYA\nR48e5atf/So7d+5ERKirq2ta/8ILL+zVJACWCFp1zfRh/P6tXTy5dg8/WHB651DGmODT0Zn7ip0r\n+MXaX3Ci/uSohHGRcdyZeyeXjQzM0Onf+c53uOWWW7j00ktZuXIlS5YsAeA//uM/OP/881mxYgW7\nd+9m7ty5TeskJiYGJJb2WBtBKwanxjN/bCZ/W1dETX2D1+EYY/zg8lGXM2foHGIjYwGIjYhlbtbc\ngCUBcM78hwwZAsBjjz3W6vxHH300YPvvLEsEbVg8M5tDx2t5ZesBr0MxxvjJT2f9lLS4NARhQPwA\n7p51d0D3t2TJEq688kqmTJnCwIEDm+bffvvt/OhHP2LSpEm9endQW8K+G+q2+HzKBQ+uZGBSLM/8\nn1m9um9jTOd0pxvqXYd3cds7t/HAnAcY2X9kgCLrfdYNdQBERAh5udnkFx6mYP8xr8MxxvjJyP4j\neW7hcyGVBHrKEkE7rpgylNioCJautqEsjTGhyxJBO1ITYvjixMGs+KCYiuq6jlcwxvS6vlC9HWg9\nLQNLBB1YnJtNVW0Dz31Q7HUoxpgW4uLiKC8vD+tkoKqUl5cTFxfX7W3YcwQdmJiVyoSh/XhidSF5\nudmIiNchGWNcQ4cOZe/evZSVhXeXMHFxcQwdOrTb61si6IS8Gdnc/uxm1n56iBkjBngdjjHGFR0d\n3fS0ruk+qxrqhC9OHExKXBRL19igNcaY0GOJoBPiYyK5YkoWr2zdT2lFtdfhGGOMX1ki6KRFucOo\na1CWryvyOhRjjPErSwSddFZ6EueOHMiTa/bYoDXGmJBiiaAL8nKHse9oNf/cXup1KMYY4zeWCLpg\n/thMMlOcQWuMMSZUWCLogqjICK6bns07O8ooLD/udTjGGOMXlgi66JrpWURGCMvsVlJjTIiwRNBF\nmSlxXHxOJsvzi6ius0FrjDF9nyWCbsjLzeZIVR0vbd7vdSjGGNNjlgi6YeaIAZyVnmiNxsaYkGCJ\noBtEnEFrNhYdYWvxUa/DMcaYHrFE0E1fmjyU+OhIG7TGGNPnWSLopn7x0SzMGcxzG4s5esIGrTHG\n9F0BSwQi8lcRKRWRrc3mLRGRYhHZ6L4+H6j994a83Gyq63z8fcNer0MxxphuC+QVwaPAglbm/0pV\nc9zXywHcf8CNG9KPScNSeWJ1YViPkGSM6dsClghU9R3gUKC2HyzyZmTzSdlxVn1c7nUoxhjTLV60\nEXxHRDa7VUf921pIRL4pIvkikh/Mw9B9YcIgUhOiWbrGGo2NMX1TbyeCPwIjgBxgP/BgWwuq6sOq\nOlVVp6anp/dWfF0WFx3J1VOzeHVbCSXHbNAaY0zf06uJQFVLVLVBVX3An4Dpvbn/QLluxjAafMpT\na63/IWNM39OriUBEBjV7ezmwta1l+5LsAYmcNzqdp9buoa7B53U4xhjTJYG8ffQpYBXwGRHZKyJf\nB+4XkS0ishk4H7g5UPvvbXm52ZQcq+HNghKvQzHGmC6JCtSGVfXaVmb/JVD789oFYzIYkhrPE6sL\nWTBuUMcrGGNMkLAni/0kMkK4bsYw/rWrnI/LKr0OxxhjOs0SgR9dNTWL6Ehh2WprNDbG9B2WCPwo\nPTmWBeMG8cz6Ik7U2qA1xpi+wRKBny3OzeZYdT0vbNrndSjGGNMplgj8bNrw/ozOTOLx1but/yFj\nTJ9gicDPRITFudlsLT7Gpr02aI0xJvhZIgiAyyYNITHGBq0xxvQNlggCIDkumssmDeGFTfs4fLzW\n63CMMaZdnUoEIpIhIpeLyI0i8m8iMl1ELIm0Iy83m5p6H8+st0FrjDHBrd0/5iJyvoi8CrwEfA4Y\nBJwN/BjYIiJ3i0hK4MPse8YOSmHa8P4sW1OIz2eNxsaY4NVRFxOfB76hqqc9ISUiUcAlwIXAswGI\nrc/Ly83mu09v5L1dB5kzOni70jbGhLd2E4Gqfr+dz+qB5/weUQhZMO4MBiTG8MTqQksExpig1dk2\ngp+LSGqz9/1F5GeBCys0xEZFcvW0LN4sKGHfkRNeh2OMMa3qbIPv51T1SOMbVT2MU21kOnDt9GEo\n2KA1xpig1dlEECkisY1vRCQeiG1neePKSkvggs9k8PS6ImrrbdAaY0zw6WwiWAa8KSJfdweYeR14\nLHBhhZa8mdmUVdTw2ocHvA7FGGNO06lEoKr3AT8Dxrqv/1TV+wMZWCg5b1Q6WWnxPLHKnjQ2xgSf\nrjwUVgC8oqq3Ae+KSHKAYgo5ERHCohnZrPn0EDtLKrwOxxhjTtHZu4a+ATwD/Lc7awh262iXXDU1\ni5ioCOt/yBgTdDp7RXAjMBs4BqCqO4GMQAUVitISY/jC+EE8u6GY4zX1XodjjDFNOpsIalS1qfc0\n96li6zehi/Jys6msqef5jTZojTEmeHQ2EbwtIncA8SJyIfA/wAuBCys0TR6WythBKTy+ygatMcYE\nj84mgh8CZcAW4FvAyzgdz5kuaBy0ZvuBCjbsOex1OMYYA3T+9lGfqv4JWATcAzyvdkrbLQtzBpMc\nG8XS1faksTEmOHTUDfX/E5Fz3Ol+wEbgceADEbm2F+ILOYmxUXxp8hBe2ryf8soar8MxxpgOrwg+\nq6rb3OnrgR2qOh6YAtwe0MhCWF5uNrUNPpbn26A1xhjvdZQImo+zeCHuswOqan0l9MCozGRyR6Tx\n5NpCGmzQGmOMxzpKBEdE5BIRmYTzHMEr0HT7aHyggwtlebnZFB06wTs7yrwOxRgT5jpKBN8CbgIe\nAb7X7EpgHs7wlaabLjr7DNKTY3nCnjQ2xnisoxHKdgALWpn/KvBqoIIKBzFREVw7LYvfvbWLokNV\nZKUleB2SMSZMdXTX0I9FpH87n18gIpf4P6zwcM30YQjwpA1aY4zxUEeD128BXhSRamADzkNlccAo\nIAd4A/h5QCMMYYNT45k/NpO/rSvie/NHERsV6XVIxpgw1O4Vgao+r6qzgW8D24BInI7nlgLTVfVm\nVbXWzh5YPDObQ8dreWWr3YhljPFGR1cEQFNvoztFJEFVqwIcU1iZfdZAhg9I4IlVhSzMGeJ1OMaY\nMNTZ8QhmisiHwHb3/UQR+a+ARhYmIiKEvNxs8gsPU7D/mNfhGGPCUGc7nfs1cDFQDqCqm4A5gQoq\n3FwxZSixNmiNMcYjnR6qUlWLWsxqaG95EfmriJSKyNZm89JE5HUR2en+2+YdSeEkNSGGL04czIoP\niqmorvM6HGNMmOlsIigSkVmAiki0iNyGM4Zxex7l9GcQfgi8qaqjgDfd9wZYnJtNVW0Dz31Q7HUo\nxpgw09lE8G2c4SqHAMU4t47e2N4KqvoOcKjF7IXAY+70Y8BlnY40xE3MSmXC0H48sbrQBq0xxvSq\nzo5HcFBVF6lqpqpmqGqeqpZ3Y3+ZqrrfnT4AZLa1oIh8U0TyRSS/rCw87lDNm5HNjpJK1n7aMn8a\nY0zgdPauoTNF5CER+buI/KPx1ZMduwPbtHnqq6oPq+pUVZ2anp7ek131GV+cOJiUuCiWrrEnjY0x\nvadTzxHgdD/9F5xxin092F+JiAxS1f0iMggo7cG2Qk58TCRXTs3i8VW7Ka0YS0ZynNchGWPCQGfb\nCKpV9beq+paqvt346sb+/gF81Z3+KvB8N7YR0hbNGEZdg7J8XcubtIwxJjA6mwh+IyJ3uQ+WTW58\ntbeCiDwFrAI+IyJ7ReTrwL3AhSKyE5jvvjfNjEhP4tyRA3lyzR4btMYY0ys6WzU0HlgMXMDJqiF1\n37dKVdsa03hep6MLU3m5w/j20g38c3spF57dZnu6Mcb4RWcTwZXACFWt7XBJ02Pzx2aSmeIMWmOJ\nwBgTaJ2tGtoKpAYyEHNSVGQE103P5p0dZRSWH/c6HGNMiOtsIkgFtovIq/66fdS075rpWURGCMvs\nVlJjTIB1tmroroBGYU6TmRLHxedksjy/iFsuHE1ctA1aY4wJjM6OR9CdW0VND+XlZvPylgO8tHk/\nX54y1OtwjDEhqqMxi99z/60QkWPNXhUiYp3nB9jMEQM4Kz2RJ6x7amNMAHXURpAIoKrJqprS7JWs\nqim9EF9YE3EGrdlYdIStxUe9DscYE6I6SgT2RJPHvjR5KPHRkTZojTEmYDpqI8gQkVva+lBVH/Jz\nPKaFfvHRLMwZzHMbi/nR58fSLz7a65CMMSGmoyuCSCAJSG7jZXpBXm421XU+nl2/1+tQjDEhqKMr\ngv2q+tNeicS0adyQfkwalsrSNYVcP3s4IuJ1SMaYENLRFYH9xQkSeTOy+aTsOKs+7s54QMYY07aO\nEoF1EBckvjBhEKkJ0SxdY43Gxhj/ajcRqKqNmRgk4qIjuXpqFq9uK6HkWLXX4RhjQkhn+xoyQeC6\nGcNo8ClPrbX+h4wx/mOJoA/JHpDIeaPTeWrtHuoaejJiqDHGnGSJoI9ZnJtNybEa3iwo8ToUY0yI\nsETQx5w/JoMhqfHW/5Axxm8sEfQxkRHCdTOG8a9d5XxcVul1OMaYEGCJoA+6amoW0ZHCstXWaGyM\n6TlLBH1QenIsC8YN4pn1RZyobfA6HGNMH2eJoI9anJvNsep6Xti0z+tQjDF9nCWCPmra8P6Mzkzi\n8dW7UbXewo0x3WeJoI8SERbnZrO1+Bib9tqgNcaY7rNE0IddNmkIiTE2aI0xpmcsEfRhyXHRXDZp\nCC9s2sfh47Veh2OM6aMsEfRxebnZ1NT7eMYGrTHGdJMlgj5u7KAUpg3vz7I1hfh81mhsjOk6SwQh\nIC83m93lVby366DXoRhj+iBLBCFgwbgzGJAYY/0PGWO6xRJBCIiNiuTqaVm8WVDCviMnvA7HGNPH\nWCIIEddOH4aCDVpjjOkySwQhIistgQs+k8HT64qorbdBa4wxnWeJIITkzcymrKKG1z484HUoxpg+\nxBJBCDlvVDpZafE8scoajY0xnWeJIIRERAiLZmSz5tND7Cyp8DocY0wf4UkiEJHdIrJFRDaKSL4X\nMYSqq6ZmERMVYf0PGWM6zcsrgvNVNUdVp3oYQ8hJS4zhC+MH8eyGYo7X1HsdjjGmD7CqoRCUl5tN\nZU09z2+0QWuMMR3zKhEo8IaIrBeRb3oUQ8iaPCyVswel8PgqG7TGGNMxrxLBuaqaA3wOuFFE5rRc\nQES+KSL5IpJfVlbW+xH2YSJCXm422w9UsGHPYa/DMcYEOU8SgaoWu/+WAiuA6a0s87CqTlXVqenp\n6b0dYp+3MGcwybFRLF1tTxobY9rX64lARBJFJLlxGrgI2NrbcYS6xNgovjxlKC9t3k95ZY3X4Rhj\ngpgXVwSZwHsisglYC7ykqq94EEfIWzRjGLUNPpbn26A1xpi2RfX2DlX1E2Bib+83HI3KTCZ3RBpP\nri3km3NGEBkhXodkjAlCdvtoiMvLzabo0Ane2WEN7saY1lkiCHEXnX0G6cmxNmiNMaZNlghCXExU\nBNdOy+Ktj0opOlTldTjGmCBkiSAMXDN9GAI8aYPWGGNaYYkgDAxOjWf+2Ez+tq6ImvoGr8MxxgQZ\nSwRhYvHMbA4dr+WVrTZojTHmVJYIwsTsswYyfECCDVpjjDmNJYIwERHh9D+UX3iYgv3HvA7HGBNE\nLBGEkSumDCXWBq0xxrRgiSCMpCbE8MWJg1nxQTEV1XVeh2OMCRKWCMLM4txsqmobeO6DYq9DMcYE\nCUsEYWZiVioThvbjidWFNmiNMQawRBCW8mZks6OkkrWfHvI6FGNMELBEEIa+OHEwKXFRLF1jTxob\nYywRhKX4mEiunJrFK1v3U1pR7XU4xhiPWSIIU4tmDKOuQVm+rsjrUIwxHrNEEKZGpCdx7siBPLlm\nDw0+azQ2JpxZIghjebnZ7DtazT+3l3odijHGQ5YIwtj8sRmckRJng9YYE+YsEYSxqMgIrp0+jHd2\nlFFYftzrcIwxHrFEEOaumZ5FZISwzG4lNSZsWSIIc5kpcVx8TibL84uorrNBa4wJR5YIDHm52Ryp\nquOlzfu9DsUY4wFLBIaZIwZwVnoiD7/7CRf96m12lFR4HZIxphdZIjCICFdNzeKjAxXsLKnk+kfW\nUVVb73VYxpheYonAALB+z2EAFDhYWcPtz2z2NiBjTK+J8joA473l64p4d8fBpvc19T5e3rKfK//4\nPhePO4ORGUmMykxmcL84RMTDSI0xgWCJwHDfK9s50eKOIZ9C/p7DrCs83DQvMSaSkRlJjMxIZlRm\nEqMykhiVkczQ/vFERFiCMKavskRg+MGCMdz1j22nJIP46Eh+uvAc5o3NZFdpJTtLnfaDXaWVvLer\njGc37G1aNi46grPS3cSQmexcQWQkMSwtgahIq300JthZIjBcNS2Lt3eW8caHJdTU+4iNimDe2Ayu\nnJoFwPQz05h+Ztop6xw9Uceu0kp2uQliZ2kl63Yf5rmN+5qWiYmMYER6IiMzkhidmewmiiSyByQS\nbQnCmKAhfWG4wqlTp2p+fr7XYYS0qtp6LnzobfYdqWZwajyv3zKHhJiunydU1tTzcamTGHaWVrDL\nTRJFh6toPNSiIoQzByYyKtOtZnITxJkDE4mNivTzNzMmfInIelWd2uFylghMox0lFdz05AZ+f91k\nRmcm+3XbJ2ob+Lis8rRqpt3lx2nsBTtCYPiARLdx2ml/GJmRxFnpScTHWIIwpqssEZg+obqugd3l\nx5uqlxqrmj49eJx6N0OIQFb/BEZlJDHSTRCjMpI4KyOJpFir3TSmLZ1NBPYrMp6Ki45kzBkpjDkj\n5ZT5dQ0+CpsliJ2llewsqeDdnQepbfA1LTckNb6pcbqxqmlkRhL94qN7+6sY02dZIjBBKToywv2j\nnsznms2vb/BRdPgEO0sq3CsIp6ppzZpyqutOJojMlNimqqVRza4i+ifG9P6XMSbIWSIwfUpUZARn\nDkzkzIGJXHTOyfk+n1J85ERT+8OOEqeaaXl+EVW1J2+LHZgU415BJLtXEM70wKSYLj8sF8g2FWN6\nkydtBCKyAPgNEAn8WVXvbW/57rYR7Pr4NW57+zYeOO8BRp51UfeCDSOhWF6qyr6j1ewsqXCuHkrc\nxurSSipWxftqAAAO9klEQVSqT/anlJoQ7bRBNLuLaVRGMpkpsa0miKraer7y619RlfoYCUe+xuPf\n+1637rIKJ2+vf577N/yY2yf/jPOmLPQ6nD6hp2UWtI3FIhIJ7AAuBPYC64BrVfXDttbpTiKoqjrI\nZU/P5UAEDPLBimtWkpAwsCehh7RwKy9VpbSi5pTEsKukkh2lFRypqmtaLjk2ym2gdu9icqfvf2E1\n22q/Q1mUkF6vjIv9Hb9ZfIGH3yi4lR85wFXPzGsqr+VXvMmA1DO8Diuo+aPMgjkRzASWqOrF7vsf\nAajqL9papzuJ4Lalc1hZV05NRASxPh/nRw/gl3nv9CT0kGbl5VBVyo/Xure3VriN1E5j9cHKmqbl\nZg1dwkeJVdRGRBDj8zHmeCK1kb/irIxkIiKECIFIEUSESPe9M1+IlBbvIwRxl48QObl+hLv+acvj\nLCcn30uL6ZPbomkfEUKzddx9RkizbTV734nvcOr6tFu19m//ncummIqm8sqpTeYv31rdG/+lfZY/\nyiyYE8EVwAJVvcF9vxiYoao3tbVOVxPBijdu5xdFL3Ei4uTTq6LKgAYlBT/1idPqZvpafztOvMdo\noDxC0GY/ZFFlgE9Jwe7fb05RjqqPw5Gnl1f/BiXR19eOgcA7HqFWXl3UWpnF+XxcEz+XW6/5Q6e3\n0+dvHxWRbwLfBBg2bFiX1v31npc50aILAxXhWCRMjsloY60eJsQ2V+9pou3C+t2MYWXdoVMOOHDL\nS2BydGrn9x8m2iqvigiYEtO/y9tr+b/jnJtp68toG+s0n6Otfd7a+nrq5y1WOn2dVmLSVpZvfO+e\nZG6IqGyzvEb6kugUP5+vBu/TU05kGyOOn1Zm1RERPFe1klsDsFcvEkExkNXs/VB33ilU9WHgYXCu\nCLqyg+8N+/xpVwRxPuXOYV/gsnn3dSvoUNbaFZSVV9tWvHE7Py96iWorr0558OkbefrEyhbl5ePa\nhLnccnXnz27DSVtldnni3IDsz4uev9YBo0TkTBGJAa4B/uHPHVw+/37mRA8g1ufcVx7r8zE3Os1+\npG2w8uqay+ffz2ej0ohxyyvG52NOlJVXW2695g+Mr00+pbwm1CZbEmhHb5dZrycCVa0HbgJeBQqA\n5aq6zd/7+emX/k6ailPXrcLdX/q7v3cRUqy8uuZnX15xSnn955etvNrzy6ufI7XBaRtIbYD7r37O\n65CCXm+WmSd9Aavqy6o6WlXPUtV7ArGPhISB/Nd5DzHCF8EfznsopG+F9Acrr65JSBjIH93y+i8r\nrw4NSD2Dn0z6OVl1wk8m/dxuHe2E3iwz63TOGGNCVGfvGrLRQYwxJsxZIjDGmDBnicAYY8KcJQJj\njAlzfaKxWETKgMJurj4QOOjHcEKdlVfXWHl1jZVX1/WkzLJVNb2jhfpEIugJEcnvTKu5cVh5dY2V\nV9dYeXVdb5SZVQ0ZY0yYs0RgjDFhLhwSwcNeB9DHWHl1jZVX11h5dV3Ayyzk2wiMMca0LxyuCIwx\nxrQjqBKBiPxVREpFZGuzeb8Uke0isllEVohIqjs/WkQeE5EtIlLQOORlV7fv730ECxFJFZFn3O9V\n4A4R2vjZrSKiItJhT2kiMldENorINhF5u8VnkSLygYi8GIjv0FtEJE5E1orIJvd73u3Ob/W4aGc7\nC91lN4pIvoic687PEpG3RORDd/vf7Y3vFUjt/Ja+45bZNhG5v4NtjBGRVSJSIyK3tfiszeM31IjI\nzW55bRWRp0Qkrp1l54nIBvcYe09ERvolCFUNmhcwB5gMbG027yIgyp2+D7jPnb4OeNqdTgB2A8O7\nun1/7yNYXsBjwA3udAyQ6k5n4XQBXggM7GAbqcCHwDD3fUaLz28BngRe9Pr79rCsBEhyp6OBNUBu\nW8dFO9tJ4mR16wRguzs9CJjsTicDO4Czvf7ePSyz1n6r5wNvALGtHS+tbCMDmAbcA9zW4rNWj99Q\newFDgE+BePf9cuBr7Sy/AxjrTv878Kg/4giqKwJVfQc41GLea+qMYQCwGmdEM3DGdEsUkSggHqgF\njolItojsFJGBIhIhIu+KyEVtbb87+/DX9w0UEemH80P9C4Cq1qrqEffjXwG302y0PveM5K/u9Hj3\nzCQBJxH+XVX3uNspbbbOUOALwJ974SsFlDoq3bfR7kvbOi7aKi9VrVT3Fwok0jiao+p+Vd3gTlfg\njMMxpFe+XIC08Vv6P8C9qlrjLlMK7ZZXqaquA+qab6SD4zcURQHx7t+ZBGCfiKwTkbkAIvILEWns\nrl+BFHe6H7DPHwEEVSLohH8D/tedfgY4DuwH9gAPqOohVS3EOXv7I3Ar8KGqvubPffT4WwTemUAZ\n8IhbdfNnEUkUkYVAsapuarH8b4CRInI58AjwLVWtAkYD/UVkpYisF5GvNFvn1zgJxRf4rxN4bjXX\nRqAUeF1V17RYpPlx0VZ5ISKXi8h24CV3nZb7GQ5MwrnqCDWjgc+KyBoReVtEprnz2yyvNrR6/AY2\ndG+oajHwAM7fl/3AUffv1deAP4rIfGABcLe7yg3AyyKyF1gM3OuvQILqBQynRdWNO/9OYAUnL71n\nA8twzt4ygI+AEc2WfxX4GEjuzPa7s49gfQFTgXpghvv+N8Avcf749HPn7aZZ1RAwAqgEHmw27/c4\nZ8KJOI+578T5sV8C/Je7zFz6eNVQi7JLBd4CxrV1XLRVXi22Mwd4o8W8JGA98CWvv6efyuqU3xKw\nFfgdTlXbdJwqj8bfUpvlBSyhWdVQG8fvf3r9fQNUhv2BfwLp7t+Z54A897M7gGpgUrPl/96sXL4P\n/NkfcfSJKwIR+RrOH59F6pYATrXFK6pap84l6L9wDiDcao3G6p2kQOwjyO0F9urJs9pncOpzzwQ2\nichunPLZICKNwx6NwvmhDm6xnVdV9biqHgTeASbiJMhL3e08DVwgIksD+5V6hzpVEG/hnIW1dVxA\n6+XVfDvvACMaG+RFJBp4FlimqqE6ruVenKpEVdW1OFeLjTcktFterWynteM3FM0HPlXVMlWtw/lD\nP8v9bDxwBOckFBFJByY2K5e/NVu2R4I+EYjIApwqiEv11MvJPcAF7jKJOI17293P7sM5k/8J8KcA\n7SNoqeoBoEhEPuPOmgdsUNUMVR2uqsNxfmyTVfWAWyf7W5yz2AEicoW73vPAuSIS5SbXGUCBqv5I\nVYe627kG+Keq5vXeN/QvEUmXk3eKxQMXAtvbOi7aKi8RGSki4k5PBmKBcnfeX3DK7qFe/Gq97Tmc\nBmNEZDROI+/Bdo6vVrVx/H4YsKi9tQfIFZEE9ziZBxSIyJeANJwy+517fB4G+rllC85xWuCXKLy+\nNGpxmfQUTj1ZHc4fqq8Du4AiYKP7+n/usknA/wDbcA6S77vzz8Opzohsdil1fVvbd+d3aR994QXk\nAPnAZpwfaP8Wn+/GrRoC/gr8X3c6yy2PDD15+fkhzmX/91rZz1z6eNUQzh0+H7hltRX4SQfHRavl\nBfzAPVY2AquAc91lzsVp5NvcbFuf9/p797DMWvutxgBL3TLcAFzQQXmd4a57DOfMdy+Q0pnjN5Re\nOPX/291yewLIxLk7KMv9/P8Cj7nTlwNbgE3ASvxUVW1PFhtjTJgL+qohY4wxgWWJwBhjwpwlAmOM\nCXOWCIwxJsxZIjDGmDBnicAEFRGp7HipwBORS9zuDTaJ02vot9z5327R1UZXtnmZiPzEnV4iIsVu\nL5JbReRSP2z/0fbu0ReRm0TktG4vjLHbR01QEZFKVe3U0+ABjCEap3fW6aq6V0RicXqd/aiH230f\n5+G0gyKyBKhU1QdEZCzwLs6zG93uu0lEHsV5puOZNj5PAP6lqpO6uw8TmuyKwAQlccZBeFtEnheR\nT0TkXhFZJM64AVtE5Cx3uS+6nZx9ICJviEimOz9dRF4Xp5/3P4tIYbPuHvLc7WwUkf8WkcgWu0/G\n6RGyHEBVaxqTgHsmf5uIDHbXb3w1iNPzbbqIPCtO75HrRGS2u95ooEadrjpOoaoFOH3rDGy2/Shp\nowdKEZnils16EXlVRAa1Un73ulcym0XkAXc/VcBuEZne0/8fE1osEZhgNhH4NjAWp6fF0ao6Hafr\n6++4y7wH5LpnuU/jdAkBcBdO1xfn4PRVMwzAPfu+GpitqjlAA7Co+U7V6WH2H0ChOAOFLBKRiBbL\n7FPVHHcbfwKeVafn298Av1LVacCXOdlN92ycp21PIyIzcPrlKWu2/Xpa6YHSvVr5HXCFqk7BeWr3\nnhbbG4DzBOo5qjoB+Fmzj/OBz7YWhwlfUV4HYEw71qnqfgAR+Rho7E58C26fNjid5/3NPSuOwenx\nEpxuHS4HUNVXROSwO38eMAVY53YLFI/T9fQpVPUGERmP0ynYbTj9unyt5XLuGf833P3hLn+2u22A\nFBFJwhmcpqzF6jeLSB5QAVytqtpsPVR1m4g8AbwIzFTVWhEZB4wDXneXjcTp6qG5ozi9Vv5FnNHj\nmo8gVwqMafk9THizRGCCWU2zaV+z9z5OHru/Ax5S1X+41ShLOtim4PTb0uGwo6q6Bdji/jH+lBaJ\nwE0+f8Gp929s5I7AuUKpbrHsCZyBRJr7lao+0EEYp/RA6ca/TVXbHLpRVevd6p95wBXATbidJwJx\nwIkO9mnCjFUNmb6uH1DsTn+12fx/AVcBiDNCXX93/pvAFSLS2LVvmohkN9+giCQ11s27cnAaj5sv\nE43TIeEPVHVHs49e42S1FSKS404WAF0aX7aNHig/AtLFHcNXnHG1z2kZP864Ey8DN+NUsTUajdO5\nmTFNLBGYvm4J8D8ish5o3hB7N3CROIOrXwkcACpU9UPgx8BrIrIZeB2n2qY5AW4XkY/EGbXsbk6v\nFpqFMzbF3c0ajAfj9BQ51W2k/RCnjQOcsRwmSfO6n3a4Ddv34ozbuwNnkKDfqGotzln+fSKyCacn\n05Z90icDL7rf7z2csaUbzXa/szFN7PZRE5LcWz4b3GqSmcAf3YZdL2P6DfCCqr7h0f4nAbeo6mIv\n9m+Cl7URmFA1DFju3u1Ti9Og67Wf4wzu45WBwH94uH8TpOyKwBhjwpy1ERhjTJizRGCMMWHOEoEx\nxoQ5SwTGGBPmLBEYY0yYs0RgjDFh7v8DlXNezztGsWwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6541d74610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the running times\n",
    "plt.plot(xrange(runningTimeDFT.shape[0]), runningTimeDFT[:,1], '-d')\n",
    "plt.hold\n",
    "plt.plot(xrange(runningTimeWalsh.shape[0]), runningTimeWalsh[:,1], '-d')\n",
    "plt.plot(xrange(runningTimeHaar.shape[0]), runningTimeHaar[:,1], '-d')\n",
    "\n",
    "xlabels = [str(int(imge)) + 'x' + str(int(imge)) for imge in runningTimeDFT[:, 0]]\n",
    "print xlabels\n",
    "plt.xticks(xrange(len(runningTimeDFT[:, 0])), xlabels)\n",
    "plt.xlabel(\"Image Size(Pixels)\")\n",
    "plt.ylabel(\"Time(Sec)\")\n",
    "plt.legend(['DFT', 'Walsh', 'Haar'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see from the graph above, both Walsh and Haar are faster than DFT but are not as precise as the DFT. Because DFT is a complex sinusoidal wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}