CV_assignment_2.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Untitled0.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/paritoshkc/Computer-Vision-Project/blob/master/CV_assignment_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RqBQzbHBKTRo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "outputId": "edfeb4c6-f426-41db-b451-abd93e757062"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": 243,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gOIRKR_KW7I5",
        "colab_type": "text"
      },
      "source": [
        "COMPUTER VISION ASSIGNMENT 2\n",
        "\n",
        "#Loading the keras mnist Dataset and filtering images of 1 digit \n",
        "    \n",
        "\n",
        "*   [References used for loading Keras MNIST dataset]\n",
        "    (https://medium.com/@ashok.tankala/build-the-mnist-model-with-your-own-handwritten-digits-using-tensorflow-keras-and-python-f8ec9f871fd3)\n",
        "*   Total images available are 70000 with 60000 are set aside for training and 10000 for test images. \n",
        "* reshaping the train images to dimensions of 28x28 \n",
        "* Filter the values based on the labels defined for each digit in *y_train* to create filters that can be used to find them in *X_train* and *X_test*\n",
        "* I have filtered the images for finding digit \"1\" . To understand the amount of data available we can print the shape to get the total number of images in X_train.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QAtakgqPWxVD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "bde8da80-4767-4d35-902d-1be1fdc91121"
      },
      "source": [
        "from keras.datasets import mnist\n",
        "from PIL import Image\n",
        "from numpy import *\n",
        "from matplotlib import pyplot as plt\n",
        "from pylab import *\n",
        "\n",
        "(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
        "X_train = X_train.reshape(X_train.shape[0],num_pixels)\n",
        "X_test = X_test.reshape(X_test.shape[0],num_pixels)\n",
        "num_pixels = 784\n",
        "\n",
        "def get_filttered_data(img_digit):\n",
        "  train_filter = np.where(y_train == img_digit )\n",
        "  test_filter = np.where(y_test == img_digit )\n",
        "\n",
        "  X_train_digits=X_train[train_filter]\n",
        "  X_test_digits=X_test[test_filter]\n",
        "  X_train_digits=X_train_digits[X_train_digits.shape[0]-500:]\n",
        "  return X_train_digits,X_test_digits\n",
        "\n",
        "X_train_digit,X_test_digit=get_filttered_data(5)\n",
        "\n",
        "\n",
        "\n",
        "print(X_train_digit.shape)\n"
      ],
      "execution_count": 244,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(500, 784)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CkyAvg3LiQKW",
        "colab_type": "text"
      },
      "source": [
        "# 2.a Compute and display \n",
        "    1.Mean image\n",
        "      There are many ways to find the mean image for a set of images. Here are some of them which I explored :-\n",
        "\n",
        "\n",
        "*   Taking mean of the uint8 array formed after applying filter and converting it into array and displaying it. \n",
        "\n",
        "*   Using Sklearn PCA function to find the mean of image after fitting it with desired number of components from the image. [Sklearn Documentation for PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html)\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YybNvhdDodw1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "58360948-8d38-42aa-acdb-424270efd379"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "\n",
        "\n",
        "\n",
        "def show_image(image,msg):\n",
        "  figure(figsize=(4,4),constrained_layout=False)\n",
        "  plt.title(msg)\n",
        "  plt.imshow(image,cmap =plt.cm.gray)\n",
        "  plt.show()\n",
        "\n",
        "#****uncomment to display this version****\n",
        "\n",
        "# mean_img=X_train_digit.mean(axis=0)\n",
        "# reshaped_mean_image=mean_img.reshape(28,28)\n",
        "# show_image(np.asarray(reshaped_mean_image))\n",
        "\n",
        "\n",
        "\n",
        "pca = PCA(n_components=10)         #using all features of the image\n",
        "pca.fit(X_train_digit)              #using all the images in the train data to fit in the PCA model.\n",
        "digit_mean=pca.mean_.reshape(28,28)\n",
        "show_image(digit_mean,'Mean Image')\n",
        "\n",
        "principal_components=pca.components_"
      ],
      "execution_count": 245,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wPqXfnkls_kE",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "    2.Display first two principal components which have the highest eigenvalues\n",
        "\n",
        "\n",
        "*   Using Sklearn's inbuild function we can find the principal components which are returned by the library in the descending order of the eigen values.\n",
        "*   Displaying the principal components corresponding to the highest eigen values.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5ZEj5oUIwzb_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 985
        },
        "outputId": "30d9504b-25d0-48de-bbc5-af50adde9b4f"
      },
      "source": [
        "import seaborn as sn\n",
        "import pandas as pd\n",
        "pca = PCA(n_components=2)         #using all features of the image\n",
        "principalComponents=pca.fit_transform(X_train_digit)  #taking the images from the mnist dataset\n",
        "show_image(pca.components_[0].reshape(28,28),'1st Principal Component')\n",
        "show_image(pca.components_[1].reshape(28,28),'2nd Principal Component')\n",
        "\n",
        "\n",
        "principalDf = pd.DataFrame(data = principalComponents, columns = ['principal component 1', 'principal component 2'])\n",
        "\n",
        "sn.FacetGrid(principalDf, height=6).map(plt.scatter, 'principal component 1', 'principal component 2').add_legend()\n",
        "plt.title('Plotting of values')\n",
        "plt.show()"
      ],
      "execution_count": 246,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0s5Vmtrj8u6AtvRORlhnKx/gbgPMHuf4r7j63/Lu7td0SkVYLk93dHwDS6xOJSMdr5ge6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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7md1oZn1mtqZk23Iz22ZmT4Sv8xvbTRGpVSUv428Czhti+7fc/bTwdU99uyUi9ZZMdnd/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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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S2AJMhv8W1bRcTbYVBF3SLCUBck/bRwJFasSSBb3YvHwxPrt0vrIuXYDJ8N+idShdSbYV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\njUGEmiAIgtAY/n/mAA63NR54twAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 440x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jTv_VGMJznhd",
        "colab_type": "text"
      },
      "source": [
        "# 2b Compute and Display Reconstructed test image using mean image and :-\n",
        "\n",
        "\n",
        "1.   10 Principal Component associated with 10 eigen values \n",
        "2.   50 Principal Component associated with 50 eigen values\n",
        "\n",
        " [*Programming Computer Vision with Python*](https://www.oreilly.com/library/view/programming-computer-vision/9781449341916/) by Jan Erik Solem PCA is defined as -\n",
        " Principal Component Analysis (PCA) is a useful technique for dimensionality reduction and is optimal in the sense that it represents the variability of the training data with as few dimensions as possible\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sYNHKqN-4ozg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 809
        },
        "outputId": "0c5e732a-e2eb-448a-8797-9e8aad7af54c"
      },
      "source": [
        "\n",
        "show_image(X_test_digit[4].reshape(28,28),'Original Image')\n",
        "\n",
        "pca = PCA(n_components=10)\n",
        "lower_dimensional_data = pca.fit_transform(X_train_digit)\n",
        "test_lower_dimensional_data_10 = pca.transform(X_test_digit)\n",
        "approximation = pca.inverse_transform(test_lower_dimensional_data_10)\n",
        "show_image(approximation[4].reshape(28,28),'P=10')\n",
        "\n",
        "pca = PCA(n_components=50)\n",
        "lower_dimensional_data = pca.fit_transform(X_train_digit)\n",
        "test_lower_dimensional_data_50 = pca.transform(X_test_digit)\n",
        "approximation = pca.inverse_transform(test_lower_dimensional_data_50)\n",
        "show_image(approximation[4].reshape(28,28),'P=50')"
      ],
      "execution_count": 247,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Vj+wiSSjsIkko7CJJKOwiSSjsIkko7CJJKOwiSVw2ffaoNxmtGY9O5+z1dOfNm+eOnTt3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\nYRdJQmEXSUJhF0ni/wFIm7b+fyLFCQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YVkhAK3_7mBB",
        "colab_type": "text"
      },
      "source": [
        "# SSD and DFFS\n",
        "    For DFFS we need to evaluate the PCA with components that covers almost all the features in the image set. \n",
        "    To determince that we perform the pca for all the features and plot it on the graph to check which can be selected as the component value"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_yiNt4vPIyTw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "2ce44e39-c677-4a1e-eec5-63e929f6e6a7"
      },
      "source": [
        "X_train_digit,X_test_digit=get_filttered_data(1) #get images of digit 1\n",
        "pca = PCA(n_components=500)\n",
        "pca.fit(X_train_digit)\n",
        "var=np.cumsum(np.round(pca.explained_variance_ratio_, decimals=3)*100)\n",
        "plt.ylabel('% Variance Explained')\n",
        "plt.xlabel('# of Features')\n",
        "plt.title('PCA Analysis')\n",
        "plt.ylim(30,100)\n",
        "plt.style.context('seaborn-whitegrid')\n",
        "plt.plot(var)"
      ],
      "execution_count": 248,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f031d06bc18>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 248
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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R1Luj2cwsr4pMCn76yMwsv8pOCh68ZmbWQmUnBdcUzMxacFIwM7NmFZkU6v0+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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QaNPFtzyO50J",
        "colab_type": "text"
      },
      "source": [
        "By ploting the  *explained_variance_ratio_* we determine the percentage of variance explained. This can be used to determine the variables that are required to be used for SSD and DFFS"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YTergmMOp8XU",
        "colab_type": "text"
      },
      "source": [
        "# SSD (Sum of Square Difference)\n",
        "In the research paper   \" [An Overview of Various Template Matching\n",
        "Methodologies in Image Processing](https://www.ijcaonline.org/archives/volume153/number10/swaroop-2016-ijca-912165.pdf) \" SSD can be infered as the measure of variation or deviation from the mean can be represented by sum of squares.It is calculated as a summations of the squares of the variations from the mean"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ROERFuen7qDH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 698
        },
        "outputId": "0773e9f1-702a-491d-cbdd-9fb8e55a6a6a"
      },
      "source": [
        "import cv2\n",
        "from google.colab.patches import cv2_imshow\n",
        "import seaborn as sns\n",
        "\n",
        "#img_f_dffs=np.zeros((28*7,28*10))\n",
        "img_f_mean=np.zeros((28*7,28*10))\n",
        "\n",
        "path='/content/drive/My Drive/Colab Notebooks/test_Image.PNG'\n",
        "\n",
        "def get_grey_Image(path):\n",
        "  image = cv2.imread(path)\n",
        "  gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)\n",
        "  width = 280\n",
        "  height = 28*7\n",
        "  dim = (width, height)\n",
        "  resized_gray = cv2.resize(gray, dim, interpolation = cv2.INTER_AREA)\n",
        "  return resized_gray\n",
        "\n",
        "    \n",
        "def ssd_sw(image, mean_img):\n",
        "  stepSize = 28\n",
        "  (w_width, w_height) = (28,28) # window size\n",
        "  for x in range(0, image.shape[0]  , stepSize):\n",
        "    for y in range(0, image.shape[1] , stepSize):\n",
        "        window = image[x:x + w_width, y:y + w_height]\n",
        "        img_f_mean[x:x + w_width, y:y + w_height]=((window-mean_img)**2).sum(axis=-1).sum(axis=-1)\n",
        "\n",
        "\n",
        "img=get_grey_Image(path)\n",
        "cv2_imshow(img) #displaying the original image\n",
        "\n",
        "\n",
        "X_train_digit,X_test_digit=get_filttered_data(1) #get images of digit 1\n",
        "print(X_train_digit.shape)\n",
        "\n",
        "\n",
        "pca = PCA(n_components=100) #setting n_components based on the values that was infered from the plotted graph\n",
        "pca.fit(X_train_digit)\n",
        "\n",
        "\n",
        "digit_mean=pca.mean_.reshape(28,28) #Mean of all the images\n",
        "show_image(digit_mean,'mean')\n",
        "\n",
        "ssd_sw(img, digit_mean) # calling the function to get an array after the pixel maniplation\n",
        "show_image(img_f_mean,'SSD')\n"
      ],
      "execution_count": 249,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SFUzUTAEgBJM6F1YgFYAAEcmAjGUEAIKiPV8OmczaTACMdDxQBYAwkbJE9DDP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\nFDx47J+6Cf9Dlu3/H+WxkSdGbUX5AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<PIL.Image.Image image mode=L size=280x196 at 0x7F0312794278>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "(500, 784)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WNdZAwqD2Nqh9gXvrVL9682m8WSEcdrNCNB32kYafP2VQexvUvsC9daovvTX6mt3M+qfp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\nrBAOu1khHHazQvwf6l5jKqWsO5AAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQcAAADLCAYAAABj9lbcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZEoK6+0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iMC4gsz1AwZo",
        "colab_type": "text"
      },
      "source": [
        "The heat map is generated by moving a window frame across the image and substracting the mean image from the window image(part of test image) and storing the values in another array.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bBokGU480bo3",
        "colab_type": "text"
      },
      "source": [
        "#DFFS - Distance From Feature Space\n",
        "In the research paper of [Facial Feature Extraction and Principal Component Analysis for Face Detection in Color Images](http://doras.dcu.ie/285/1/lncs_3212.pdf) DFFS is defined as substraction of ssd with sum of all prinicipal components."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7NQa1pkyr6K",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "5aa868f2-53a0-4035-b056-37d3908b68d9"
      },
      "source": [
        "img_dffs=[]\n",
        "\n",
        "\n",
        "def sliding_window_dffs(image, mean_img,reconstructed):\n",
        "  stepSize = 28\n",
        "  (w_width, w_height) = (28,28) # window size\n",
        "  #show_image(mean_img,'dffs_mean')\n",
        "  for x in range(0, image.shape[0]  , stepSize):\n",
        "    for y in range(0, image.shape[1] , stepSize):\n",
        "        window = image[x:x + w_width, y:y + w_height]\n",
        "        img_dffs.append(np.sqrt(np.sum(np.square(np.subtract(np.subtract(window,mean_img),reconstructed)))).sum(axis=-1).sum(axis=-1))\n",
        "\n",
        "\n",
        "pca_components=pca.components_ #extracting all the pca components\n",
        "pca_component_sum=np.sum(np.square(pca_components)) #summation of the squares\n",
        "\n",
        "sliding_window_dffs_test(img,digit_mean,approximation[0].reshape(28,28))\n",
        "plt.figure()\n",
        "ax = plt.axes()\n",
        "sns.heatmap(np.array(img_dffs).reshape(7,10),cmap='gray',ax=ax)\n",
        "ax.set_title('DFFS')\n",
        "plt.show()\n",
        "\n",
        "\n"
      ],
      "execution_count": 250,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CZUJ_q6K9Drl",
        "colab_type": "text"
      },
      "source": [
        "The heat map is generated by moving a window frame across the image and substracting the reconstrcuted image from the substraction of window image(part of test image) and mean.The values are stored in another array."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jttU4rk9-UF4",
        "colab_type": "text"
      },
      "source": [
        "# Evaluation of DFFS and SSD\n",
        "For evaluation of the methods, I took a randome image from the train dataset and ploted the heatmap.\n",
        "Both the heatmap suggests that the mean image plays an important role for getting an accurate prediction. \n",
        "SSD heatmap shows that the digit 1 is displayed more clearly than when passed the mean. The mean image of digit 1 shows lines in many angles which when used for SSD or DFFS doesnt allow the window to be detected.\n",
        "When the mean is clear ( as shown below by assuming a single image as the mean) the heatmaps can clearly make a difference."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zBvcYPsJujyR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 748
        },
        "outputId": "e9e33b1b-5196-470c-dc5f-e311d95a0e97"
      },
      "source": [
        "img_dffs=[]\n",
        "show_image(X_train_digit[3].reshape(28,28),'Original Image')\n",
        "\n",
        "#dffs\n",
        "sliding_window_dffs(img,digit_mean,X_train_digit[3].reshape(28,28))\n",
        "plt.figure()\n",
        "ax = plt.axes()\n",
        "sns.heatmap(np.array(img_dffs).reshape(7,10),cmap='gray',ax=ax)\n",
        "ax.set_title('DFFS')\n",
        "plt.show()\n",
        "\n",
        "#ssd \n",
        "img_f_mean=np.zeros((28*7,28*10))\n",
        "ssd_sw(img, X_train_digit[3].reshape(28,28)) # calling the function to get an array after the pixel maniplation\n",
        "show_image(img_f_mean,'SSD')"
      ],
      "execution_count": 251,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jtX52dU9/PvB9dkkHAM8Ci4Ex4BHgvIhYN9BCWpA0CiyKiNovwJD0W8DrwDcmp9aS9CVg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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7gZci4oGIeKDdhyJiUUScHBEnv/vd7y7vbM3MuigrnCXNkHSfpMckrZN0VWo/VNIySY+n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\nbGaWof8D4aVwbNaDpK8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}