implementation_jupyter_notebooks/Face_recognition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2 \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np \n",
    "import os\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import LabelEncoder\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class PCA_class:\n",
    "    \"\"\"\n",
    "    Principal Component Analysis (PCA) class.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    n_components : int, optional\n",
    "        Number of components to keep.\n",
    "    svd_solver : str, optional\n",
    "        Solver to use for the decomposition. Currently not used.\n",
    "    \"\"\"\n",
    "    def __init__(self, n_components=None, svd_solver='full'):\n",
    "        self.n_components = n_components\n",
    "        self.svd_solver = svd_solver\n",
    "        self.mean = None\n",
    "        self.components = None\n",
    "        self.explained_variance_ratio_ = None\n",
    "\n",
    "    def fit(self, X, method='svd'):\n",
    "        \"\"\"\n",
    "        Fit the model with X using the specified method.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : array-like, shape (n_samples, n_features)\n",
    "            Training data.\n",
    "        method : str, optional\n",
    "            Method to use for the decomposition ('svd' or 'eigen').\n",
    "        \"\"\"\n",
    "        # Mean centering\n",
    "        self.mean = np.mean(X, axis=0)  # Compute the mean of X\n",
    "        X = X - self.mean  # Subtract the mean from X\n",
    "\n",
    "        # Handle number of components\n",
    "        if self.n_components is None:\n",
    "            self.n_components = min(X.shape) - 1\n",
    "\n",
    "\n",
    "        if method == 'svd':\n",
    "            # Compute SVD\n",
    "            U, S, Vt = np.linalg.svd(X, full_matrices=False)  # Perform SVD on X\n",
    "\n",
    "            # Compute explained variance ratio\n",
    "            explained_variance_ = (S ** 2) / (X.shape[0] - 1)  # Compute the explained variance\n",
    "            total_variance = explained_variance_.sum()  # Compute the total variance\n",
    "            explained_variance_ratio_ = explained_variance_ / total_variance  # Compute the explained variance ratio\n",
    "\n",
    "            self.components = Vt[:self.n_components]  # Keep the first n_components components\n",
    "            self.explained_variance_ratio_ = explained_variance_ratio_[:self.n_components]  # Keep the explained variance ratio for the first n_components\n",
    "\n",
    "        elif method == 'eigen':\n",
    "            # Compute covariance matrix\n",
    "            covariance_matrix = np.dot(X.T, X)  # Compute the covariance matrix of X\n",
    "\n",
    "            # Compute eigenvalues and eigenvectors\n",
    "            eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix)  # Compute the eigenvalues and eigenvectors of the covariance matrix\n",
    "\n",
    "            # Sort eigenvalues and eigenvectors by decreasing eigenvalues\n",
    "            idx = eigenvalues.argsort()[::-1]  # Get the indices that would sort the eigenvalues in decreasing order\n",
    "            eigenvalues = eigenvalues[idx]  # Sort the eigenvalues\n",
    "            eigenvectors = eigenvectors[:, idx]  # Sort the eigenvectors accordingly\n",
    "\n",
    "            # Compute explained variance ratio\n",
    "            total_variance = eigenvalues.sum()  # Compute the total variance\n",
    "            explained_variance_ratio_ = eigenvalues / total_variance  # Compute the explained variance ratio\n",
    "\n",
    "            self.components = eigenvectors[:, :self.n_components].T  # Keep the first n_components components\n",
    "            self.explained_variance_ratio_ = explained_variance_ratio_[:self.n_components]  # Keep the explained variance ratio for the first n_components\n",
    "\n",
    "        else:\n",
    "            raise ValueError(\"Invalid method. Expected 'svd' or 'eigen'.\")\n",
    "        return self\n",
    "\n",
    "    def project(self, X):\n",
    "        \"\"\"\n",
    "        Apply dimensionality reduction to X.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : array-like, shape (n_samples, n_features)\n",
    "            New data.\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        X_new : array-like, shape (n_samples, n_components)\n",
    "            Transformed values.\n",
    "        \"\"\"\n",
    "        X = X - self.mean  # Mean centering\n",
    "        return np.dot(X, self.components.T)  # Project X onto the principal components\n",
    "\n",
    "    def fit_transform(self, X, method='svd'):\n",
    "        \"\"\"\n",
    "        Fit the model with X and apply the dimensionality reduction on X.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : array-like, shape (n_samples, n_features)\n",
    "            Training data.\n",
    "        method : str, optional\n",
    "            Method to use for the decomposition ('svd' or 'eigen').\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        X_new : array-like, shape (n_samples, n_components)\n",
    "            Transformed values.\n",
    "        \"\"\"\n",
    "        self.fit(X, method)  # Fit the model with X\n",
    "        return self.transform(X)  # Apply the dimensionality reduction on X\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Function to store the images according to folders structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configured by the user \n",
    "structure_number = 'one' # Dataset folder, containing subfolders named after subjects, each containing a minimum of 5 images, with extra images limited to the quantity of the smallest subject folder.\n",
    "dataset_dir = '../face_recognition_dataset'\n",
    "# Test size is 20% by default\n",
    "# PCA cumulativa variance is 90% by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of principal components: 319\n",
      "(96, 320)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Backend():\n",
    "\n",
    "    def __init__(self) -> None:\n",
    "        self.weights = None\n",
    "        self.eigen_faces = None\n",
    "        self.face_recognition_threshold = 2900\n",
    "\n",
    "        \n",
    "    \n",
    "    def store_dataset_method_one(self, dataset_dir):\n",
    "        self.faces_train = dict()\n",
    "        self.faces_test = dict()\n",
    "\n",
    "        # Initialize a variable to store the size of the first image\n",
    "        self.first_image_size = None\n",
    "\n",
    "        for subject in os.listdir(dataset_dir): \n",
    "            images = []\n",
    "            if subject == 'no match':\n",
    "                # Add to self.faces_test['no match']\n",
    "                subject_dir = os.path.join(dataset_dir, subject)\n",
    "                self.faces_test[subject] = [cv2.imread(os.path.join(subject_dir, filename), cv2.IMREAD_GRAYSCALE) for filename in sorted(os.listdir(subject_dir))]\n",
    "                continue\n",
    "           \n",
    "            # if subjcet is not 'no match'\n",
    "            subject_dir = os.path.join(dataset_dir, subject)\n",
    "            \n",
    "            for filename in sorted(os.listdir(subject_dir)):\n",
    "                image = cv2.imread(os.path.join(subject_dir, filename), cv2.IMREAD_GRAYSCALE)\n",
    "                \n",
    "                # If first_image_size is None, this is the first image\n",
    "                # So, store its size and don't resize it\n",
    "                if self.first_image_size is None:\n",
    "                    self.first_image_size = image.shape\n",
    "                \n",
    "                images.append(image)\n",
    "\n",
    "            # Warning for the user that the minimum number of faces per subject is 5\n",
    "            if len(images) >= 5 :\n",
    "                # Split the data: 80% for training, 20% for testing\n",
    "                split_index = int(len(images) * 0.8)\n",
    "                self.faces_train[subject] = images[:split_index]\n",
    "                self.faces_test[subject] = images[split_index:]\n",
    "\n",
    "        # Resize images of 'no match' to match the size of the first image\n",
    "        if 'no match' in self.faces_test:\n",
    "            for i, image in enumerate(self.faces_test['no match']):\n",
    "                self.faces_test['no match'][i] = cv2.resize(image, (self.first_image_size[1], self.first_image_size[0]))\n",
    "\n",
    "        return self.faces_train, self.faces_test\n",
    "\n",
    "\n",
    "    def store_dataset(self, structure_number: str = 'one', dataset_dir: str = None) -> None:\n",
    "\n",
    "        # Define a dictionary that maps structure numbers to functions\n",
    "        methods = {\n",
    "            'one': self.store_dataset_method_one,\n",
    "        }\n",
    "\n",
    "        # Get the function from the dictionary\n",
    "        func = methods.get(structure_number)\n",
    "\n",
    "        # Check if the function exists\n",
    "        if func is not None:\n",
    "            # Call the function\n",
    "            func(dataset_dir)\n",
    "        else:\n",
    "            print(f\"No function named 'store_dataset_method_{structure_number}' found.\")\n",
    "\n",
    "    def train_pca(self, faces_train: dict):\n",
    "\n",
    "        faces_train_pca = faces_train.copy()\n",
    "        # Use list comprehension to flatten images and create labels\n",
    "        train_faces_matrix = []\n",
    "        self.train_faces_labels = []\n",
    "        for subject, images in faces_train_pca.items():\n",
    "            train_faces_matrix.extend(img.flatten() for img in images)\n",
    "            self.train_faces_labels.extend([subject] * len(images))\n",
    "        self.train_faces_matrix = np.array(train_faces_matrix)\n",
    "        # Create instance of the class\n",
    "        pca = PCA_class().fit(self.train_faces_matrix, 'svd')\n",
    "        sorted_eigen_values = np.sort(pca.explained_variance_ratio_)[::-1]\n",
    "        print(f\"The number of principal components: {len(sorted_eigen_values)}\")\n",
    "        cumulative_variance = np.cumsum(sorted_eigen_values)\n",
    "        # let's assume that we will consider just 90 % of variance in the data, so will consider just first 101 principal components  \n",
    "        upto_index = np.where(cumulative_variance < 0.9)[0][-1] # the last one \n",
    "        no_principal_components = upto_index + 1\n",
    "        self.eigen_faces = pca.components[:no_principal_components]\n",
    "        self.weights = self.eigen_faces @ (self.train_faces_matrix - np.mean(self.train_faces_matrix, axis=0)).transpose()\n",
    "        print(self.weights.shape) # row vector for each image in the face matrix which indicates the linear conbination of the PCAs what would generate that image.  \n",
    "        return self\n",
    "\n",
    "    def recognise_face(self, test_face: np.ndarray):\n",
    "\n",
    "        test_face_to_recognise = test_face.copy()\n",
    "        if test_face_to_recognise.shape != self.first_image_size:\n",
    "            test_face_to_recognise = cv2.resize(test_face_to_recognise, self.first_image_size)\n",
    "        test_face_to_recognise = test_face_to_recognise.reshape(1,-1)\n",
    "        test_face_weights = self.eigen_faces @ (test_face_to_recognise - np.mean(self.train_faces_matrix, axis=0)).transpose()\n",
    "        distances = np.linalg.norm(self.weights - test_face_weights, axis = 0 ) # compare row wise \n",
    "        best_match = np.argmin(distances)\n",
    "        best_match_subject, best_match_subject_distance = self.train_faces_labels[best_match] , distances[best_match]\n",
    "        if best_match_subject_distance > self.face_recognition_threshold:\n",
    "            best_match_subject = 'no match'\n",
    "        else: best_match_subject = best_match_subject\n",
    "    \n",
    "        return best_match_subject, best_match_subject_distance, best_match\n",
    "\n",
    "    def test_faces_and_labels(self, test_faces_dict:dict) -> (list, list): # type: ignore\n",
    "        test_faces_dictionary = test_faces_dict.copy()\n",
    "        # Flatten the test faces and create corresponding labels\n",
    "        test_faces = []\n",
    "        test_labels = []\n",
    "        for subject, faces in test_faces_dictionary.items():\n",
    "            for face in faces:\n",
    "                test_faces.append(face)\n",
    "                # Encode the labels, no match -> 0, otherwise -> 1\n",
    "                label = 0 if subject == 'no match' else 1\n",
    "                test_labels.append(label)\n",
    "        return test_faces, test_labels\n",
    "\n",
    "\n",
    "    def ROC_curve(self, test_faces_dict: dict):\n",
    "\n",
    "        test_faces_dictionary = test_faces_dict.copy()\n",
    "        test_faces_list, test_labels_list = self.test_faces_and_labels(test_faces_dictionary)\n",
    "        # Calculate the distances for each test face\n",
    "        _, distances, _ = zip(*[self.recognise_face(face) for face in test_faces_list])\n",
    "\n",
    "        # Define the thresholds based on the distances\n",
    "        thresholds = np.linspace(min(distances), max(distances), 100)\n",
    "\n",
    "        tpr_values = []\n",
    "        fpr_values = []\n",
    "\n",
    "        for threshold in thresholds:\n",
    "            true_positive = 0\n",
    "            false_positive = 0\n",
    "            true_negative = 0\n",
    "            false_negative = 0\n",
    "\n",
    "            for i, distance in enumerate(distances):\n",
    "                if distance < threshold and test_labels_list[i] == 1:\n",
    "                    true_positive += 1\n",
    "                elif distance < threshold and test_labels_list[i] == 0:\n",
    "                    false_positive += 1\n",
    "                elif distance >= threshold and test_labels_list[i] == 1:\n",
    "                    false_negative += 1\n",
    "                elif distance >= threshold and test_labels_list[i] == 0:\n",
    "                    true_negative += 1\n",
    "\n",
    "            tpr = true_positive / (true_positive + false_negative)\n",
    "            fpr = false_positive / (false_positive + true_negative)\n",
    "\n",
    "            tpr_values.append(tpr)\n",
    "            fpr_values.append(fpr)\n",
    "\n",
    "        plt.plot(fpr_values, tpr_values)\n",
    "        plt.plot([0, 0.93], [0, 1], linestyle='--')\n",
    "        plt.xlabel('False Positive Rate')\n",
    "        plt.ylabel('True Positive Rate')\n",
    "        plt.title('Receiver Operating Characteristic (ROC) Curve')\n",
    "\n",
    "        # Highlight the 2900 threshold\n",
    "        threshold_2900_tpr = tpr_values[np.argmin(np.abs(thresholds - 2900))]\n",
    "        threshold_2900_fpr = fpr_values[np.argmin(np.abs(thresholds - 2900))]\n",
    "        plt.scatter(threshold_2900_fpr, threshold_2900_tpr, color='red')\n",
    "        plt.text(threshold_2900_fpr, threshold_2900_tpr, 'Threshold 2900')\n",
    "\n",
    "        plt.show()\n",
    "\n",
    "    def show_test_images(self,test_faces_dict: dict, indx): \n",
    "        test_faces_dictionary = test_faces_dict.copy()\n",
    "        test_faces_list, test_labels_list = self.test_faces_and_labels(test_faces_dictionary)\n",
    "\n",
    "        indx = indx % len(test_labels_list)\n",
    "        best_match_subject, best_match_subject_distance, best_match_indx = self.recognise_face(test_faces_list[indx]) \n",
    "        if best_match_subject_distance < self.face_recognition_threshold:\n",
    "            # Visualize\n",
    "            fig, axes = plt.subplots(1,2,sharex=True,sharey=True,figsize=(8,6))\n",
    "            axes[0].imshow(test_faces_list[indx], cmap=\"gray\")\n",
    "            axes[0].set_title(\"Query\")\n",
    "            axes[1].imshow(self.train_faces_matrix[best_match_indx].reshape(self.first_image_size), cmap=\"gray\")\n",
    "            axes[1].set_title(\"Best match\")\n",
    "            axes[0].axis(\"off\")\n",
    "            axes[1].axis(\"off\")\n",
    "        else: \n",
    "            print('Query out of threshold')\n",
    "            # Visualize\n",
    "            fig, axes = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(8, 6))\n",
    "            axes[0].imshow(test_faces_list[indx], cmap=\"gray\")\n",
    "            axes[0].set_title(\"Query\")\n",
    "            # Display a blank image as placeholder for no matching subject\n",
    "            no_match_image = np.full_like(self.train_faces_matrix[0].reshape(self.first_image_size), 255, dtype=np.uint8)  \n",
    "            axes[1].imshow(no_match_image, cmap=\"gray\")\n",
    "            axes[1].set_title(\"No matching subject\")\n",
    "            axes[0].axis(\"off\")\n",
    "            axes[1].axis(\"off\")\n",
    "\n",
    "    \n",
    "backend_instance = Backend()\n",
    "# each one is a dictionary, where the keys() are the subject names, the values() are a list of images\n",
    "# for example, to acess the 2nd image in subject 's2' in the training dataset is: faces_train['s2'][1] -> 2D greyscale array\n",
    "faces_train, faces_test = backend_instance.store_dataset_method_one(dataset_dir)\n",
    "backend_instance.train_pca(faces_train) # Here, we create an instance of PCA_class and train it\n",
    "backend_instance.show_test_images(faces_test,20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "backend_instance.ROC_curve(faces_test)"
   ]
  }
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