Support Vector Machines

import cv2
import numpy as np
import matplotlib.pyplot as plt
import dlib

# Step 1: Read the Image
image_path = "Nihar.jpg"  # Replace with your image path
image = cv2.imread(image_path)
plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
plt.title("Original Image")
plt.show()

# Step 2: Convert to Grayscale
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
plt.imshow(gray, cmap='gray')
plt.title("Grayscale Image")
plt.show()

# Step 3: Compute Gradients
gx = cv2.Sobel(gray, cv2.CV_32F, 1, 0, ksize=1)
gy = cv2.Sobel(gray, cv2.CV_32F, 0, 1, ksize=1)
magnitude, angle = cv2.cartToPolar(gx, gy, angleInDegrees=True)
plt.imshow(magnitude, cmap='gray')
plt.title("Gradient Magnitude")
plt.show()
plt.imshow(angle, cmap='gray')
plt.title("Gradient Direction")
plt.show()

# Step 4: Create HOG Descriptors
cell_size = 8
bin_size = 9
angle_unit = 360 // bin_size
cell_x = gray.shape[1] // cell_size
cell_y = gray.shape[0] // cell_size
hog_descriptor = np.zeros((cell_y, cell_x, bin_size))
for i in range(cell_y):
    for j in range(cell_x):
        cell_magnitude = magnitude[i * cell_size: (i + 1) * cell_size, j * cell_size: (j + 1) * cell_size]
        cell_angle = angle[i * cell_size: (i + 1) * cell_size, j * cell_size: (j + 1) * cell_size]
        histogram, _ = np.histogram(cell_angle, bins=bin_size, range=(0, 360), weights=cell_magnitude)
        hog_descriptor[i, j, :] = histogram
plt.imshow(hog_descriptor[:, :, 0], cmap='gray')
plt.title("HOG Descriptor")
plt.show()

detector = dlib.get_frontal_face_detector()
faces = detector(gray)
for face in faces:
    x, y, w, h = face.left(), face.top(), face.width(), face.height()
    cv2.rectangle(image, (x, y), (x + w, y + h), (0, 255, 0), 2)
plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
plt.title("Detected Faces")
plt.show()

SVM Classification: The HOG features are fed into an SVM classifier that has been trained to distinguish between face and non-face regions.

In face detection, the SVM is trained to distinguish between face and non-face regions using HOG features extracted from the images.

Training Phase

Feature Extraction: Extract HOG features from a set of training images that contain faces and non-faces.
Training the SVM: Use these HOG features to train the SVM classifier. The positive examples (faces) are labeled as +1 and the negative examples (non-faces) are labeled as −1.

The trained SVM model finds the optimal hyperplane that separates the face and non-face HOG feature vectors.

Detection Phase Sliding Window: The trained SVM classifier slides a fixed-size window over the input image at multiple scales and positions. HOG Feature Extraction: For each window, compute the HOG features. Classification: Use the SVM classifier to classify the HOG feature vector of each window as face (+1) or non-face (−1). The SVM decision function for a window with feature vector h is: score = 𝑤⋅ℎ + b If the score is positive, the window is classified as containing a face; otherwise, it is classified as a non-face.

import cv2
import numpy as np
from sklearn import svm
from skimage.feature import hog
from skimage import data, exposure

# Load training images and labels
face_image_paths = ["Modi.jpg","Nihar.jpg"]  # List of face images
non_face_image_paths = ["backg1.jpeg","backg2.jpeg"]  # List of non-face images

# Function to extract HOG features from a resized image
def extract_hog_features(image, resize_dim=(64, 128)):
    # Resize image to a fixed size
    resized_image = cv2.resize(image, resize_dim)
    features, hog_image = hog(resized_image, pixels_per_cell=(8, 8), cells_per_block=(2, 2), visualize=True, multichannel=True)
    return features

# Load images and extract HOG features
face_features = [extract_hog_features(cv2.imread(image_path)) for image_path in face_image_paths]
non_face_features = [extract_hog_features(cv2.imread(image_path)) for image_path in non_face_image_paths]

# Create training data and labels
X_train = np.array(face_features + non_face_features)
y_train = np.array([1] * len(face_features) + [-1] * len(non_face_features))

# Train the SVM classifier
clf = svm.LinearSVC()
clf.fit(X_train, y_train)

<ipython-input-25-e60a415a1f7b>:15: FutureWarning: `multichannel` is a deprecated argument name for `hog`. It will be removed in version 1.0. Please use `channel_axis` instead.
  features, hog_image = hog(resized_image, pixels_per_cell=(8, 8), cells_per_block=(2, 2), visualize=True, multichannel=True)

LinearSVC()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

# Load the test image
test_image = cv2.imread('people.jpg')
gray_test_image = cv2.cvtColor(test_image, cv2.COLOR_BGR2GRAY)

# Define the sliding window size and step
window_size = (64, 128)
step_size = 16

# Function to extract HOG features for a grayscale image
def extract_hog_features_gray(image, resize_dim=(64, 128)):
    resized_image = cv2.resize(image, resize_dim)
    features, hog_image = hog(resized_image, pixels_per_cell=(8, 8), cells_per_block=(2, 2), visualize=True, channel_axis=None)
    return features

# Perform sliding window
for y in range(0, gray_test_image.shape[0] - window_size[1], step_size):
    for x in range(0, gray_test_image.shape[1] - window_size[0], step_size):
        window = gray_test_image[y:y + window_size[1], x:x + window_size[0]]
        if window.shape[0] != window_size[1] or window.shape[1] != window_size[0]:
            continue

        # Extract HOG features from the window
        window_hog_features = extract_hog_features_gray(window)

        # Predict using the trained SVM
        prediction = clf.predict([window_hog_features])

        # If a face is detected, draw a rectangle around it
        if prediction == 1:
            cv2.rectangle(test_image, (x, y), (x + window_size[0], y + window_size[1]), (0, 255, 0), 2)

# Display the result
plt.imshow(cv2.cvtColor(test_image, cv2.COLOR_BGR2RGB))
plt.title("Detected Faces")
plt.show()

Face alignment is a crucial preprocessing step in many facial recognition and facial analysis applications. The goal of face alignment is to transform the input face image so that the key facial landmarks (such as the eyes, nose, and mouth) are aligned in a standardized way. This improves the performance and accuracy of subsequent face processing tasks, such as recognition, by ensuring that the faces are consistently positioned and scaled.

Imagine you have a dataset of face images where the faces are captured from different angles and positions. Directly using these images for tasks like face recognition could lead to poor performance because the variability in pose, scale, and alignment can introduce significant noise. By aligning the faces, we aim to reduce this variability and standardize the representation of each face.

Face alignment involves detecting key facial landmarks (e.g., the corners of the eyes, the tip of the nose, the corners of the mouth) and transforming the face image so that these landmarks are placed in predefined positions.

Key Steps in Face Alignment

Landmark Detection: Detect key points on the face, such as the corners of the eyes, the tip of the nose, and the corners of the mouth. Commonly used landmark detectors include dlib's 68-point facial landmark detector and more advanced deep learning-based detectors.
Affine Transformation: Calculate the transformation matrix that maps the detected landmarks to a set of predefined landmark positions (e.g., the average positions of the landmarks in a standardized face model). Apply this transformation to the entire face image to align it.

Mathematical Formulation

Let's break down the mathematics involved in these steps:

Landmark Detection: Given an image 𝐼, the landmark detection algorithm identifies a set of points {(𝑥𝑖,𝑦𝑖)} for 𝑖 = 1 to 𝑛, where n is the number of landmarks (e.g., 68 for dlib).
Affine Transformation: The affine transformation maps the detected landmarks {(𝑥𝑖,𝑦𝑖)} to a set of predefined target points {(𝑥𝑖′,𝑦𝑖′)}. An affine transformation can be represented by a matrix A and a translation vector 𝑡: [𝑥𝑖′ 𝑦𝑖′]^T=𝐴[𝑥𝑖 𝑦𝑖]^t+ 𝑡. The affine transformation matrix 𝐴 and the translation vector 𝑡 can be computed using the least-squares method to minimize the error between the transformed landmarks and the target landmarks. This involves solving the following system of linear equations:𝑋′ = 𝐴𝑋 + 𝑇 where:𝑋 is a 2×𝑛 matrix of detected landmark coordinates.𝑋′is a 2×𝑛 matrix of target landmark coordinates.𝐴 is a 2×2 transformation matrix. 𝑇 is a 2×1 translation vector. The least-squares solution can be found using standard linear algebra techniques.
Applying the Transformation: Once 𝐴 and 𝑇 are computed, the affine transformation can be applied to the entire image using techniques such as bilinear interpolation to produce the aligned face image.

import cv2
import numpy as np
import matplotlib.pyplot as plt

# Step 1: Face Detection
face_cascade = cv2.CascadeClassifier(cv2.data.haarcascades + 'haarcascade_frontalface_default.xml')
image_path = "Kohli.jpg"  # Replace with your image path
image = cv2.imread(image_path)
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
faces = face_cascade.detectMultiScale(gray, scaleFactor=1.1, minNeighbors=5, minSize=(30, 30))

# Display detected faces
for (x, y, w, h) in faces:
    cv2.rectangle(image, (x, y), (x+w, y+h), (255, 0, 0), 2)
plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
plt.title("Detected Faces")
plt.show()


# Step 2: Landmark Detection (Manual Input via Code)
def manual_landmarks(image, face):
    x, y, w, h = face
    cropped_face = image[y:y+h, x:x+w]
    plt.imshow(cv2.cvtColor(cropped_face, cv2.COLOR_BGR2RGB))
    plt.title("Face Region")
    plt.show()

    # Manually enter coordinates here
    left_eye = [110, 150]
    right_eye = [300, 150]
    nose = [220, 200]
    left_mouth_corner = [130, 300]
    right_mouth_corner = [300, 300]

    points = np.array([
        left_eye,
        right_eye,
        nose,
        left_mouth_corner,
        right_mouth_corner
    ], dtype=np.float32)

    return points + [x, y]

face = faces[0]
landmarks = manual_landmarks(image, face)

# Display annotated landmarks
for (x, y) in landmarks:
    cv2.circle(image, (int(x), int(y)), 6, (0, 255, 0), -1)
plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
plt.title("Annotated Landmarks")
plt.show()

# Step 3: Affine Transformation
target_landmarks = np.array([
    [30.2946, 51.6963],  # Left eye
    [65.5318, 51.5014],  # Right eye
    [48.0252, 71.7366],  # Nose
    [33.5493, 92.3655],  # Left mouth corner
    [62.7299, 92.2041]   # Right mouth corner
], dtype=np.float32)
M, _ = cv2.estimateAffinePartial2D(landmarks, target_landmarks)

# Step 4: Applying the Transformation
aligned_face_size = (96, 112)
aligned_face = cv2.warpAffine(image, M, aligned_face_size)

# Display the aligned face
plt.imshow(cv2.cvtColor(aligned_face, cv2.COLOR_BGR2RGB))
plt.title("Aligned Face")
plt.show()

The goal of face embeddings is to map face images to a compact, fixed-size vector representation in a high-dimensional space, such that:

Faces of the same person are mapped to vectors that are close to each other.

Faces of different people are mapped to vectors that are far apart.

This is typically achieved using deep learning models, specifically Convolutional Neural Networks (CNNs), trained with a large dataset of face images. The CNN learns to extract features from the face images that are robust to variations in pose, lighting, and expressions.

Convolutional Neural Networks (CNNs): CNNs are the backbone of most face embedding systems. A CNN consists of several layers, including convolutional layers, activation layers (ReLU), pooling layers, and fully connected layers.

Convolutional Layers: Apply a set of learnable filters to the input image, producing feature maps that capture various features like edges, textures, etc.
Activation Layers (ReLU): Apply a non-linear function to introduce non-linearity into the model.
Pooling Layers: Downsample the feature maps to reduce dimensionality and computation.
Fully Connected Layers: Combine the features to produce the final output, which is the face embedding.

Face Embedding Representation:

Mathematically, a face embedding is a vector 𝑓 ∈ 𝑅^𝑑, where 𝑑 is the dimensionality of the embedding space. For example, 𝑑 might be 128, 256, or even higher.

Given a face image 𝑥, the CNN outputs the face embedding 𝑓(𝑥).

Loss Functions:

To train the CNN to produce meaningful embeddings, a suitable loss function is used. Common loss functions include: Triplet Loss: Ensures that the distance between an anchor face and a positive face (same person) is smaller than the distance between the anchor face and a negative face (different person) by a margin 𝛼.

Mathematically:

L(a,p,n)=max(0, ∥f(a)−f(p)∥ ^2 − ∥f(a)−f(n)∥ ^2 + α) where 𝑎 is the anchor image, 𝑝 is the positive image, and 𝑛 is the negative image.

Contrastive Loss: Similar to triplet loss but uses pairs of images. Minimizes the distance between embeddings of similar pairs and maximizes the distance between embeddings of dissimilar pairs. Mathematically:

𝐿(𝑥1,𝑥2,𝑦) = 𝑦⋅∥ 𝑓(𝑥1) − 𝑓(𝑥2) ∥₂^2 + (1−𝑦)⋅max(0,𝑚−∥ 𝑓(𝑥1)−𝑓(𝑥2) ∥₂)^2 where 𝑦 is 1 if 𝑥1 and 𝑥2 are the same person, and 0 otherwise. 𝑚 is the margin.

Distance Metrics To compare face embeddings, a distance metric is used. The most common metric is the Euclidean distance:

𝑑( 𝑓(𝑥1), 𝑓(𝑥2)) = ∥ 𝑓(𝑥1) − 𝑓(𝑥2) ∥^2 Alternatively, cosine similarity can also be used: cosine(𝑓(𝑥1),𝑓(𝑥2)) = 𝑓(𝑥1)⋅𝑓(𝑥2) / ∥𝑓(𝑥1)∥⋅∥𝑓(𝑥2)∥

import numpy as np
import cv2
import matplotlib.pyplot as plt

def display_image(image, title="Image"):
    plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
    plt.title(title)
    plt.axis('off')
    plt.show()

For more detailed view on CNN and for viewing CNN from scratch you can view this project https://github.com/Nihar1402-iit/Animal-Classification and for understanding significance of each layer's output you can view this .ipynb file https://github.com/Nihar1402-iit/Animal-Classification/blob/main/Visualising_CNN_layer_outputs%20(1).ipynb


def conv_layer(input_data, filters, kernel_size):
    output = np.zeros((input_data.shape[0] - kernel_size + 1, input_data.shape[1] - kernel_size + 1, filters))
    for f in range(filters):
        kernel = np.random.rand(kernel_size, kernel_size, input_data.shape[2])
        for i in range(output.shape[0]):
            for j in range(output.shape[1]):
                output[i, j, f] = np.sum(input_data[i:i + kernel_size, j:j + kernel_size] * kernel)
    return output

def create_embedding(image):
    conv1 = conv_layer(image, filters=16, kernel_size=3)
    conv1_flat = conv1.flatten()
    embedding = np.random.rand(128)  # Simulated embedding for simplicity
    return embedding

def euclidean_distance(embedding1, embedding2):
    distance = np.sqrt(np.sum((embedding1 - embedding2)**2))
    return distance

# Load and preprocess images
image1_path = 'Nihar.jpg'
image2_path = 'Photo.jpg'

image1 = cv2.imread(image1_path)
image2 = cv2.imread(image2_path)

# Display the images
display_image(image1, title="Image 1")
display_image(image2, title="Image 2")

# Create embeddings for the two images
embedding1 = create_embedding(image1)
embedding2 = create_embedding(image2)
print("Embedding 1:", embedding1)
print("Embedding 2:", embedding2)

# Compute the Euclidean distance between the embeddings
distance = euclidean_distance(embedding1, embedding2)

# Output the result
print("Euclidean distance between the embeddings:", distance)

Embedding 1: [0.50090798 0.68556543 0.60634613 0.04555698 0.42117226 0.12389472
 0.40752322 0.69771166 0.65115706 0.78907634 0.39659054 0.01229054
 0.57648175 0.35039318 0.36786503 0.30195382 0.16743631 0.14183538
 0.07252658 0.96740281 0.56131913 0.007655   0.95579219 0.96250862
 0.2458595  0.05771523 0.6862438  0.48944646 0.02867164 0.71319904
 0.28748339 0.90596183 0.13229311 0.14710764 0.30011579 0.57796062
 0.97774559 0.19173074 0.32664853 0.50124601 0.03151652 0.73231335
 0.54809433 0.40108866 0.67184793 0.14517403 0.92590791 0.88231625
 0.76225221 0.78073746 0.05698118 0.65362558 0.50942832 0.20717422
 0.28720273 0.00114903 0.28490813 0.97015143 0.56660218 0.09821421
 0.27156248 0.08910303 0.68425606 0.246987   0.01158745 0.38798838
 0.71085834 0.82676391 0.2726909  0.6268035  0.36295264 0.51363099
 0.27311266 0.61309813 0.07133517 0.32779402 0.14759681 0.18086154
 0.67829921 0.65782799 0.74371878 0.05855871 0.25407141 0.93440054
 0.75849447 0.13894913 0.90272469 0.5385578  0.27763779 0.48986428
 0.45899466 0.89208973 0.40126875 0.33737506 0.7536663  0.27940002
 0.96141973 0.2672932  0.19475347 0.013819   0.01967799 0.22462044
 0.27899598 0.06760692 0.68082595 0.82954954 0.14560864 0.73959653
 0.81081425 0.35216434 0.16212163 0.50074827 0.25690969 0.87048844
 0.02342349 0.97865821 0.07346921 0.90255308 0.50150539 0.34858276
 0.84423242 0.52909897 0.98113529 0.48001996 0.50258278 0.52209856
 0.46787589 0.28034589]
Embedding 2: [0.40707889 0.78145408 0.53775274 0.68582284 0.318276   0.10673259
 0.92552835 0.32845766 0.07799383 0.27152369 0.95083546 0.38553018
 0.74564498 0.11482168 0.36641813 0.46872199 0.92990912 0.51832993
 0.03675482 0.44998455 0.61781097 0.65173081 0.93114862 0.01958604
 0.25150304 0.19779058 0.88188435 0.90822207 0.52104796 0.66136107
 0.32725397 0.61574707 0.61524569 0.7277313  0.35390828 0.36508688
 0.38357755 0.81641608 0.18896015 0.92411114 0.84417664 0.08990048
 0.96946097 0.17931247 0.09034329 0.39285994 0.81858604 0.67794773
 0.62443164 0.32195309 0.86982373 0.89203423 0.45888061 0.84243765
 0.02167378 0.47555125 0.26876598 0.0457461  0.94192152 0.32707493
 0.75178676 0.13816513 0.75829763 0.25496302 0.28597139 0.02790209
 0.86403075 0.3044784  0.57123578 0.90040627 0.52512916 0.56068001
 0.5420624  0.52091622 0.62101642 0.65614532 0.379391   0.89098246
 0.93327701 0.92080779 0.94056103 0.37036275 0.07806965 0.59555389
 0.51757477 0.44527472 0.50852663 0.61203073 0.79005372 0.18054729
 0.66857457 0.27305091 0.38963139 0.24818901 0.04095087 0.50686962
 0.33605933 0.37118557 0.33361385 0.36380735 0.39793351 0.41927725
 0.8207811  0.33351102 0.16702583 0.60985687 0.67621718 0.47734072
 0.15022712 0.113156   0.98807971 0.43934677 0.02361379 0.46766381
 0.86040533 0.13629998 0.88679597 0.33920613 0.1885231  0.23448822
 0.72638796 0.48868084 0.74158088 0.91484917 0.40087097 0.65283275
 0.20496932 0.24280169]
Euclidean distance between the embeddings: 1.144180441627088

# Load and preprocess images
image1_path = 'ABD.jpeg'
image2_path = 'Photo.jpg'

image1 = cv2.imread(image1_path)
image2 = cv2.imread(image2_path)

# Display the images
display_image(image1, title="Image 1")
display_image(image2, title="Image 2")

# Create embeddings for the two images
embedding1 = create_embedding(image1)
embedding2 = create_embedding(image2)
print("Embedding 1:", embedding1)
print("Embedding 2:", embedding2)

# Compute the Euclidean distance between the embeddings
distance = euclidean_distance(embedding1, embedding2)

# Output the result
print("Euclidean distance between the embeddings:", distance)

Embedding 1: [0.42915152 0.14450937 0.42106832 0.12403381 0.57705514 0.69841666
 0.5023928  0.14045134 0.18144308 0.48563223 0.08831167 0.49786946
 0.87023444 0.6129135  0.0583797  0.23443961 0.77558832 0.23584132
 0.14184071 0.07888598 0.44880824 0.57653653 0.52740697 0.16966592
 0.35396347 0.80510237 0.61334737 0.09533667 0.11971344 0.76291824
 0.50361654 0.24467738 0.20922351 0.16274174 0.63290519 0.07223353
 0.43825876 0.61856285 0.70695157 0.80766254 0.5568173  0.00477979
 0.20778051 0.98435932 0.77154716 0.65583431 0.98649087 0.10180467
 0.77744441 0.5660854  0.79197367 0.19115178 0.78215893 0.37929528
 0.51495333 0.07561589 0.62455161 0.83527455 0.68737513 0.14424087
 0.73594241 0.62191399 0.37791929 0.54838246 0.42689653 0.11205038
 0.85614482 0.26649988 0.38550346 0.37051301 0.26802579 0.05220999
 0.64266024 0.4790959  0.02509311 0.46656224 0.67320809 0.74300029
 0.49072747 0.03361778 0.50305003 0.80380809 0.15044487 0.27496374
 0.27689056 0.37203888 0.87851442 0.15180087 0.71505334 0.86398127
 0.0268368  0.2067848  0.94621239 0.47328881 0.00352634 0.45382081
 0.4388015  0.88320874 0.1793939  0.25046008 0.59530011 0.18087924
 0.436415   0.17280871 0.02777885 0.2693864  0.54330909 0.72101838
 0.88327367 0.97708073 0.27574186 0.81023383 0.71482667 0.72601973
 0.38436422 0.05197138 0.84975448 0.07296656 0.20391881 0.66876278
 0.14505876 0.42808342 0.10355774 0.74406651 0.79945757 0.79479832
 0.05520095 0.27249089]
Embedding 2: [0.02307597 0.89277339 0.26573991 0.89939564 0.46048021 0.44573955
 0.36998779 0.88054925 0.86087557 0.7015089  0.51024037 0.57779455
 0.16485369 0.30319802 0.01530814 0.82933482 0.67268835 0.48128209
 0.62548777 0.65244767 0.60093039 0.74246289 0.84772435 0.93126437
 0.00591811 0.26941669 0.58330435 0.58743071 0.49160196 0.69620039
 0.18484647 0.95181865 0.6788908  0.86245059 0.02847861 0.63293369
 0.79328434 0.00607425 0.87510021 0.89948011 0.46384724 0.10176334
 0.35381204 0.12768356 0.26029603 0.91543653 0.83649377 0.02277863
 0.7328796  0.77098442 0.12014739 0.77724742 0.0418065  0.72141856
 0.5447721  0.27646813 0.10682262 0.83357216 0.40993082 0.09260579
 0.70401718 0.36389313 0.06479282 0.41196076 0.98364302 0.16985866
 0.83264502 0.21117039 0.90510552 0.32828453 0.43805702 0.23809758
 0.27804553 0.46560637 0.51461762 0.63171827 0.67932022 0.01976233
 0.20375323 0.73834901 0.96933845 0.00706723 0.65171849 0.94213684
 0.8114543  0.46855068 0.25206881 0.97407779 0.27622368 0.45920011
 0.63811725 0.72522369 0.51283743 0.38173128 0.55347245 0.81371482
 0.43138638 0.07585522 0.28828567 0.24372746 0.96198271 0.81942255
 0.48480163 0.14326023 0.93063813 0.16788817 0.95672316 0.41542856
 0.12884057 0.05684331 0.8071643  0.83969342 0.61913881 0.15840827
 0.71602283 0.69884705 0.04376727 0.75614174 0.51060469 0.2569266
 0.15995467 0.84021051 0.80049285 0.09775558 0.91283511 0.13845791
 0.65585756 0.29661978]
Euclidean distance between the embeddings: 5.132558660460171

What is dlib?

dlib is a powerful toolkit that provides a range of machine learning algorithms and tools for creating complex software. It's widely used for tasks like face detection, image processing, and, of course, face recognition.

Understanding Face Recognition

At its core, face recognition is about identifying or verifying a person's identity using their face. This process involves three main steps:

Step 1: Face Detection

Objective: Locate faces within an image.

The detector scans the image, looking for regions with the right pattern of edges to identify faces.

To know more about HOG you can have a look at this blog https://nihar1402-iit.github.io/_pages/HOG_blogs.html

HOG(Histogram of Oriented Gradients)

Detect Faces

SVM Classification: The HOG features are fed into an SVM classifier that has been trained to distinguish between face and non-face regions.

In face detection, the SVM is trained to distinguish between face and non-face regions using HOG features extracted from the images.

Training Phase

I have trained them on very linited images so the result may not be as good as the actual dlib face_recognition library but it will give you a sense of it

The prediction is not very good because it has been trained on just 2 face_images and 2 non_face images

Step 2: Face Alignment

Objective: Normalize the face to a standard position and size.

Face alignment involves detecting key facial landmarks (e.g., the corners of the eyes, the tip of the nose, the corners of the mouth) and transforming the face image so that these landmarks are placed in predefined positions.

Key Steps in Face Alignment

Mathematical Formulation

Step 3: Creating Face Embeddings

Objective: Convert faces into a set of numbers (embeddings) that can be compared.

dlib’s face recognition model uses Convolutional Neural Network (CNN), to transform the aligned face image into a high-dimensional vector. This vector is the face embedding—a list of numbers that represents the unique features of the face.

Mathematical Breakdown:

The goal of face embeddings is to map face images to a compact, fixed-size vector representation in a high-dimensional space, such that:

Faces of the same person are mapped to vectors that are close to each other.

Faces of different people are mapped to vectors that are far apart.

This is typically achieved using deep learning models, specifically Convolutional Neural Networks (CNNs), trained with a large dataset of face images. The CNN learns to extract features from the face images that are robust to variations in pose, lighting, and expressions.

Steps to Create Face Embeddings

Step 1: Define a basic CNN layer

Step 2: Create a simple embedding function

The Euclidean dist between the two comparisons is clearly indicating that the face is more like Face 1 than like Face 2

The embeddings may not be accurate and the results may not be like the one's you would get using the face_recognition model.

This is just to help you visualize what is happening therefor a simple CNN is used

What is dlib?

dlib is a powerful toolkit that provides a range of machine learning algorithms and tools for creating complex software. It's widely used for tasks like face detection, image processing, and, of course, face recognition.

Understanding Face Recognition

At its core, face recognition is about identifying or verifying a person's identity using their face. This process involves three main steps:

Step 1: Face Detection

Objective: Locate faces within an image.

The detector scans the image, looking for regions with the right pattern of edges to identify faces.

To know more about HOG you can have a look at this blog https://nihar1402-iit.github.io/_pages/HOG_blogs.html

HOG(Histogram of Oriented Gradients)

Detect Faces

SVM Classification: The HOG features are fed into an SVM classifier that has been trained to distinguish between face and non-face regions.

In face detection, the SVM is trained to distinguish between face and non-face regions using HOG features extracted from the images.

Training Phase

I have trained them on very linited images so the result may not be as good as the actual dlib face_recognition library but it will give you a sense of it

The prediction is not very good because it has been trained on just 2 face_images and 2 non_face images

For more information related to SVM you can view these two blogs : https://nihar1402-iit.github.io/_pages/Blog_SVM.html and https://nihar1402-iit.github.io/_pages/SVM_kernals.html

Step 2: Face Alignment

Objective: Normalize the face to a standard position and size.

Face alignment involves detecting key facial landmarks (e.g., the corners of the eyes, the tip of the nose, the corners of the mouth) and transforming the face image so that these landmarks are placed in predefined positions.

Key Steps in Face Alignment

Mathematical Formulation

Step 3: Creating Face Embeddings

Objective: Convert faces into a set of numbers (embeddings) that can be compared.

dlib’s face recognition model uses Convolutional Neural Network (CNN), to transform the aligned face image into a high-dimensional vector. This vector is the face embedding—a list of numbers that represents the unique features of the face.

Mathematical Breakdown:

The goal of face embeddings is to map face images to a compact, fixed-size vector representation in a high-dimensional space, such that:

Faces of the same person are mapped to vectors that are close to each other.

Faces of different people are mapped to vectors that are far apart.

This is typically achieved using deep learning models, specifically Convolutional Neural Networks (CNNs), trained with a large dataset of face images. The CNN learns to extract features from the face images that are robust to variations in pose, lighting, and expressions.

Steps to Create Face Embeddings

Step 1: Define a basic CNN layer

Step 2: Create a simple embedding function

The Euclidean dist between the two comparisons is clearly indicating that the face is more like Face 1 than like Face 2

The embeddings may not be accurate and the results may not be like the one's you would get using the face_recognition model.

This is just to help you visualize what is happening therefor a simple CNN is used