eigenfaces.ipynb

Kernel: Python 3 (Ubuntu Linux)

Eigenfaces

We used the faces94 dataset for this implementation: https://cswww.essex.ac.uk/mv/allfaces/faces94.zip

import numpy as np
import matplotlib.pyplot as plt
from PIL import Image

%matplotlib inline

Enrollment Process

ids = ['9336923','9338535','anpage','asamma','asewil','astefa','drbost','ekavaz','elduns',
                  'kaknig','klclar','ksunth','lfso','mbutle','phughe','sbains','slbirc','vstros','yfhsie',
      'anonym','anonym1','anonym2','cwang','doraj','fordj','hartb','hensm','ieorf','lyond','macci',
                    'martin','michael','moors','obeidn','robin','sandm','spacl','tony','voudcx'
      ]

f94 = {'female': ['9336923','9338535','anpage','asamma','asewil','astefa','drbost','ekavaz','elduns',
                  'kaknig','klclar','ksunth','lfso','mbutle','phughe','sbains','slbirc','vstros','yfhsie'],
      'malestaff': ['anonym','anonym1','anonym2','cwang','doraj','fordj','hartb','hensm','ieorf','lyond','macci',
                    'martin','michael','moors','obeidn','robin','sandm','spacl','tony','voudcx']}

For each set of faces, we take the first one and add it to the training set.

base = [Image.open(f'faces94/faces94/{cat}/{p}/{p}.1.jpg').convert('L')  for cat in f94 for p in f94[cat]]

M = len(base)

X = np.array([base[i].getdata() for i in range(M)])

mean = np.mean(X, 0)

phi = X - mean

We compute for the eigenvalues and eigenvectors using singular value decomposition.

e_faces, sigma, v = np.linalg.svd(phi.transpose(), full_matrices=False)

weights = [np.dot(X[i]-mean, e_faces) for i in range(M)]

np.shape(weights)

(39, 39)

This is what the first eigenface looks like.

display(plt.matshow(np.reshape(e_faces.T[0], (200,180)), cmap='gray'))

<matplotlib.image.AxesImage at 0x7f2bd78e5c18>

Face Recognition

input_img = Image.open(f'faces94/faces94/malestaff/spacl/spacl.19.jpg').convert('L')
input_img

Projection

gamma = np.array(input_img.getdata())

test_phi = gamma - mean

test_weights = np.dot(test_phi, e_faces)

Distance computation

dist = [np.linalg.norm(phi[i] - test_phi) for i in range(M)]
d_min = np.min(dist)

Match finding

threshold = 7000

if d_min < threshold:
    name = ids[np.argmin(dist)]
    print(f'{name}\ndist={d_min}')
else:
    print('No match found.')

spacl
dist=6604.41185875018

Visualization of the face space

We plot the projections of each training image onto the face space spanned by the first two eigenfaces. The projected input image is represented in the plot as a square.

def identify(img):
    gamma = np.array(img.getdata())
    test_phi = gamma - mean
    test_weights = np.dot(test_phi, e_faces)
    return test_weights[0:2]

plt.style.use('fivethirtyeight')

plt.figure(figsize=(15,10))
i = 0
for faceclass in ['malestaff','female']:
    for setname in f94[faceclass]:
        iset = [Image.open(f'faces94/faces94/{faceclass}/{setname}/{setname}.{i}.jpg').convert('L') for i in range(1,2)]
        x, y = np.array([identify(pic) for pic in iset]).T
        plt.scatter(x,y, s=50)
        plt.text(x * (1 + 0.02), y * (1 + 0.02), setname)
        i += 1
plt.scatter(*identify(input_img), label='Input image', marker=',', c='k', s=100)
plt.xlabel('Eigenface 1')
plt.ylabel('Eigenface 2')
plt.title('Face Space')
plt.legend(frameon=True)

<matplotlib.legend.Legend at 0x7f2bd77a8dd8>