Analysis of the Celebrities in Frontal-Profile Wild (CPFW) Dataset

 

Analysis of the Celebrities in Frontal-Profile Wild (CPFW) Dataset

In this analysis, we will use Python to conduct a thorough examination of the genuine and impostor score distributions derived from the similarity matrix of the CPFW dataset. Our tasks include visualizing score distributions, calculating d-prime, plotting ROC curves, generating CMC curves, and plotting FMR and FNMR curves.

Below is a structured approach to achieving these objectives.

Required Libraries

We will use the following libraries:

– NumPy for numerical operations
– Matplotlib for plotting graphs
– Scikit-learn for calculating ROC and AUC

1. Setup and Data Preparation

First, let’s assume we have the genuine and impostor scores extracted from a similarity matrix (you would need to replace this with your actual data).

import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve, auc

# Example genuine and impostor scores for demonstration purposes
genuine_scores = np.random.normal(loc=0.8, scale=0.1, size=1000) # Genuine scores
impostor_scores = np.random.normal(loc=0.4, scale=0.1, size=1000) # Impostor scores

2. Score Distribution Histograms

a. Generate and Plot Histograms

plt.figure(figsize=(10, 6))
plt.hist(genuine_scores, bins=30, alpha=0.5, label=’Genuine Scores’, color=’blue’, density=True)
plt.hist(impostor_scores, bins=30, alpha=0.5, label=’Impostor Scores’, color=’red’, density=True)
plt.title(‘Score Distribution Histograms’)
plt.xlabel(‘Score’)
plt.ylabel(‘Density’)
plt.legend()
plt.grid()
plt.show()

b. Relative Score Distribution

# Calculate the relative distribution
genuine_density, bins_genuine = np.histogram(genuine_scores, bins=30, density=True)
impostor_density, bins_impostor = np.histogram(impostor_scores, bins=30, density=True)

# Plotting relative distribution
plt.figure(figsize=(10, 6))
plt.plot(bins_genuine[:-1], genuine_density, label=’Genuine Density’, color=’blue’)
plt.plot(bins_impostor[:-1], impostor_density, label=’Impostor Density’, color=’red’)
plt.title(‘Relative Score Distribution’)
plt.xlabel(‘Score’)
plt.ylabel(‘Density’)
plt.legend()
plt.grid()
plt.show()

3. D-prime Calculation

def calculate_d_prime(genuine_mean, impostor_mean, genuine_std, impostor_std):
return (genuine_mean – impostor_mean) / np.sqrt((genuine_std**2 + impostor_std**2) / 2)

genuine_mean = np.mean(genuine_scores)
impostor_mean = np.mean(impostor_scores)
genuine_std = np.std(genuine_scores)
impostor_std = np.std(impostor_scores)

d_prime_value = calculate_d_prime(genuine_mean, impostor_mean, genuine_std, impostor_std)
print(f”D-prime (d’) value: {d_prime_value:.2f}”)

4. Receiver Operating Characteristic (ROC) Curve

a. Calculate TPR and FPR

# Concatenate scores and labels for ROC calculation
y_true = np.array([1] * len(genuine_scores) + [0] * len(impostor_scores))
scores = np.concatenate([genuine_scores, impostor_scores])

# Calculate ROC curve
fpr, tpr, thresholds = roc_curve(y_true, scores)

# Calculate AUC
roc_auc = auc(fpr, tpr)

# Plot ROC curve
plt.figure(figsize=(10, 6))
plt.plot(fpr, tpr, color=’blue’, lw=2, label=’ROC curve (area = {:.2f})’.format(roc_auc))
plt.plot([0, 1], [0, 1], color=’red’, linestyle=’–‘)
plt.title(‘Receiver Operating Characteristic (ROC) Curve’)
plt.xlabel(‘False Positive Rate’)
plt.ylabel(‘True Positive Rate’)
plt.legend(loc=’lower right’)
plt.grid()
plt.show()

5. Cumulative Match Characteristic (CMC) Curve

# Assuming we have rank data for the CMC curve
# For demonstration purposes let’s simulate some rank data
rank_data = np.random.rand(1000)

# Calculate CMC curve
cmc_curve = np.cumsum(np.sort(rank_data))

# Plot CMC curve
plt.figure(figsize=(10, 6))
plt.plot(cmc_curve / np.max(cmc_curve), label=’CMC Curve’)
plt.title(‘Cumulative Match Characteristic (CMC) Curve’)
plt.xlabel(‘Rank’)
plt.ylabel(‘Cumulative Match Rate’)
plt.legend()
plt.grid()
plt.show()

6. False Match Rate (FMR) and False Non-Match Rate (FNMR) Curves

# Calculate FMR and FNMR
fmr = fpr # FPR is equal to FMR in this context
fnmr = 1 – tpr # FNMR is the complement of TPR

# Plot FMR and FNMR curves
plt.figure(figsize=(10, 6))
plt.plot(thresholds, fmr, label=’False Match Rate (FMR)’, color=’blue’)
plt.plot(thresholds, fnmr, label=’False Non-Match Rate (FNMR)’, color=’red’)
plt.title(‘FMR and FNMR Curves’)
plt.xlabel(‘Thresholds’)
plt.ylabel(‘Rate’)
plt.legend()
plt.grid()
plt.show()

Saving the Code

The above code can be saved as a Python file named cpfw_analysis.py. Ensure that you have all required libraries installed in your Python environment.

echo “# CPFW Analysis” > cpwf_analysis.py
cat <> cpwf_analysis.py

EOT

Conclusion

This comprehensive analysis of the CPFW dataset allows researchers to assess the performance of biometric systems through various metrics including score distributions, d-prime values, ROC curves, CMC curves, and FMR/FNMR evaluations. By using Python for this analysis, we can easily visualize and interpret the performance metrics necessary for understanding biometric recognition systems.