Principal components as basis images — mix them to reconstruct synthetic faces
PC 1 — Global brightness
PC 2 — Contrast
PC 3 — Eyes/brows
PC 4 — Mouth
PC 5 — Texture
Reconstruct a Face
Variance explained:
Reconstructed Face
Using all 5 PCs
About: Principal Component Analysis (PCA) finds directions of maximum variance in high-dimensional data. Applied to images of faces (Turk & Pentland 1991), the eigenvectors of the covariance matrix are "eigenfaces" — they form a basis for the face space. Any face can be approximated as: face ≈ mean + Σ wᵢ·PCᵢ. The first PC captures the most variance (global illumination), subsequent PCs capture progressively finer features. This lab uses synthetic face-like patterns generated from mathematical basis functions (Gabor-like and structural kernels) to demonstrate the concept. Real eigenfaces trained on databases like AT&T Faces achieve ~95% recognition using only the top 40 PCs from a 10,304-dimensional pixel space — a 250× compression.