Fisherfaces

Fisherfaces is a face recognition method that uses Fisher's Linear Discriminant Analysis (LDA) to find a subspace that best separates face classes. It was introduced by Belhumeur, Hespanha, and Kriegman in 1997 as an improvement over earlier eigenface approaches, particularly under varying illumination and facial appearance.

Technical approach: The method first reduces the high-dimensional image data with Principal Component Analysis (PCA) to a smaller, decorrelated space. Then LDA is applied to maximize the ratio of between-class scatter to within-class scatter, yielding a set of discriminant directions called Fisherfaces. The final projection matrix combines PCA and LDA, and images are projected into a low-dimensional discriminative subspace.

Classification is typically performed by comparing projected feature vectors with labeled training samples, using a simple classifier such as nearest class mean or a nearest-neighbor rule in the Fisherspace. The number of discriminant components is at most C-1, where C is the number of training classes.

Advantages include improved robustness to lighting changes and a compact representation when many images per person are available. Limitations include dependence on labeled data, potential sensitivity to misalignment or noise, and the need for an initial PCA step to avoid singular within-class scatter matrices.

Applications include biometric systems and identity verification, and it remains a foundational approach in the family of eigenface-based methods.