DCT Transformation on AR Face Database with Fisher Discriminant Analysis and Cosine Classifier

The workflow begins by applying Discrete Cosine Transform (DCT) to the AR face database. This transformation converts facial images from spatial domain to frequency domain representation, allowing better capture of facial details through frequency component analysis. In code implementation, this typically involves using dct2() function in MATLAB or similar DCT functions in Python's OpenCV/sci-kit image libraries to process each image matrix. Subsequently, Fisher Discriminant Analysis (FDA) is employed for feature extraction. This technique maximizes between-class scatter while minimizing within-class scatter, effectively selecting the most discriminative features and reducing redundant information. Implementation-wise, this involves calculating scatter matrices and solving generalized eigenvalue problems to obtain optimal projection vectors. Finally, a cosine similarity classifier performs face classification. This classifier measures the cosine angle between feature vectors in the transformed space, where smaller angles indicate higher similarity. The classification decision is made by comparing test samples against class prototypes using cosine distance metric. This approach is computationally efficient and particularly suitable for high-dimensional feature spaces. This integrated methodology significantly enhances face classification accuracy and stability by leveraging frequency-domain processing, optimal feature selection, and robust similarity measurement. The DCT stage provides compact representation, FDA ensures feature discriminability, and the cosine classifier offers reliable classification performance with minimal computational overhead.