Eigenfaces As we discussed last time, we can reduce the computation by dimension reduction using PCA –Suppose we have a set of N images and there are c classes –We define a linear transformation –The total scatter of the training set is given by –

For PCA, it chooses to maximize the total scatter of the transformed feature vectors, which is –Mathematically, we have Eigenfaces

One Difficulty: Lighting The same person with the same facial expression, and seen from the same viewpoint, can appear dramatically different when light sources illuminate the face from different directions.

Another Difficulty: Facial Expression Facial expressions changes also create variations that PCA will hold unto, yet these variations may confuse recognition.

Fisherfaces The idea here is to try to throw out the variability that is not useful for recognition and hold onto the variability that is…

Fisherfaces Using Fisher’s linear discriminant to find class-specific linear projections –More formally, we define the between-class scatter –The within-class scatter –Then we choose to maximize the ratio of the determinant of the between-class scatter matrix to the within-class scatter of the projected samples

Fisherfaces That is,

Comparison of PCA and FDA

Fisherfaces Singularity problem –The within-class scatter is always singular for face recognition –This problem is overcome by applying PCA first, which can be called PCA/LDA

Experimental Results Variation in lighting

Experimental Results

Variations in Facial Expression, Eye Wear, and Lighting

Glasses Recognition Glasses / no glasses recognition