## Anti-Face Model Specification and Calculation Details

Update 10/2013: We have implemented this in a free iPhone app which is available here:

https://itunes.apple.com/us/app/anti-face/id690376775

Our site FaceField.org (and now the iPhone app) uses the EigenFaces methodology as implemented in Open CV to calculate a special kind of face that we have labelled an ‘Anti Face’.

Model specification:
– Over 1000 faces were used.
– The faces were all facing the camera straight-on. We used a specially designed Haar classifier to ensure that we excluded faces looking to the side.
– The faces that we fed into the PCA calculation are slightly larger than what the Haar classifier detected so that we didn’t cut off the chins.
– The faces were all subject to histogram equalization.
– The faces were all sized to 200×200 pixels.
– We took the first 60 eigenvectors.

The Antiface calculation is simple: we do a subspace projection of the uploaded face into the 60-dimensional EigenFace space. It is interesting to view this ‘reconstructed face’ as we call it. In a normal face recognition calculation you would then compute the nearest face to this reconstructed face. The anti-face is simply the reconstructed face except that every weight is multiplied by -1.

In other words:

Let Ω ∋ R⁶⁰ be the subspace projection of the uploaded face.

Ω=(w₁,w₂,..w₆₀) where wᵢ= uᵢᵀ(Γ-Ψ) for i=1…60.

u ∋ R⁶⁰ is the Eigenface. Γ is the uploaded face image and Ψ is the mean face.

Then the antiface, Ω’ is (-1*w₁,-1*w₂,..-1*w₆₀).

So prominent features in the reconstructed faces (with high weighting, meaning far from the mean) would be equally prominent, though opposite, in the anti-face.

Why 60 dimensions? Originally we tried higher numbers like 200 because at that point the reconstructed face looks indistinguishable from the original face. However the anti-face looks very little like a face and is highly distorted and muddied. It seems that it such high-dimension space not everything looks like a face, however in a lower dimension space like 60 you’re likely to get a face no matter where you land.

Two Face/Anti-Face pairs as examples: