Thresholds for Eigenface Recognition 1.1 2004/12/16 21:53:32 US/Central 2004/12/17 22:55:49.593 US/Central Jon Krueger jkrue@rice.edu Doug Kochelek kochelek@rice.edu Marshall Robinson mbr@rice.edu Matthew D. Escarra matte@rice.edu Jon Krueger jkrue@rice.edu Doug Kochelek kochelek@rice.edu Marshall Robinson mbr@rice.edu Matthew D. Escarra matte@rice.edu Eigenfaces Error Threshold This describes the basic threshold values that can be computed to determine the identity of a new test image. When a new image comes into the system, there are three special cases for recognition. Image is a known face in the database Image is a face, but of an unknown person Image is not a face at all. May be a coke can, a door, or an animal. For a real system, where the pictures are of standard format like a driver’s license photo, the first two cases are useful. In general, the case where one tries to identify a random picture, such a slice of pizza, with a set of faces images is pretty unrealistic. Nonetheless, one can still define these threshold values to characterize the images. Looking back at the weight matrix of values using M eigenfaces, let’s define the face space as an M-dimensional sphere encompassing all weight vectors in the entire database. A fairly approximate radius of this face space will then be half the diameter of this sphere, or mathematically, half the distance between the furthest points in the sphere.

θ threshold = 1 2 max⁡( ||Ω− Ω k | | 2 ) To judge whether a new image falls within this radius, let's calculate the reconstruction error between the image and its reconstruction using M eigenfaces. If the image projects fairly well onto the face space (image follows a face distribution), then the error will be small. However a non face image will almost always lie outside the radius of the face space. Φ recon = ∑ i=1 M ω i μ i ε 2 =|| Φ image − Φ recon | | 2 ε> θ threshold If the resulting reconstruction error is greater than the threshold, then the tested image probably is not a face image. Similar thresholds can be calculated for images of like faces. If a image passes the initial face test, it can be compared to the threshold values of faces in the database. A similar match process can be used as mentioned earlier. Also the removal or averaging technique can be applied for detection as previously described.