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Thresholds for Eigenface Recognition

Module by: Jon Krueger, Doug Kochelek, Marshall Robinson, Matthew Escarra. E-mail the authors

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Summary: This describes the basic threshold values that can be computed to determine the identity of a new test image.

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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.

Figure 1
Figure 1 (radius1.jpg)

θ threshold = 1 2 max⁡( ||Ω− Ω k | | 2 ) θ threshold = 1 2 max⁡( ||Ω− Ω k | | 2 ) (1)

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 Φ recon = ∑ i=1 M ω i μ i (2)

ε 2 =|| Φ image − Φ recon | | 2 ε 2 =|| Φ image − Φ recon | | 2 (3)

ε> θ threshold ε> θ threshold (4)

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.

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