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## Geometrical Tests

We test a pair of symmetry peaks to see if their position on the face is geometrically valid. If these peaks are not horizontally aligned or have insufficient intra-ocular distance, they could not be eyes and are to be discarded.

Horizontal Alignment of Eyes
The first test computes the line formed by the pair of symmetry peaks. This line should be roughly perpendicular to the axis of the face as detected by the face contour estimation. Symmetry peaks that form a line that is not perpendicular to within degrees from the face's axis could not be eyes and are discarded.
Sufficient Intra-Ocular Distance
A pair of interest peaks within the eye band must have a certain intra-ocular distance separating them. If they are too close together, they cannot be eyes. Since the dimensions of the face contour are already known, we can estimate a minimum threshold distance between the eyes. However, the intra-ocular distance varies as the facial pose changes. For example, out of plane rotation induced when the subject is not looking straight into the camera will cause a reduction of the intra-ocular distance. Additionally, as the person rotates to the left or the right, the eyes do not seem centered within the facial contour in a 2D sense. Eyes travel to either side of the face as it is rotated severely. Thus, a threshold on the intra-ocular distance should be a function of the position of the center point between the two eyes relative to the face. In a near profile shot, as depicted in Figure  the center point between the two eyes is near the left side of the facial contour (note that 'left' and 'right' are defined with respect to the image viewer, not the photographed subject). The axis of the facial contour is marked with a vertical line while the midpoint between the two eyes is marked with a cross. We propose to compute the threshold on the intra-ocular distance as follows (refer to Figure ). We compute the midpoint between the two symmetry peaks under test which is shown in Figure . The eyes are shown in the Figure within the eye-band (of width b). The horizontal distances from the midpoint to the sides of the eye-band are cm and b-cm where cm < b-cm. A variable threshold on dintra-ocular is then computed using Equation . The constant kintra-ocular is typically set to 0.2. This is a very conservative setting which can be tweaked if desired.

 (3.1)

Next: Rotation Transformation for Mouth Up: Eye Localization Previous: Detecting Eye Regions
Tony Jebara
2000-06-23