Vertical Signatures

We now consider the use of vertical signatures of the projected gradient map to isolate the nose. This technique is reminiscent of Kanade's [19] signature analysis.

  

Figure 3.28: Nose height. (a) Search space. (b) Gradient map projected along upwards vertical with corresponding nose signature. Note that this is not quite a conventional signature since a triangular summation region is used.

We define the spatial search space using the previously localized eyes and mouth. This will restrict the signature analysis so that no facial contours or external edges will affect edge signature analysis. Figure  shows the region where signature analysis will be performed. The edges contained by this triangle are summed into bins corresponding to their yvalue. These bins form the vertical signature of the nose. The bin with the strongest edge content is the one that corresponds to the vertical position of the nose's bottom. Figure  also shows the projected gradient map and the signature that was computed in the search space. The nose's bottom position corresponds to the peak value of the signature.

However, we are interested in the nose tip, not the nose bottom. The nose tip characterizes 3D pose more clearly since it strongly protrudes from the ellipsoidal structure of the head. Assume the nose bottom was detected at position noseBottom_y at the peak signature value of noseBottom_value. We search a window of height of up to $0.2 \times EM$ above the nose bottom for a weaker signature value. The nose tip is defined as the closest point in the window with a signature value below $40\% \times noseBottom_{value}$. This simple adjustment is depicted in Figure . The positions of the nose bottom and the nose tip are shown as horizontal lines in Figure . Note the effect of this computation is quite minor and the nose-tip is only 2 pixels above the nose-bottom. Although the definition of the nose-tip and the use of the 40% threshold are somewhat arbitrary, we merely wish to move out of the region corresponding to the nose bottom (nostrils and shading) by a marginal amount so that the position detected has a 3D height. In other words, we wish to move upwards a small distance so that we localize a point somewhere on the nose, taking advantage of its 3D protrusion on the face (which specifies pose more exactly than non-protruding features on the face). Furthermore, the small upwards adjustment from nose-bottom to nose-tip does not have to be exact as long as we are somewhere on the nose and not on the junction between the nose-bottom and the face (which is not a 3D protrusion). Usually, the nose tip is brighter than the rest of the nose and the nose bottom is darker. However, the transition from nose tip to nose bottom or bright to dark is somewhat gradual. By moving upwards in search of a 40% signature value (rather than the maximum), we are searching for the beginning of this transition and moving closer to the true nose position in the process.

  

Figure 3.29: Finding the nose tip from the nose bottom using the edge signature.

  

Figure 3.30: The nose-bottom-line and the nose-tip-line.

Thus, we have roughly determined the height of the nose tip with respect to the eyes. However, we are uncertain of the exact horizontal position of the nose. The required localization is difficult to perform using simple signature analysis. This is mainly due to the fact that noses have the same tone as the rest of the skin-covered face and hence have low perceptual significance. Thus, a more sensitive nose finding technique will be utilized to isolate the horizontal position of the nose. This technique requires the introduction of normalization and recognition algorithms which will be detailed in Chapter 4. For now, the nose-localization module merely outputs a height value at the nose-tip position so we do not have a single locus for the nose but, rather, a line of possible loci for the nose. This nose-line lies between the two eyes at a fixed perpendicular distance below them. Thus, the output of the nose detection defines a nose-line (as opposed to a nose locus) along which the nose is situated as depicted in Figure . The nose-line crosses the nose tip and is parallel to the line formed by the two eyes. Additionally, its length is equal to the intra-ocular distance. In other words, the nose-line starts below the left eye and ends below the right eye.