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## Nose Localization Revisited

At this point, we recall the problem of nose-localization that was discussed in Chapter 3. The solution for the exact horizontal position of the nose was deferred because it was too difficult to obtain using the direct image processing techniques introduced in Chapters 2 and 3. However, Chapter 4 has introduced a reliable DFFS'' measure based on Karhunen-Loeve statistical signal detection. We can use this measure to to assist us in locating the nose.

Recall that at the end of Chapter 3, we detected the eyes and the mouth but only had a line representing the nose. This situation is represented in Figure . This image is similar to the final result of the detection performed in Chapter 3. The horizontal position of the nose with respect to the eyes was uncertain and could be anywhere on the solid white line.

The nose localization problem is solved using an algorithm based on the development in Chapter 4. Along the horizontal line across the nose, a set of equally spaced points are picked. Each point is then used as the anchor point for the nose in the 3D normalization process. Then, we obtain a mug-shot of the face from the 4 detected anchor points (eyes, mouth and the nose being tested). This image is transformed into a key and a residue value via the KL-decomposition. Using Equation , the distance to face-space of the image is evaluated. This process is repeated for several trial anchor points along the line crossing the nose and generates several mug-shot images as in Figure . Also shown is the DFFS value for each mug-shot image. Note how misdetected noses generate a mug-shot image that is very far from face-space and how the minimum DFFS'' value is registered when the nose anchor point is properly localized on the nose in the image.

As we attempt different possible nose points, we are generating a trajectory in the 61-dimensional space which crosses through our cluster of database faces. The point at which the trajectory in the 61-dimensional space is closest'' to face-space or has a maximum faceness'' value corresponds to the a point on the nose-line. Using the sampled DFFS measures for each trial nose-line point, we can select the best nose point as the one that minimizes DFFS. Thus, the problem of finding the nose is overcome by testing each possible nose position on the line. The final, fully localized face is shown in Figure .

Thus, the face detection algorithm ends up with 4 anchor points corresponding to the eyes, the nose tip and the mouth as well as a DFFS'' measure. It also has a 60-element key to represent it as well as a residue value (generate from the KL transform).

Next: Discarding Non-Faces before the Up: Karhunen-Loeve Decomposition for Statistical Previous: Using KL as a
Tony Jebara
2000-06-23