Nose Localization

If a successful mouth point has been found, we can add this data to our knowledge of the current face. It is then relatively easy to search for a nose at this stage due to the well defined search space that can be cut out. The nose is a very useful feature since it accurately gives us an estimate for the pose of the individual. This is due to the significant displacement the nose undergoes in a 2D sense as facial pose changes. The nose position relative to the eyes tells us quite precisely if the subject is looking to the left, to the right or is in frontal view. The mouth and the facial contour, on the other hand, are not as reliable for estimating pose. Furthermore, the nose is mostly rigid, so its locus cannot change with facial expression.

In most images, the nose is one of the brightest regions of the face. It protrudes from the face and is thus better illuminated than other regions. Simultaneously, the nostrils and its bottom surface are significantly darker than the rest of the nose. Even if the black nostrils are not present, a dark contour around the bottom of the nose is visible due to the shading under the nose and the steep foreshortening at the bottom of the nose tip. Thus, we can model the nose as a region of brightness with a dark boundary on the bottom.

We are interested in detecting this change of intensity from brightness to darkness as we travel from the eyes to the mouth. From the gradient and phase maps derived by Sobel edge detection, we can compute the projection of the gradient magnitude of each edge along the vertical. Thus, we only consider vertical contrast changes. Actually, more specifically, we consider contrast changes that occur from bright to dark as we move downwards along the vertical. Figure (a) contains the original gradient map and Figure (b) shows the effect of projecting the edges along the upward vertical. Equation  illustrates the projection of an edge i with magnitude $\lambda_{i}$ and phase $\phi_i$ (where $\phi=0$corresponds to a vertical edge whose normal is along the horizontal). This generates the horizontally projected magnitude value, $\lambda_i'$.

$$\lambda_i'=\lambda_i \times \vert \sin(\phi_i) \vert$$ (3.4)

  

Figure 3.27: Nose edge data. (a) Sobel gradient map. (b) Gradient map projected along vertical.