Face Recognition with Distance Measures

Once we have a fully normalized mug-shot of a true, fully localized face, we can use it to probe for a match in the database of previously detected individuals. Each mug-shot in the database is stored as a 60-dimensional key (after KL). The most similar mug-shot in the database will be used to identify the probe mug-shot. We compute the Euclidean distance between the test image's 60-dimensional key and all the 60-dimensional keys in the database [44] using Equation . The key which is geometrically closest to our probe's key will yield the lowest distance (d_min as in Equation ). This is the best match for the face, as given by Equation . The equation assumes that there are P entries in the database and that the xth face in the database is called face_x, where $0 \leq x < P$. The key of the xth face is c_xi where $0 \leq i < 60$; in other words, i is the dimension of the coefficient in the key:

$$d(probe,face_x)=\sqrt{\sum_{i=0}^{59}(c_{x_i} - c_{probe_i})^2}$$ (4.44)

 

d_min=min_x=0^x<P d(probe,face_x) (4.45)

$$match = z \: \: such \: that \: \: d(probe,face_z)=d_{min}$$ (4.46)

In this way, we obtain the best match in the database, face z, as the output of the recognition stage.

We illustrate the matching or recognition process for the test face in Figure . In Figure (a) and Figure (b) the test image and the closest five matches in the database are presented with their Euclidean distance d(probe,face_z) from the test face. These are database matches ordered from nearest to farthest (left to right). Additionally, we present the original test image and the most similar original database images in Figure (c). The original image is shown with the features localized in the top left and the database images around it are ordered from nearest to farthest (left to right and top to bottom).