### Analytic Functions by Stanislaw Saks

By Stanislaw Saks

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As such, their running times were much faster than those of Faltemier et al. [1] but utilized a distinctly different process. This process is distinct from much of the previous 3D face recognition approaches in that it is not based upon a 3D distance metric. Russ et al. [4] proposed using a 3D PCA-based approach to calculate a unique 3D face vector that was used with PCA to perform recognition. The vectors were produced utilizing a combination of nearest neighbor and normal searches in order to ensure a complete vector.

Often both facial expression classiﬁcation and face recognition are simultaneously required. For example, an intelligent robot system in a social environment requires a robust facial expression classiﬁcation and a face recognition system. e neutral face variations among diﬀerent people. Similarly, expression variations can aﬀect the accuracy of face recognition systems. Decomposing a face into an estimated neutral face and an expression residue can assist in both expression classiﬁcation and face recognition.

However, if a consensus is not achieved, we threshold from the maximum possible scores towards ts and search for consensus. e the class which result from thresholding using the highest t). In all cases, we consider that a fundamental expression is detected if it appears in 3 or more subspaces when applying tw and in addition to the previously detected expressions also forms a valid expression class. Fig. 3 shows examples of correctly classiﬁed expressions. (a) Fig. 3. extents happy3 happy2 4 (b) (c) (d) (e) Examples of correctly classiﬁed facial expressions.