In many facial tracking algorithms based on constrained local models (CLM), such as this one and also this one, the first step of the algorithm is to learn a 'patch expert' which learns if a proposed patch is correctly aligned or not.

In the first cited paper above, the description is that this equation represents a logistic model to determine if a patch is aligned:

$$p(l_i = \text{aligned} | I, x) = \frac{1}{1 + e^{α C_i (I; x) + β}}$$

Where $C_i$ is the real output of some other linear classifier:

$$C_i (I; x) = w_i^T \text{patch(I; x)} + b_i$$

However, it is unclear from the articles what the classifier $C_i$ is supposed to be predicting. What is the intuition in learning a 'patch expert' in stages like this?

  • $\begingroup$ Possibly they are simply trained jointly, and the term 'classifier' is simply a misnomer since $C_i$ does not actually work to classify anything? However, it seems that by simply substituting $C_i$ into the first equation, a simplified model consisting of a single multinomial logit is obtained. So there must be a good reason to split it up like this... $\endgroup$ – Scott Mar 4 at 17:27

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