Active appearance model

The aim of the active appearance search is to find the best parameters of the statistical appearance model that fits a previously unseen image. The active appearance model search is base on the idea that the reconstruction of the image should be close to the original image. So we want to minimize :

$$\delta {\bf I}={\bf I}_i-{\bf I}_m$$

where ${\bf I}_i$ denotes the intensities in the image and ${\bf I}_m$ denotes the intensities in a synthesis of the model.

As the parameters of the model are correlated to the intensities in the image, we can assume that :

$$\delta {\bf c}={\bf A\delta I}$$

Given this model of image differences, we generate random displacements of $\delta {\bf c}$ for training images in order to find the corresponding $\delta {\bf I}$ by synthesis and image difference. This gives us a set of couple $(\delta {\bf c}, \delta {\bf I})$. We can then learn the matrix ${\bf A}$ by multivariate linear regression.

Once the relationship between differences of parameters and differences of intensities in the images is learnt, we can derive the following search algorithm in order to locate the face :

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Compute the error $\delta {\bf g}_0={\bf g}_s-{\bf g}_m$, if ${\bf g}_s$ is the current estimate of the model parameters.

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Evaluate the current $E_0=\vert\delta {\bf g}_0\vert^2$.

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Compute $\delta {\bf c}={\bf A} \delta {\bf g}_0$

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Set k=1.

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Let ${\bf c}_1={\bf c}_0- k \delta {\bf c}$.

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Calculate the new error $\delta {\bf g}_1$.

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If $\vert\delta {\bf g}_1\vert < E_0$ :

• accept the parameter ${\bf c}_1$.
• if converged, stop.
• otherwise go to the first step with ${\bf c}_1$ as the new estimate.

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Otherwise try $k$ at 1.5, 0.5, 0.25, etc.

Figure 3.5 shows an example of the application of this algorithm.

Figure 3.5: Example of application of the AAM search algorithm.