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Learning Correlations in the Active Appearance Model

To improve the search performance, good choice of parameters adjustments is required. It is desirable to learn some correlations off-line and use them along with the model above to form a robust and efficient search. Observations are made to learn the correlation between the change in parameter values (usually each mode independently considered) and the pixel intensity difference that incurs. This means that for each change in the parameter values or for a collective change of several parameters, some change, in certain parts of the image in particular, will be quite apparent. A matrix of pixels (where rows represent horizontal scan lines in the image) is used to record the difference that a re-parameterisation imposes. More mathematically, for $c_{i}$ which are the parameters as described above, a change $\delta c$ is applied and the difference in intensities is calculated as follows:

$$\delta I=I_{model}-I_{image}.$$ (6)

Usually sum-of-squares is used here to penalise more harshly for blunt differences and ensure a summation of only positive values ( $\forall x\subset\mathbb{Z}x^{2}>0$). Taking this intensity difference into consideration, the main correlation can now be expressed as:

$$c_{i}\rightarrow c_{i}+\delta c\rightarrow\delta I$$ (7)

which simply means that certain offsets to the parameters $c_{i}$cause a certain change in intensity. This correlation is recorded as follows:

$$\delta c=A\delta I$$ (8)

where A is a matrix recording the change in intensities due to the reparameterisation $\delta c$.

For each mode of variation and each pixel in the mean shape, weighting (negative or positive) is assigned to guide what the search will attempt to focus on. These ``maps'' of weights consume considerable amount of space, but are the only known paradigm for speeding-up through off-line computation. Wavelet compression can be used to reduce the space requirements and make active appearance models rather compact.