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Model Fitting

The second stage in active appearance models involves use of the model obtained, along with the correlations learned for that model, in order to do the fitting []. It is possible to perform an image search which is driven by the observed difference between the model and a given target image. Fitting is done by changing the values of model parameters. The state of the active model is defined by parameter values which, assuming the model is fitted successfully, contain information about the target image.

The model, as illustrated in Figure and Figure cap:A-target-image-2, is initially placed somewhere inside the image frame, with reasonable proximity to its target. The reason why good proximity (initialisation) is essential is that significantly large displacements are rarely learned off-line. The model is quite meaningless unless there is at least partial overlap or commonality to drive the optimiser in the right direction.

The algorithm which is used to perform the search adopts the following general form:

• Place the appearance model M somewhere in the image, preferably at the centre where the target of interest (to be denoted by I) is likely to lie^3.7.
• With the appearance model in its current state and the static target, perform the following:
  • Calculate the differences between the model and the target. This can be done by synthesising M and calculating
    $\delta$I = M - I.
  • Save the new state of the appearance model if the difference has been lowered, i.e. similarity is being approached.
  • Adjust the value of Euclidean parameters, potentially with inclusion of a scaling coefficient $k=1.5,0.5,0.25$  and so forth. This often achieves good results, although it is a heuristics-driven technique.
  • Using the correlations learned off-line^3.8, set new values for the parameters $\mathbf{c}_{i}$ of M where $\delta\mathbf{c}$ is a function of $k$ (see above).
  • Compute the new difference measures between the model and the target (as previously).
• Iterate while no state of convergence has been reached and improvements are still observed at times.

Figure: Model and target fitting.

The technique of matching an appearance model to a target image can be depicted using a large sequence of images (an animation) resembling one which is shown in Figure . Only a few dozens of iterations are required in order to get good matching. This depends on the algorithm and the scale of the problem.