We have described the construction of `hierarchical' PDMs, using a piecewise linear PCA strategy. We have performed both qualitative and quantitative analyses on synthetic data, and also examined performance on automatically-collected real data, with promising results. The HPDM is a viable solution to the problem of fully-automated construction of deformable models.
The hierarchical approach requires a large amount of training data to build good models. However, this problem is negated by the fact that training data can be collected automatically. In the example of the hand we gave, it took less than 5 minutes to collect all the training data and build the model. More intelligent training data collection (eg. Hill and Taylor's approach [7]) might give rise to a less complex shape space which could then be modelled with fewer linear pieces.
Another issue is that of speed. When applying the shape constraints it is necessary to calculate distances to every cluster. This process is order n in the number of clusters. Bregler and Omohundro suggest the use of `Bumptrees' [8] (a tree-like data structure for representing functions and constraints) to decrease the number of calculations. A related approach would be to extend the hierarchical model to more than two levels, inserting intermediate-sized PCA spaces between the coarsest (global) and finest levels to give a multi-level tree structure. Search for the nearest cluster(s) would descend through the tree, giving at worst order n log n performance and maybe better in the case of only a partial tree descent.
Tracking using HPDMs has proven relatively successful, proceeding in much the same way as for a standard PDM [3]; HPDMs are less likely to be distracted by image noise and background clutter. However, in the case of automatically trained models, some deformations are not tracked well, specifically those which require landmarks to `slide' around the model boundary or those which give rise to sudden shape changes. A solution to this problem is discussed in [5].