Our existing models and techniques are powerful, but there are a number of areas which are relatively new and in which research is at an early stage. For instance, the statistical methods we employ work best with large numbers of training examples. When only a few examples are available we must employ other approaches to develop useful models. Early results combining finite element methods with our statistical models have been promising [20] but more techniques may be necessary. We have also begun developing models which represent non-linear variations [24] and others have been looking at automatic generation of the landmark positions [25]. These areas are complex and likely to require study and development beyond the scope of existing projects. The duration and flexibility of a fellowship would allow research to be continued to a greater depth.

All the models we have used so far are based on landmark points representing important parts of the image structure. Boundaries are represented by sequences of points at suitable spacings. For some objects where significant landmarks are sparse it is more natural to use lines and curves to define the boundaries. Methods using trigonometric functions [6,7] and spline curves [13,14] have been described. Baumberg & Hogg [32] represent curves using B-splines whose control points are modelled by a Point Distribution Model. We would like to experiment with these methods and compare them with point based methods. A goal would be to develop a framework to encompass both point and curve based models.

Our existing scheme deals with complex assemblies by building models in which all landmarks on all components are treated equally in a `flat' model. This has proved powerful, encapsulating as it does both component shape variation and inter-component relationships in a single model. However there are some circumstances in which this system is inefficient. It cannot deal with rotating sub-components (without using non-linear models) and during search all components are located at once. We would like to explore a hierarchical system in which the relationships between components are slightly looser, but still defined statistically. Thus there would be a shape model for each component individually, and a higher level model which represented the relationships between component locations and their first few shape parameters. This decoupling may allow more flexible and efficient search strategies to evolve, in which individual components can be located separately, with the higher level model propagating constraints about the system.

Although earlier aspects of our work with 2-D shape models and image search has been successfully extended to 3-D [21] and time sequence data [1] there remains much scope for recent developments (grey-level models, multi-resolution search) to improve the results obtained in these more complex data sets.

To summarise, the intention is to investigate

- building models from small training sets
- non-linear models
- automatic landmark placement
- line/curve based models
- hierarchical models
- the application of recent ideas to 3-D and time sequences