"Functant" in a functional model: a theoretical consideration of reasoning about shape, structure, and function

Object models in image understanding systems are conventionally represented by geometric features of objects based on shape or a configuration of parts, with each part defined by its shape. Shape-based models such as these are useful in matching to the results of image processing for recognition purposes. Shape-based models, however, are so specific to individual objects that a large number of object models would be required to ensure robust performance in a vision system. By contrast, normal instances of an object can often share a single model if they might be represented by their function. This is the great advantage of the functional approach to representation. An essential task of vision systems for a movable robot should be to find free space to move around, which is a kind of a functional expression of a widely defined road in the similar way to that a space with suitable size and configuration for a person to sit down is that of a chair. The disadvantage of using only the function-based representation of objects is that the results of processing an image are usually described by geometric features and it is not necessarily easy to match these features to the corresponding functional representations. What is needed is an inference scheme which can deduce shape from a functional description. In this way the functional representation will provide a generic framework for describing object models. However, there has been essentially no investigation of the deduction of shapes and structures from functions, that is, how functions can be related to the shape, especially structure and size of objects. This is the essence of the research presented here.