Next: Description Evidence Up: Theory: Evidence and Association Previous: Supercomponent Associations

## Subcomponent Associations

This relationship gives direct evidence for the presence of an object, given the presence of its subcomponents. It is stronger than the supercomponent relationship, because the subcomponents are necessary features of the objects, but it is not a complete implication because the subcomponents may be present without the presence of the assembled object. The computation described below only requires the presence of the subcomponents and does not consider their geometric relations.

This computation is defined by several constraints:

• The more subcomponents present, the more plausible is the object's presence.
• Even if all subcomponents are present, this does not guarantee the presence of the object.
• Subcomponents are typically seen in viewpoint dependent groupings, and are seen from only one viewpoint at a time.
• The more plausible a subcomponent's presence, the more plausible is the object's presence.
• The context of all subcomponents must lie within the context of the object.

The computation is formalized below and looks for the most plausible candidate for each of the subcomponents in the given context, and averages the subcomponent's contributions towards the plausibility of the object being seen from key viewpoints. The final plausibility is the best of the viewpoint plausibilities. Each of the individual contributions is weighted. The averaging of evidence arises because each subcomponent is assumed to give an independent contribution towards the whole object plausibility. Because all subcomponents must lie within the same surface cluster as the object, the context of evidence collection is that of the hypothesis and all contained subcontexts.

The formal definition of the subcomponent relationship calculation is:

 Given: a model instance of type in image context a set {()} of subcomponents of , where is the weight of subcomponent sets = {} of subcomponents representing groups of subcomponents visible from typical viewpoints a set {} of subcontexts of the context including itself a set of model instances of type , in context , with plausibility value

The weight factors designate significance within the group, with larger weights emphasizing more important or significant features. The subcomponent weights are the sum of the weights of the property evidence specified for the subcomponents.

The first value calculated is the best evidence for each subcomponent type in the subcontexts:

This is implemented as a tree of binary "max" units. Then, the evidence for each viewpoint is calculated by integrating the evidence for the expected viewpoints using the modified harmonic mean function described above:

over all subcomponents in .

Finally, the evidence from the different viewpoints is integrated, by selecting the best evidence:

The assumption is that if the object is present, then there should be exactly one visibility group corresponding to the features visible in the scene. Subcomponent evidence has a weighting that is the maximum visibility group's weight, which is the sum of the weights of the subcomponents and their properties:

Relative importances between subcomponents and properties can be modified by scaling the relevant weights. The network structure for this computation is similar to those previously shown. If no subcomponent evidence is available, this computation is not applied.

Next: Description Evidence Up: Theory: Evidence and Association Previous: Supercomponent Associations
Bob Fisher 2004-02-26