Followup to: Patterns of structure, Enumerating patterns.
As structure waves propagate through the scene, they bring up more and more details. Their progress is shaped by structural context in the wave-front, overall content of the current scene (salience of maps) and knowledge of maps from the past scenes. In every scene, it’s possible to infer huge number of specific facts, on different levels of representation, and that’s what structure waves do.
Representation keeps knowledge about the scene in a fluid format, converting elements of representation of different types into each other as the context demands. It can’t and doesn’t need to explicitly enumerate all the facts that could be inferred. Some irrelevant details uncovered by structure waves need to fade out of scene, if they can’t find enough support.
A pattern, as it exists in the scene, is embedded in its context. It’s connected by relations to other elements of the scene, and assigned properties specific to its place in the scene rather than to the pattern itself. On one hand, a pattern can be seen as a class, substructure containing elements repeating in most of its instances, and on the other, as an instance, form assumed in the scene, with all the context-specific details.
When structure wave starts reconstructing a pattern, it’s done with a certain level of detail, ranging from a closed atomic property like color from which there is no inference, to a scene root that leads to every element of the scene around the pattern. Depending on how specific origin of the wave is, it can lead to instantiation of different other patterns in the scene, with different levels of detail.
As wave propagates, there are two pressures on the level of detail present in reconstructed patterns. First, wave avoids ambiguity, which creates a hierarchy of patterns, running from instances to classes of their properties. But second, wave acquires details as it proceeds, being guided by salience of maps and knowledge of other maps. As a result, the hierarchy turns upside down, if structure wave is allowed to run long enough and doesn’t start from a complete dead end. Starting from a class of pattern, structure wave exits to the scene from the other side, where it can pick up a root of any other pattern.
This makes pattern hierarchy a fleeting description that applies only for the few steps, around a specific pattern instance in the scene. Keeping the hierarchy an adequate description of restoration process requires considering only structure waves that originate in the patterns of the hierarchy and that don’t run for too long. Scene graph is not hierarchical, and neither is its map representation. Hierarchy appears locally, and describes the way structure waves enumerate structural contexts of the scene. It also describes most of the salient maps in patterns instantiated by the waves, giving a bound on inferred details to be included in the scene. A significant reorganization of existing hierarchies can occur as a result of changes in map salience created by deviations of waves from exact patterns of a hierarchy.
Multiple hierarchies can coexist describing the reconstruction of the same scene, because they describe the same areas of scene graph with different levels of detail. Each hierarchy runs from instances to classes, abstracting out relations between the core of a pattern and its context in patterns further from the root. But the same patterns with context included in it can be at the root in another hierarchy. As this description was constructed, joining different hierarchies together complicates the picture, as patterns are implicit and different hierarchies will have different patterns included in them.
From this perspective, the scene can be seen as casting multiple hierarchical shadows wrapped around each other, each driving elaboration of detail in its specific direction, but stopping at some point and fading into other hierarchies. This is a way to stop combinatorial explosion by shifting to different aspects all the time, where search for a solution is simply conversion of the scene representation from one aspect to another, from a question to an answer, through many intermediate steps guided by unified scene representation.
