Given the above object representation, the following furniture rela tionships are extracted automatically from positive input example Spatial relationships: The key prior relationships are the distanc of an object to its nearest wall ¯ di and its relative orientation to th wall ¯ θi. They are respectively estimated as the clustered means o input examples, where we can assign one of the clustered means a ¯ di and ¯ θi respectively for object i during optimization. The numbe of clusters can be preset or estimated by [Grunwald 2007]. Hierarchical relationships: Given two objects A and B, objec A is defined as the parent of B (and B as the.
