| This thesis investigates the concept of generalized attributed hypergraph (GAH) and its applications on object modeling, recognition and categorization. After a review of the existing object modeling methods based on relational graph and attributed hypergraph is made, the concept of "hyperedge of hyperedges" is proposed to form the foundation of the generalized attributed hypergraph. Unlike the traditional graph and hypergraph approach, where an edge/hyperedge is a subset of the vertex set, a generalized hyperedge of a GAH consists of vertices and other generalized hyperedges. Thus, a GAH representation of an object can explicitly encode the hierarchy information on the concepts and knowledge of the object. Though hypergraph representation in principle is free of hierarchy, hierarchical information, if well applied, proves to be very useful to interpret a representation and to guide the object recognition problem.; The mathematics of GAH representation and its primary operators is included in this thesis. It presents a general approach to construct GAH representation, to match two GAH's with subgraph isomorphism and to synthesize GAH representation of the object from multiple views. As a hierarchical and generic representation, GAH enables structural pattern matching, recognition, synthesis and manipulation to be carried out at different representation levels depending on the context of the subject matters. The procedure of generating a compact and efficient GAH representation by hyperedge re-organization and redundancy elimination is illustrated.; This thesis also studies the problem of automatic visual object categorization and recognition based on structural representation. By applying an adapted pattern discovery technique, high order significant patterns (or compound events) representing the geometrical, topological or statistical significance of the relations among the primary features or feature groups in training images have been extracted and represented as a generalized attributed hypergraph. When multiple object categories are presented, the compound events are labeled with attributes that are compatible among different categories. To simplify object categorization and recognition, any high order compound events are represented by the combination of a set of lower order patterns. Using patented indexed searching scheme for stochastic pattern and other traditional pattern recognition approach, the proposed method avoids the difficulty arising from the sequential comparison of a test view to all views for all categories. |
