- Author:
- Hong-Qian Lu,
- Chair:
- T. W. Sze
This dissertation presents a new methodology of representing, recognizing and reconstucting an important class of surfaces called the developable surface. The constant ratio property, special property of a developable surface, is presented. Congruence conditions for two developable surface segments are proposed and mathematically proved. It is important that these conditions depend only on geometric and numerically computable quantities of a surface. These results provide better understanding of developable surfaces and serve as the theoretical basis of this work.
A surface description, named line of curvature description, is introduced to represent a developable surface. The description is simple in form, independent of surface parametrization, and possesses a property equivalent to view-invariant property when used for matching. The continuous developable surface without planar regions can be uniquely represented by such a description.
According to the congruence conditions, a recognition procedure is proposed that matches an unknown developable surface with surface models, by their descriptions, to identify the unknown surface. This approach can handle the situations such as the unknown and model surfaces having different attitude and scale, the unknown surface being a part of a model surface. The attitude of the unknown surface can be determined as well.
A procedure of reconstructing a developable surface from a line of curvature desciption is presented. The reconstruction demonstrates not only the significance of the descriptor from graphics point of view, but also the sufficiency of the descriptor for recognition purpose.
Three-dimensional object representation and model matching are addressed in this dissertation. A relational graph is used to delineate the adjacency relation among the segmented surfaces of an object. The relational graph is carefully defined so that there is exactly one relational graph for each object model, and the sensed graph of an object from a given view direction is likely a subgraph of the model graph of the object. Matching an unknown object with models consists of topological match and surface pair match.
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