Reconstruction of Orthogonal Polyhedra

In this thesis I study reconstruction of orthogonal polyhedral surfaces and orthogonal polyhedra from partial information about their boundaries. There are three main questions for which I provide novel results. The first question is "Given the dual graph, facial angles and edge lengths of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the dihedral angles?" The second question is "Given the dual graph, dihedral angles and edge lengths of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the facial angles?" The third question is "Given the vertex coordinates of an orthogonal polyhedral surface or polyhedron, is it possible to reconstruct the edges and faces, possibly after rotating?" For the first two questions, I show that the answer is "yes" for genus-0 orthogonal polyhedra and polyhedral surfaces under some restrictions, and provide linear time algorithms. For the third question, I provide results and algorithms for orthogonally convex polyhedra. Many related problems are studied as well

Design and evaluation of a shape retrieval system

PhD ThesisWhile automated storage and retrieval systems for textual and numeric data are now commonplace, the development of analogous systems for pictorial data has lagged behind - not through the lack of need for such systems, but because their development involves a number of significant problems. The aim of this project is to investigate these problems by designing and evaluating an information retrieval system for a specific class of picture, 2-dimensional engineering drawings. This involves consideration of the retrieval capabilities needed by such· a system, what storage structures it would require, how the salient features of each drawing should be represented, how query and stored shapes should be matched, what features were of greatest importance in retrieval, and the interfaces necessary to formulate queries and display results. A form of hierarchical boundary representation has been devised for stored shapes, in which each boundary can be viewed as a series of levels of steadily increasing complexity. A set of rules for boundary and segment ordering ensures that as far as possible, each shape has a unique representation. For each level at which each boundary can be viewed, a set of invariant shape features characterizing that level is extracted and added to the shape representation stored in the database. Two classes of boundary feature have been defmed; global features, characteristic of the boundary as a whole, and local features, corresponding to individual fragments of the boundary. To complete the shape description, position features are also computed and stored, to specify the pattern of inner boundaries within the overall shape. Six different tYPes of shape retrieval have been distinguished, although the prototype system can offer only three of these - exact shape matching, partial shape matching and similarity matching. Complete or incomplete query shapes can be built up at a terminal, and subjected to a feature extraction process similar to that for stored drawings, yielding a query fIle that can be matched against the shape database. A variety of matching techniques is provided, including similarity estimation using global or local features, tests for the existence of specified local features in stored drawings, and cumulative angle vs distance matching between query and stored shape boundaries. Results can be displayed in text or graphical form. The retrieval performance of the system in similarity matching mode has been evaluated by comparing its rankings of shapes retrieved in response to test queries with those obtained by a group of human subjects faced with the same task. Results, expressed as normalized recall and precision, are encouraging, particularly for similarity estimation using either global or local boundary features. While the detailed results are of limited significance until confrrmed with larger test collections, they appear sufficiently promising to warrant the development of a more advanced prototype capable of handling 3-D geometric models. Some design aspects of the system would appear to be applicable to a wider range of pictorial information systems