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Abstract: Formal models can be useful in computer graphics as a conceptual framework supporting representation systems. This allows to formally derive properties and algorithms and proof their correctness and validity. This paper describes a formal model based on a geometric algebra. This algebra has been used to obtain specific representation systems and study their equivalence. The representation systems derived in a natural way from this model are based on simplicial coverings and can be applied to non-manifold solids and to solids with holes. Representations have been developed for polyhedral and free-form solids. Algorithms described and proved include boolean operations and representation conversion. The paper covers the three abstraction levels: theoretical model, representations and derived algorithms. As a practical application an experimental modeller for free-form solid has been developed (ESC-MOD system: “Extended Simplicial Chains MOdeller”). [Copyright &y& Elsevier]

Abstract: Thinning is a critical pre-processing step to obtain skeletons for pattern analysis. Quadtree and octree are hierarchical data representations in image processing and computer graphics. In this paper, we present new 2-D area-based and 3-D surface-based thinning algorithms for directly converting quadtree and octree representations to skeletons. The computational complexity of our thinning algorithm for a 2-D or a 3-D image with each length N is respectively O(N 2) or O(N 3), which is more efficient than the existing algorithms of O(N 3) or O(N 4). Furthermore, our thinning algorithms can lessen boundary noise spurs and are suited for parallel implementation. [Copyright &y& Elsevier]

In this paper, adaptive mathematical morphology and its application to edge linking are presented to fill in the gaps between edge segments. Broken edges are extended along their slope directions by using the adaptive dilation operation with the suitable sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to the local properties, such as slope and curvature. Post-processes of thinning and pruning are also applied. The edge-linking operation is performed in an iterative manner, so that the broken edges can be linked up gradually and smoothly while the details of the object shape are preserved. [ABSTRACT FROM AUTHOR]