Algebraic decomposition of regular curves
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A Cooperating Strategy for Objects Recognition
Shape, Contour and Grouping in Computer Vision
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
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The paper describes the combination a multi-views approach to represent connected components of 2D binary images. The approach is based on the Object Connectivity Graph (OCG), which is a subgraph of the connectivity graph generated by the Discrete Cylindrical Algebraic Decomposition(DCAD) performed in the 2D discrete space. This construction allows us to find the number of connected components, to determine their connectivity degree, and to solve visibility problem. We show that the CAD construction, when performed on two orthogonal views, supply information to avoid ambiguities in the interpretation of each image component. The implementation of the algorithm is outlined and the computational complexities is given.