On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Offsetting operations in solid modelling
Computer Aided Geometric Design
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
A mathematical model for shape description using Minkowski operators
Computer Vision, Graphics, and Image Processing
Computer Vision, Graphics, and Image Processing
An algebra of polygons through the notion of negative shapes
CVGIP: Image Understanding
Mathematical morphological operations of boundary-represented geometric objects
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
An algorithm to compute the Minkowski sum outer-face of two simple polygons
Proceedings of the twelfth annual symposium on Computational geometry
Minkowski operations for satellite antenna layout
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Mathematical Morphology and Its Applications to Image and Signal Processing
Mathematical Morphology and Its Applications to Image and Signal Processing
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A kinetic framework for computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
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This paper proposes a new formulation of the Minkowski algebra for figures. In the conventional Minkowski algebra, the sum operation was always defined, but its inverse was not necessarily defined. On the other hand, the proposed algebra forms a group, and hence every element has its inverse, and the sum and the inverse operation can be taken freely. In this new algebraic system, some of the elements does not correspond to the figures in an ordinary sense; we call these new elements "hyperfigures". Physical interpretations and practical usage of the hyperfigures are also discussed.