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Computer Aided Geometric Design
Application of vector sum operator
Computer-Aided Design
A Representation Theory for Morphological Image and Signal Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
A coordinate-free approach to geometric programming
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Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
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Minkowski operations for satellite antenna layout
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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A Reflective Symmetry Descriptor
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Image Analysis and Mathematical Morphology
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
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IEEE Transactions on Computers
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
A kinetic framework for computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
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Computer Aided Geometric Design
Configuration products in geometric modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Mathematical morphology in computer graphics, scientific visualization and visual exploration
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Non-commutative morphology: Shapes, filters, and convolutions
Computer Aided Geometric Design
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
Solving inverse configuration space problems by adaptive sampling
Computer-Aided Design
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A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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Group morphology is an extension of mathematical morphology with classical Minkowski sum and difference operations generalized respectively to Minkowski product and quotient operations over arbitrary groups. We show that group morphology is a proper setting for unifying, formulating and solving a number of important problems, including translational and rotational configuration space problems, mechanism workspace computation, and symmetry detection. The proposed computational approach is based on group convolution algebras, which extend classical convolutions and the Fourier transform to non-commutative groups. In particular, we show that all Minkowski product and quotient operations may be represented implicitly as sublevel sets of the same real-valued convolution function.