Using Pythagorean triangles to approximate angles
American Mathematical Monthly
Three-dimensional rotations by three shears
Graphical Models and Image Processing
Using Quaternions for Parametrizing 3-D Rotations in Unconstrained Nonlinear Optimization
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Two-dimensional pattern matching with rotations
Theoretical Computer Science
Global Optimization through Rotation Space Search
International Journal of Computer Vision
Computing upper and lower bounds of rotation angles from digital images
Pattern Recognition
Hinge Angles for 3D Discrete Rotations
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
A generic approach for n-dimensional digital lines
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Generalized perpendicular bisector and circumcenter
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
An algorithm to decompose n-dimensional rotations into planar rotations
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
The rational approximations of the unitary groups
Quantum Information Processing
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In this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence.