Oriented projective geometry
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Illicit expressions in vector algebra
ACM Transactions on Graphics (TOG)
New Geometric Methods for Computer Vision: An Application toStructure and Motion Estimation
International Journal of Computer Vision
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
Applications of Geometric Algebra in Computer Science and Engineering
Applications of Geometric Algebra in Computer Science and Engineering
Object Modelling and Collison Avoidance Using Clifford Algebra
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
On the geometry and algebra of the point and line correspondences between N images
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Journal of Mathematical Imaging and Vision
Gaigen 2:: a geometric algebra implementation generator
Proceedings of the 5th international conference on Generative programming and component engineering
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)
Geometric Algebra with Applications in Engineering
Geometric Algebra with Applications in Engineering
A general framework for subspace detection in unordered multidimensional data
Pattern Recognition
| Hi-index | 0.00 |
Geometric problems in visual computing (computer graphics, computer vision, and image processing) are typically modeled and solved using linear algebra (LA). Thus, vectors are used to represent directions and points in space, while matrices are used to model transformations. LA, however, presents some well-known limitations for performing geometric computations. As a result, one often needs to aggregate different formalisms (e.g., quaternions and Plücker coordinates) to obtain complete solutions. Unfortunately, such extensions are not fully compatible among themselves, and one has to get used to jumping back and forth between formalisms, filling in the gaps between them. Geometric algebra (GA), on the other hand, is a mathematical framework that naturally generalizes and integrates useful formalisms such as complex numbers, quaternions and Plücker coordinates into a high-level specification language for geometric operations. Due to its consistent structure, GA equations are often universal and generally applicable. They extend the same solution to higher dimensions and to all kinds of geometric elements, without having to handle special cases, as it happens in conventional techniques. This tutorial aims at introducing the fundamental concepts of GA as a powerful mathematical tool to describe and solve geometric problems in visual computing.