Search

Your search keyword '"geometric algebra"' showing total 2 results
Start Over Descriptor "geometric algebra" Search Limiters Full Text Topic geometric analysis Publication Year Range Last 50 years
2 results on '"geometric algebra"'

1. Measuring the closeness to singularities of a planar parallel manipulator using geometric algebra.

Author

Yao, Huijing, Li, Qinchuan, Chen, Qiaohong, and Chai, Xinxue

Subjects
*GEOMETRIC analysis, *MATHEMATICAL singularities, *MATHEMATICAL models, *SIMULATION methods & models, *POLYNOMIALS
Abstract

A new index for measuring the closeness to the singularities of parallel manipulators using geometric algebra is proposed in this paper. Constraint wrenches acting on the moving platform of a parallel manipulator are derived using the outer product and dual operations. Removing the redundant constraint wrenches, a singularity polynomial is obtained when the coefficient of the outer product of all the non-redundant constraint wrenches equals zero. A singularity surface can be drawn using the singularity polynomial. Similarly, an approximate singularity polynomial and approximate singularity surface can be obtained by imposing a threshold to the singular polynomial. Then the singularity volume is calculated as the space between singularity surface and approximate singularity surface. The new index is derived by calculating the ratio of the non-singularity workspace volume (the workspace volume minus the singularity volume) to the workspace volume. The proposed index is coordinate-free and has a clear geometrical and physical interpretation. This index can be a basis for selecting structural parameters, path planning and mechanism design. [ABSTRACT FROM AUTHOR]

Published
2018
Full Text
View/download PDF

2. GA-SIFT: A new scale invariant feature transform for multispectral image using geometric algebra.

Author

Li, Yanshan, Liu, Weiming, Li, Xiaotang, Huang, Qinghua, and Li, Xuelong

Subjects
*GENETIC algorithms, *SCALE invariance (Statistical physics), *FEATURE extraction, *MULTISPECTRAL imaging, *GEOMETRIC analysis, *COLOR image processing
Abstract

Feature analysis plays an important role in many multispectral image applications and scale invariant feature transform (SIFT) has been successfully applied for extraction of image features. However, the existing SIFT algorithms cannot extract features from multispectral images directly. This paper puts forward a novel algorithmic framework based on the SIFT for multispectral images. Firstly, with the theory of the geometric algebra (GA), a new representation of multispectral image including spatial and spectral information is put forward and discussed. Secondly, a new method for obtaining the scale space of the multispectral image is proposed. Thirdly, following the procedures of the SIFT, the GA based difference of Gaussian images are computed and the keypoints can be detected in the GA space. Fourthly, the feature points are finally detected and described in the mathematical framework of the GA. Finally, the comparison results show that the GA-SIFT outperforms some previously reported SIFT algorithms in the feature extraction from a multispectral image, and it is comparable with its counterparts in the feature extraction of color images, indicating good performance in various applications of image analysis. [ABSTRACT FROM AUTHOR]

Published
2014
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results