Abstract
This paper introduces a novel and matrix-free implementation of the widely used Levenberg-Marquardt algorithm, in the language of Geometric Algebra. The resulting algorithm is shown to be compact, geometrically intuitive, numerically stable and well suited for efficient GPU implementation. An implementation of the algorithm and the examples in this paper are publicly available.
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References
Tingelstad, L., Egeland, O.: Motor parameterization. Adv. Appl. Clifford Algebras 28, 34 (2018)
Lasenby, J., Fitzgerald, W.J., Lasenby, A.N., Doran, C.J.L.: New geometric methods for computer vision: an application to structure and motion estimation. Int. J. Comput. Vis. 26(3), 191–213 (1998)
Guennebaud, G., Jacob, B. et al.: Eigen v3 (2010). http://eigen.tuxfamily.org
Moré, J.J., Sorensen, D.C., Hillstrom, K.E., Garbow, B.S.: The MINPACK project, in sources and development of mathematical software. In: Cowell, W.J. (ed.) pp. 88–111. Prentice-Hall (1984). http://www.netlib.org/minpack/
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C : The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)
Tingelstad, L., Egeland, O.: Automatic multivector differentiation and optimization. Adv. Appl. Clifford Algebras 27, 707 (2017). https://doi.org/10.1007/s00006-016-0722-6
Fletcher, R.: A modified marquardt subroutine for nonlinear least squares. Atomic Energy Research Establishment report R6799, Harwell, England (1971)
Gunn, C.: Geometry, Kinematics, and Rigid Body Mechanics in Cayley-Klein Geometries. Ph.D. thesis, Technical University, Berlin (2011). http://opus.kobv.de/tuberlin/volltexte/2011/3322
Gunn, C.: On the homogeneous model of Euclidean geometry. In: Dorst, L., Lasenby, J. (eds.) A Guide to Geometric Algebra in Practice, chapter 15, pp. 297–327. Springer, London (2011). https://doi.org/10.1007/978-0-85729-811-9_15, https://arxiv.org/abs/1101.4542
Gunn, C.: Geometric algebras for Euclidean geometry. Adv. Appl. Clifford Algebras 27(1), 185–208 (2017). https://arxiv.org/abs/1411.650
Rall, L.B. (ed.): Automatic Differentiation: Techniques and Applications. LNCS, vol. 120. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10861-0
De Keninck, S.: Ganja.js: Geometric Algebra - Not Just Algebra (2017). https://github.com/enkimute/ganja.js
Acknowledgment
The authors would like to thank Charles Gunn for his valuable feedback on, and Hugo Hadfield and Vincent Nozick for their proofreading of an early version of this article.
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De Keninck, S., Dorst, L. (2019). Geometric Algebra Levenberg-Marquardt. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_51
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DOI: https://doi.org/10.1007/978-3-030-22514-8_51
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