Abstract
Following recent advances on parameterized hypercomplex multiplication [21], we explore the usefulness of hypercomplex convolutions and deconvolutions in a document labeling task. We show that the proposed Hypercomplex Generative Adversarial Networks achieve excellent results while requiring significantly less independent parameters than real-valued models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cui, Y., Jia, M., Lin, T.Y., Song, Y., Belongie, S.: Class-balanced loss based on effective number of samples. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), pp. 9268–9277 (2019)
Dimitrakopoulos, P., Sfikas, G., Nikou, C.: ISING-GAN: annotated data augmentation with a spatially constrained generative adversarial network. In: 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI), pp. 1600–1603. IEEE (2020)
Dyson, F.J.: Quaternion determinants. Helv. Phys. Acta 45(2), 289 (1972)
Ell, T.A., Sangwine, S.J.: Hypercomplex Fourier transforms of color images. IEEE Trans. Image Process. 16(1), 22–35 (2007)
Fraleigh, J.B.: A First Course in Abstract Algebra, 7th edn. (2002)
Giotis, A.P., Sfikas, G., Nikou, C., Gatos, B.: Shape-based word spotting in handwritten document images. In: 13th International Conference on Document Analysis and Recognition (ICDAR), pp. 561–565. IEEE (2015)
Grassucci, E., Zhang, A., Comminiello, D.: Lightweight convolutional neural networks by hypercomplex parameterization. arXiv preprint arXiv:2110.04176 (2021)
Jain, A.K.: Fundamentals of Digital Image Processing. Prentice-Hall Inc., Hoboken (1989)
Kuipers, J.B.: Quaternions and Rotation Sequences: A Primer with Application to Orbits, Aerospace and Virtual Reality. Princeton University Press, Princeton (1999)
Le Bihan, N., Mars, J.: Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing. Signal Process. 84(7), 1177–1199 (2004)
Parcollet, T., Morchid, M., Linarès, G.: Quaternion convolutional neural networks for heterogeneous image processing. In: ICASSP 2019–2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 8514–8518. IEEE (2019)
Parcollet, T., Morchid, M., Linarès, G.: A survey of quaternion neural networks. Artif. Intell. Rev. 53(4), 2957–2982 (2019). https://doi.org/10.1007/s10462-019-09752-1
Parcollet, T., et al.: Quaternion convolutional neural networks for end-to-end automatic speech recognition. arXiv preprint arXiv:1806.07789 (2018)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Sangwine, S.J.: Biquaternion (complexified quaternion) roots of- 1. Adv. Appl. Clifford Algebras 16(1), 63–68 (2006). https://doi.org/10.1007/s00006-006-0005-8
Sfikas, G., Giotis, A.P., Retsinas, G., Nikou, C.: Quaternion generative adversarial networks for inscription detection in byzantine monuments. In: Del Bimbo, A., et al. (eds.) ICPR 2021. LNCS, vol. 12667, pp. 171–184. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68787-8_12
Sfikas, G., Ioannidis, D., Tzovaras, D.: Quaternion Harris for multispectral keypoint detection. In: 2020 IEEE International Conference on Image Processing (ICIP), pp. 11–15. IEEE (2020)
Sfikas, G., Nikou, C., Galatsanos, N., Heinrich, C.: MR brain tissue classification using an edge-preserving spatially variant Bayesian mixture model. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008. LNCS, vol. 5241, pp. 43–50. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85988-8_6
Sfikas, G., Nikou, C., Galatsanos, N., Heinrich, C.: Majorization-minimization mixture model determination in image segmentation. In: CVPR 2011, pp. 2169–2176. IEEE (2011)
Vince, J.: Quaternions for Computer Graphics. Springer, Cham (2011). https://doi.org/10.1007/978-1-4471-7509-4
Zhang, A., et al.: Beyond fully-connected layers with quaternions: parameterization of hypercomplex multiplications with \(1/n \) parameters. arXiv preprint arXiv:2102.08597 (2021)
Zhang, F.: Quaternions and matrices of quaternions. Linear Algebra Appl. 251, 21–57 (1997)
Acknowledgments
This research has been partially co-financed by the EU and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the calls “OPEN INNOVATION IN CULTURE” (project Bessarion - T6YB\(\varPi \)-00214) and “RESEARCH - CREATE - INNOVATE” (project Culdile - T1E\(\varDelta \)K-03785).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Sfikas, G., Retsinas, G., Gatos, B., Nikou, C. (2022). Hypercomplex Generative Adversarial Networks for Lightweight Semantic Labeling. In: El Yacoubi, M., Granger, E., Yuen, P.C., Pal, U., Vincent, N. (eds) Pattern Recognition and Artificial Intelligence. ICPRAI 2022. Lecture Notes in Computer Science, vol 13363. Springer, Cham. https://doi.org/10.1007/978-3-031-09037-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-031-09037-0_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-09036-3
Online ISBN: 978-3-031-09037-0
eBook Packages: Computer ScienceComputer Science (R0)