Invariant Scattering Convolution Networks
Abstract
A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.
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Many approaches have been presented to enhance robustness, aiming at learning invariant CNN representations with respect to different types of transformations such as scale, rotation, or both.
“Therefore, many approaches have been presented to enhance robustness, aiming at learning invariant CNN representations with respect to different types of transformations such as scale (Kim et al. 2014;Bruna and Mallat 2013), rotation (Bruna and Mallat 2013;Cheng et al. 2016;Worrall et al. 2017;Zhou et al. 2017b), or both (Jaderberg et al. 2015).”
From Deep Learning for Generic Object Detection: A Survey (2020) · cites this paper as Bruna and Mallat 2013
Cites
Distinctive Image Features from Scale-Invariant Keypoints
Lowe, D. G. (2004) · International Journal of Computer Vision · doi:10.1023/b:visi.0000029664.99615.94 · Cited by 55,589 · see citing works
LIBSVM: A library for support vector machines
Chang, C.-C., & Lin, C.-J. (2011) · ACM Transactions on Intelligent Systems and Technology · doi:10.1145/1961189.1961199 · Cited by 40,918 · see citing works
Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories
Lazebnik, S., Schmid, C., & Ponce, J. (2006) · 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2 (CVPR'06) · doi:10.1109/cvpr.2006.68 · Cited by 7,916 · see citing works
Fei-Fei, L., Fergus, R., & Perona, P. (2007) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2005.09.012 · Cited by 2,359 · see citing works
What is the best multi-stage architecture for object recognition?
Jarrett, K., Kavukcuoglu, K., Ranzato, M. A., & LeCun, Y. (2009) · 2009 IEEE 12th International Conference on Computer Vision · doi:10.1109/iccv.2009.5459469 · Cited by 2,153 · see citing works
Representing and Recognizing the Visual Appearance of Materials Using Three-Dimensional Textons
Leung, T., & Malik, J. (2001) · International Journal of Computer Vision · doi:10.1023/a:1011126920638 · Cited by 1,498 · cited 1× · see citing works
“For texture analysis, many researchers [21], [31] have been using averaged wavelet coefficient amplitudes jx ? j ?”
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Deformable Convolutional Networks
Dai, J., Qi, H., Xiong, Y., Li, Y., Zhang, G., Hu, H., & Wei, Y. (2017) · 2017 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.89 · Cited by 7,513 · see citing works
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2693418 · Cited by 3,661 · see citing works
Self-citationDeep Learning for Generic Object Detection: A Survey
Liu, L., Ouyang, W., Wang, X., Fieguth, P., Chen, J., Liu, X., & Pietikäinen, M. (2020) · International Journal of Computer Vision · doi:10.1007/s11263-019-01247-4 · Cited by 2,965 · see citing works
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Zhou, D.-X. (2020) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2019.06.004 · Cited by 530 · see citing works
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Golestaneh, S. A., Dadsetan, S., & Kitani, K. M. (2022) · 2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) · doi:10.1109/wacv51458.2022.00404 · Cited by 465 · see citing works
Local binary features for texture classification: Taxonomy and experimental study
Liu, L., Fieguth, P., Guo, Y., Wang, X., & Pietikäinen, M. (2017) · Pattern Recognition · doi:10.1016/j.patcog.2016.08.032 · Cited by 369 · see citing works
Seeing it all: Convolutional network layers map the function of the human visual system
Eickenberg, M., Gramfort, A., Varoquaux, G., & Thirion, B. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2016.10.001 · Cited by 338 · see citing works
A Survey of Handwritten Character Recognition with MNIST and EMNIST
Baldominos, A., Saez, Y., & Isasi, P. (2019) · Applied Sciences · doi:10.3390/app9153169 · Cited by 279 · see citing works
Seo, H., Badiei Khuzani, M., Vasudevan, V., Huang, C., Ren, H., Xiao, R., Jia, X., & Xing, L. (2020) · Medical Physics · doi:10.1002/mp.13649 · Cited by 300 · see citing works
Brain Tumor Segmentation Using Convolutional Neural Networks in MRI Images
Thaha, M. M., Kumar, K. P. M., Murugan, B. S., Dhanasekeran, S., Vijayakarthick, P., & Selvi, A. S. (2019) · Journal of Medical Systems · doi:10.1007/s10916-019-1416-0 · Cited by 244 · see citing works
Deep Learning for Generic Object Detection: A Survey
Liu, L., Ouyang, W., Wang, X., Fieguth, P., Chen, J., Liu, X., & Pietikäinen, M. (2018) · arXiv · doi:10.48550/arxiv.1809.02165 · Cited by 2,965 · see citing works
A mathematical motivation for complex-valued convolutional networks
Tygert, M., Bruna, J., Chintala, S., LeCun, Y., Piantino, S., & Szlam, A. (2016) · Neural Computation · doi:10.1162/neco_a_00824 · Cited by 88 · see citing works
Leveraging Equivariant Features for Absolute Pose Regression
Musallam, M. A., Gaudilliere, V., Del Castillo, M. O., Al Ismaeil, K., & Aouada, D. (2022) · 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr52688.2022.00675 · Cited by 27 · see citing works
Diagnosis of pathological speech with streamlined features for long short-term memory learning
Pham, T. D., Holmes, S. B., Zou, L., Patel, M., & Coulthard, P. (2024) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2024.107976 · Cited by 23 · see citing works
The changing fortunes of pattern recognition and computer vision
Chellappa, R. (2016) · Image and Vision Computing · doi:10.1016/j.imavis.2016.04.005 · Cited by 8 · see citing works
- Authors
- Bruna, J., & Mallat, S.
- Affiliations
- Courant Institute of Mathematical Sciences (US)
- École Normale Supérieure - PSL (FR)
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2013-08
- Volume
- 35
- Issue
- 8
- Pages
- 1872-1886
- ISSN
- 0162-8828 (ISSN-L)
- 2160-9292
- OpenAlex
- W2072072671
- Cited by
- 1,633
- References
- 6
- Citations by year
- 2026: 98 · 2025: 119 · 2024: 149 · 2023: 169 · 2022: 148 · 2021: 171 · 2020: 164 · 2019: 152 · 2018: 142 · 2017: 120 · 2016: 84 · 2015: 72 · 2014: 34 · 2013: 9 · 2012: 2
- FWCI
- 121.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Pattern Analysis and Machine Intelligence (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Agence Nationale de la Recherche
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Retrieval and Classification Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image and Video Retrieval Techniques
- Keywords
- wavelet scattering network, translation invariance, image classification, SIFT descriptors, texture discrimination, stationary processes, higher-order moments, Fourier power spectrum, handwritten digit recognition
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