# Increasing the Stability of CNNs using a Denoising Layer Regularized by Local Lipschitz Constant in Road Understanding Problems

### Hamed H. Aghdam, Elnaz J. Heravi, Domenec Puig

#### Abstract

One of the challenges in problems related to road understanding is to deal with noisy images. Especially, recent studies have revealed that ConvNets are sensitive to small perturbations in the input. One solution for dealing with this problem is to generate many noisy images during training a ConvNet. However, this approach is very costly and it is not a certain solution. In this paper, we propose an objective function regularized by the local Lipschitz constant and train a ReLU layer for restoring noisy images. Our experiments on the GTSRB and the Caltech-Pedestrian datasets show that this lightweight approach not only increases the accuracy of the classification ConvNets on the clean datasets but it also increases the stability of the ConvNets against noise. Comparing our method with similar approaches shows that it produces more stable ConvNets while it is computationally similar or more efficient than these methods.

#### References

- Aghdam, H. H., Heravi, E. J., and Puig, D. (2015). Recognizing Traffic Signs using a Practical Deep Neural Network. In Robot 2015: Second Iberian Robotics Conference, pages 399-410, Lisbon. Springer.
- Aghdam, H. H., Heravi, E. J., and Puig, D. (2016). Analyzing the Stability of Convolutional Neural Networks Against Image Degradation. In Proceedings of the 11th International Conference on Computer Vision Theory and Applications.
- Alhussein Fawzi, Omar Fawzi, and Pascal Frossard (2015). Analysis of classifiers' robustness to adversarial perturbations. (2014):1-14.
- Angelova, A., Krizhevsky, A., View, M., View, M., Vanhoucke, V., Ogale, A., and Ferguson, D. (2015). RealTime Pedestrian Detection With Deep Network Cascades. Bmvc2015, pages 1-12.
- Bittel, S., Kaiser, V., Teichmann, M., and Thoma, M. (2015). Pixel-wise Segmentation of Street with Neural Networks. pages 1-7.
- Burger, H. C., Schuler, C. J., and Harmeling, S. Image denoising Can plain neural networks compete with BM3D .
- Cirean, D., Meier, U., Masci, J., and Schmidhuber, J. (2012). Multi-column deep neural network for traffic sign classification.Neural Networks, 32:333-338.
- Dollár, P., Wojek, C., Schiele, B., and Perona, P. (2009). Pedestrian detection: A benchmark. 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009, pages 304-311.
- Dong, C., Loy, C. C., and He, K. (2014). Image Super-Resolution Using Deep Convolutional Networks. arXiv preprint, 8828(c):1-14.
- Goodfellow, I. J., Shlens, J., and Szegedy, C. (2015). Explaining and Harnessing Adversarial Examples. Iclr 2015, pages 1-11.
- Gu, S. and Rigazio, L. (2014). Towards Deep Neural Network Architectures Robust to Adversarial Examples. arXiv:1412.5068 [cs], (2013):1-9.
- He, K., Zhang, X., Ren, S., and Sun, J. (2015). Deep Residual Learning for Image Recognition. In arXiv prepring arXiv:1506.01497.
- Hradi, M. (2015). Convolutional Neural Networks for Direct Text Deblurring. Bmvc, (1):1-13.
- Jain, V. and Seung, S. (2009). Natural Image Denoising with Convolutional Networks. pages 769-776.
- Krizhevsky, A., Sutskever, I., and Hinton, G. (2012). Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pages 1097-1105. Curran Associates, Inc.
- Levi, D., Garnett, N., and Fetaya, E. (2015). StixelNet: a deep convolutional network for obstacle detection and road segmentation. Bmvc, pages 1-12.
- Papernot, N., McDaniel, P., Jha, S., Fredrikson, M., Celik, Z. B., and Swami, A. (2015). The Limitations of Deep Learning in Adversarial Settings.
- Sabour, S., Cao, Y., Faghri, F., and Fleet, D. J. (2015). Adversarial Manipulation of Deep Representations. arXiv preprint arXiv:1511.05122, (2015):1-10.
- Sermanet, P. and Lecun, Y. (2011). Traffic sign recognition with multi-scale convolutional networks. Proceedings of the International Joint Conference on Neural Networks, pages 2809-2813.
- Simonyan, K. and Zisserman, A. (2015). Very Deep Convolutional Networks for Large-Scale Image Recognition. In International Conference on Learning Representation (ICLR), pages 1-13.
- Srivastava, R. K., Greff, K., and Schmidhuber, J. (2015). Highway Networks. arXiv:1505.00387 [cs].
- Stallkamp, J., Schlipsing, M., Salmen, J., and Igel, C. (2012). Man vs. computer: Benchmarking machine learning algorithms for traffic sign recognition. Neural Networks, 32:323-332.
- Svoboda, P., Hradis, M., Marsik, L., and Zemcik, P. (2016). CNN for License Plate Motion Deblurring.
- Szegedy, C., Reed, S., Sermanet, P., Vanhoucke, V., and Rabinovich, A. (2014a). Going deeper with convolutions. In arXiv preprint arXiv:1409.4842, pages 1-12.
- Szegedy, C., Zaremba, W., and Sutskever, I. (2014b). Intriguing properties of neural networks.

#### Paper Citation

#### in Harvard Style

Aghdam H., Heravi E. and Puig D. (2017). **Increasing the Stability of CNNs using a Denoising Layer Regularized by Local Lipschitz Constant in Road Understanding Problems** . In *Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017)* ISBN 978-989-758-226-4, pages 218-225. DOI: 10.5220/0006123602180225

#### in Bibtex Style

@conference{visapp17,

author={Hamed H. Aghdam and Elnaz J. Heravi and Domenec Puig},

title={Increasing the Stability of CNNs using a Denoising Layer Regularized by Local Lipschitz Constant in Road Understanding Problems},

booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017)},

year={2017},

pages={218-225},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006123602180225},

isbn={978-989-758-226-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017)

TI - Increasing the Stability of CNNs using a Denoising Layer Regularized by Local Lipschitz Constant in Road Understanding Problems

SN - 978-989-758-226-4

AU - Aghdam H.

AU - Heravi E.

AU - Puig D.

PY - 2017

SP - 218

EP - 225

DO - 10.5220/0006123602180225