Abstract. We present differentiable implementations of several common image processing algorithms: Canny edge detector, Niblack thresholding and Harris corner detector. The implementations are presented in the form of fully convolutional networks and explicitly arranged exactly to the original algorithms. Usage of such form of algorithms allows to tune their parameters with gradient descend. As a part of these implementations we introduce a generalization of pooling algorithm, which allows to use arbitrary structure element. We also analyze the given architectures and show the connections with contemporary approaches. Keywords: canny edge detector, Harris corner detector, Niblack thresholding, fully convolutional network. PP. 108116. DOI: 10.14357/20790279180512 References 1. S. Xie and Z. Tu. Holisticallynested edge detection, ICCV, 2015. 2. I. Kokkinos. Pushing the boundaries of boundary detection using deep learning, ICLR, 2016. 3. K.K. Maninis, J. PontTuset, P. Arbeláez, and L. Van Gool. Convolutional Oriented Boundaries, ECCV, 2016. 4. K.K. Maninis, J. PontTuset, P. Arbeláez, and L. Van Gool. Convolutional Oriented Boundaries: From Image Segmentation to HighLevel Tasks, TPAMI, 2018. 5. I. Pratikakis, K. Zagoris, G. Barlas, B. Gatos. ICDAR2017 Competition on Document Image Binarization (DIBCO 2017), ICDAR, 2017. 6. K. Lenc, A. Vedaldi. Learning Covariant Feature Detectors, GMLD workshop at ECCV, 2016. 7. M. Jaderberg, K. Simonyan, A. Zisserman, K. Kavukcuoglu. Spatial Transformer Networks, NIPS, 2015. 8. A. Sheshkus, A. Ingacheva, D.P. Nikolaev, Vanishing Points Detection Using Combination of Fast Hough Transform and Deep Learning, Proc. SPIE 10696, Tenth International Conference on Machine Vision (ICMV 2017), 106960H, pp. 18, 2018, DOI: 10.1117/12.2310170. 9. Audet C., Dennis J.E. Mesh Adaptive Direct Search Algorithms for Constrained Optimization, SIAM J. Optim. 17, 2006. p.188–217. 10. M. Aliev, D. Nikolaev, A. Saraev. Construction of fast computational schemes for tuning the Niblack binarization algorithm, [Postroenie bystrykh vychislitelnykh skhem nastroyki algoritma binarizatsii Nibleka], in Russian, Proceedings of the ISA RAS, 2014. 11. J. Long, E. Shelhamer, T. Darrell. Fully Convolutional Networks for Semantic Segmentation, CVPR, 2015. 12. W. Niblack. An Introduction to Digital Image Processing, Englewood Cliffs, PrenticeHall, 1986 13. C. Harris, M. Stephens. A Combined Corner and Edge Detector, Alvey Vision Conference, 15, 1988. 14. R. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, H. S. Seung. Digital selection and analogue amplification coexist in a cortexinspired silicon circuit, Nature, 405, pp. 947–951, 2000. 15. J. Serra. Image Analysis and Mathematical Morphology, ISBN 0126372403, 1982. 16. Canny, J. A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8(6):679–698, 1986. 17. D. Martin, C. Fowlkes, D. Tal, J. Malik. A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics, Proc. 8th ICCV, 2001. 18. G.E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, R.R. Salakhutdinov. Improving neural networks by preventing coadaptation of feature detectors, arXiv:1207.0580, 2012. 19. S. Ioffe, C. Szegedy. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift, ICML, 2015. 20. K. Simonyan, A. Zisserman. Very Deep Convolutional Networks for LargeScale Image Recognition, ICLR, 2015.
