, The single channel equivalent was trained with the same data but only for elevation set one. The tuples were of the form <slr_dem, lr_dem>, where slr_dem: the super-low resolution elevation data and lr_dem: the GT low-resolution elevation data

A. I. and M. Link, Fully Connected Layers in Convolutional Neural Networks: The Complete Guide, vol.9, 2019.

R. Alshehhi, P. Marpu, W. Woon, and M. M. Dalla, Simultaneous extraction of roads and buildings in remote sensing imagery with convolutional neural networks, ISPRS Journal of Photogrammetry and Remote Sensing, vol.130, pp.139-149, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01672877

M. Baranov, R. Olea, . Van-den, and G. Bogaart, Chasing Uptake: Super-Resolution Microscopy in Endocytosis and Phagocytosis, Trends in cell biology, 2019.

P. Benecki, M. Kawulok, D. Kostrzewa, and . Skonieczny, Evaluating super-resolution reconstruction of satellite images, Acta Astronautica, vol.153, pp.15-25, 2018.

Y. Bengio, A. Bordes, and X. Glorot, Deep sparse rectifier neural networks, Proceedings of the fourteenth international conference on artificial intelligence and statistics, pp.315-323, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00752497

F. Biegler-könig and F. Bärmann, A learning algorithm for multilayered neural networks based on linear least squares problems, Neural Networks, vol.6, issue.1, pp.127-131, 1993.

S. &. Borman, Super-resolution from image sequences-a review, pp.374-378, 1998.

J. Brownlee, Machine learning mastery, vol.9, 2019.

A. E. Bryson, A gradient method for optimizing multi-stage allocation processes, Proc. Harvard Univ. Symposium on digital computers and their applications, vol.72, 1961.

A. Bryson and W. Denham, A steepest-ascent method for solving optimum programming problems, Journal of Applied Mechanics, vol.29, issue.2, pp.247-257, 1962.

J. Canny, A computational approach to edge detection, IEEE Transactions, issue.6, pp.679-698, 1986.

W. Cho, Y. Jwa, H. Chang, and S. Lee, Pseudo-grid based building extraction using airborne LIDAR data, Int. Arch. Photogramm. Remote Sens, vol.35, pp.378-381, 2004.

D. Comanciu and P. Meer, Mean shift: a robust approach toward feature space analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.5, pp.603-619, 2002.

D. Datsenko and M. Elad, Example-based single document image super-resolution: a global MAP approach with outlier rejection. Multidimensional Systems and Signal Processing, vol.18, pp.103-121, 2007.

P. Dayan, G. Hinton, R. Neal, and R. Zemel, The helmholtz machine, Neural computation, vol.7, issue.5, pp.889-904, 1995.

C. Dong, Image Super-Resolution Using Deep Convolutional Networks, Retrieved from Image Super-Resolution Using Deep Convolutional Networks, 2019.

C. Dong, C. Loy, K. He, and X. Tang, Image super-resolution using deep convolutional networks, IEEE transactions on pattern analysis and machine intelligence, vol.38, pp.295-307, 2015.

S. E. Fahlman, An empirical study of learning speed in back-propagation networks, 1991.

A. Fog, 09 03). A History of Deep Learning. Retrieved from import, 2019.

C. Fraser, E. Baltsavias, and A. Gruen, Processing of Ikonos imagery for submetre 3D positioning and building extraction, Journal of Photogrammetry and Remote Sensing, vol.56, issue.3, pp.177-194, 2002.

K. Fukushima, Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position, In Biological cybernetics, vol.36, issue.4, pp.193-202, 1980.

N. Haala and C. Nrenner, Extraction of buildings and trees in urban environments, Isprs journal of photogrammetry and remote sensing, vol.54, pp.130-137, 1999.

G. Hinton, S. Osindero, and Y. Teh, A fast learning algorithm for deep belief nets, Neural computation, vol.18, issue.7, pp.1527-1554, 2006.

B. Huang, W. Wang, M. Bates, and X. Zhuang, Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, Science, issue.5864, pp.810-813, 2008.

H. &. Huang, Super-resolution method for face recognition using nonlinear mappings on coherent features, IEEE Transactions on Neural Networks, vol.22, issue.1, pp.121-130, 2010.

J. S. Judd, Neural network design and the complexity of learning, 1990.

H. J. Kelley, Gradient theory of optimal flight paths, Ars Journal, vol.30, issue.10, pp.947-954, 1960.

A. Khan, A. Sohail, U. Zahoora, and A. Qureshi, A survey of the recent architectures of deep convolutional neural networks, 2019.

T. Kim and J. Muller, Development of a graph-based approach for building detection, Image and Vision Computing, vol.17, issue.1, pp.3-14, 1999.

A. S. Krizhevsky, Imagenet classification with deep convolutional neural networks, Advances in neural information processing systems, pp.1097-1105, 2012.

A. Krizhevsky, I. Sutskever, and G. Hinton, Imagenet classification with deep convolutional neural networks, Advances in neural information processing systems, pp.1097-1105, 2012.

V. K?rková, Kolmogorov's theorem and multilayer neural networks, Neural networks, vol.5, issue.3, pp.501-506, 1992.

F. Lafarge, X. Descombes, J. Zerubia, and M. Pierot-deseilligny, Automatic building extraction from DEMs using an object approach and application to the 3D-city modeling, ISPRS Journal of photogrammetry and remote sensing, vol.63, pp.365-381, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00781689

F. Lang, 3D-city modeling with a digital one-eye stereo system, Proceedings of the XVIII ISPRS-Congress, 1996.

K. Lang, A. Waibel, and G. Hinton, A time-delay neural network architecture for isolated word recognition, Neural networks, vol.3, issue.1, pp.23-43, 1990.

Q. V. Le, A tutorial on deep learning part 2: Autoencoders, convolutional neural networks and recurrent neural networks, Google Brain, pp.1-20, 2015.

Y. Lecun, Une procedure d'apprentissage ponr reseau a seuil asymetrique, Proceedings of Cognitiva, vol.85, pp.599-604, 1985.

Y. Lecun, Y. Bengio, and G. Hinton, Deep learning, Nature, vol.521, issue.7553, p.436, 2015.

E. Lee, Y. Kim, N. Kim, and D. Kang, Deep into the brain: artificial intelligence in stroke imaging, Journal of stroke, vol.19, issue.3, p.277, 2017.

Y. Lee, J. Chen, C. Tseng, and S. Lai, Accurate and robust face recognition from RGB-D images with a deep learning approach, p.123, 2016.

S. Linnainmaa, The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors, Helsinski: Univ. Helsinki, pp.6-7, 1970.

D. Marr and E. Hildreth, Theory of edge detection, Proc. Roy.Soc. London B, vol.207, pp.187-217, 1980.

S. Mason and E. Balisavias, Automatic extraction of man-made objects from aerial and space images, pp.97-108, 1997.

H. Mass and G. Vosselman, Two algorithms for extracting building models from raw laser altimetry data. ISPRS Journal of photogrammetry and remote sensing, vol.54, pp.153-163, 1999.

. Matconvnet, MatConvNet: CNNs for MATLAB

J. Mcclelland, D. Rumelhart, &. Pdp-reserach, and . Group, Parallel distributed processing, vol.1, 1987.

C. Mineo, S. Pierce, and R. Summan, Novel algorithms for 3D surface point cloud boundary detection and edge reconstruction, Journal of Computational Design and Engineering, vol.6, issue.1, pp.81-91, 2019.

M. Minsky and S. Papert, Perceptrons: An introduction to computational geometry, 2017.

M. C. Mozer, A focused backpropagation algorithm for temporal. Backpropagation: Theory, architectures, and applications, p.137, 1995.

C. Nicholson, 09 05). A Beginner's Guide to Neural Networks and Deep Learning, 2019.

M. Nielsen, How the backpropagation algorithm works, 2019.

A. Ok, C. Senaras, and B. Yuksel, Automated detection of arbitrarily shaped buildings in complex environments from monocular VHR optical satellite imagery, Neural computation, vol.12, issue.10, pp.2385-2404, 2012.

M. Ortner, X. Descombes, and J. Zerubia, Building outline extraction from digital elevation models using marked point processes, In International Journal of Computer Vision, vol.72, issue.2, pp.107-132, 2007.

G. Panchai, A. Ganatra, P. Shah, and D. Panchal, Determination of over-learning and overfitting problem in back propagation neural network, International Journal on Soft Computing, vol.2, issue.2, pp.40-51, 2011.

M. Paparoditis, M. Cord, and J. Corquerez, Building Detection and Reconstruction fromMid-and High-Resolution Aerial Imagery, COMPUTER VISION AND IMAGE UNDERSTANDING, pp.122-142, 1998.

J. Peng and Y. Liu, The role of context and model in urban aerial image interpretation focusing on buildings, IEEE International Conference on Networking, Sensing and Control, vol.1, pp.1-12, 2004.

J. Prager, Extracting and labeling boundary segments in natural scenes, IEEE Transactions on Pattern Analysis and Machine Intelligence, pp.16-27, 1980.

J. M. Prager, Extracting and labeling boundary segments in natural scenes, IEEE Transactions on Pattern Analysis and Machine Intelligence, issue.1, pp.16-27, 1980.

P. Ramachandran, B. Zoph, and Q. Le, Searching for activation functions, 2017.

A. Ramiya, R. Nidamanuri, and R. Krishnan, Segmentation based building detection approach from LiDAR point cloud, The Egyptian Journal of Remote Sensing and Space Science, vol.20, issue.1, pp.71-77, 2017.

M. Riedmiller and I. Rprop, Rprop-description and implementation details, 1994.

F. &. Rottensteiner, A. g. images, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00535124

F. Rottensteiner and C. Briese, A new method for building extraction in urban areas from highresolution LIDAR data, International Archives of Photogrammetry Remote Sensing and Spatial Information Sciences, vol.34, p.295, 2002.

D. E. Rumelhart, Learning internal representations by error propagation (No. ICS-8506), 1985.

D. Rumelhart, G. Hinton, and R. Williams, Learning internal representations by error propagation (No. ICS-8506), 1985.

J. Schmidhuber, The neural heat exchanger, 1996.

J. Schmidhuber, Deep learning in neural networks, 2015.

D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Mathematics of computation, vol.24, issue.111, pp.647-656, 1970.

S. Sharma, Activation Functions in Neural Networks, 2019.

J. Shavlik and G. Towell, COMBINING EXPLANATION-BASED AND NEURAL LEARNING: AN ALGORITHM AND EMPmiCAL RESULTS, 1989.

K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, pp.1409-1556, 2014.

G. &. Sohn, G. Sohn, and I. Dowman, Data fusion of high-resolution satellite imagery and LiDAR data for automatic building extraction, ISPRS Journal of Photogrammetry and Remote Sensing, vol.62, pp.43-63, 2007.

M. Sonka, V. Hlavac, and R. Boyle, Image processing, analysis, and machine vision, Cengage Learning, 2014.

B. Speelpenning, Compiling fast partial derivatives of functions given by algorithms, 1980.

, UIUCDCS-R-80-1002)

J. Stoer, F. Bauer, and R. Bulirsch, Numerische Mathematik, vol.5, 1989.

T. A. Tang, L. Mhamdi, D. Mclernon, S. Zaidi, and M. Ghgho, Deep learning approach for network intrusion detection in software defined networking, International Conference on Wireless Networks and Mobile Communications, 2016.

M. Vakalopoulou, K. Karantzalos, N. Komodaki, and N. Paragios, Building detection in very high resolution multispectral data with deep learning features, IEEE International Geoscience and Remote Sensing Symposium (IGARSS), p.1873, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01264084

N. Vassilas, . Charou, . Petsa, and . Grammatikopoulos, Intelligent pattern recognition techniques for the development of multimodal representation of urban areas, 2013.

N. Vassilas, T. Tsenoglou, and D. Ghazanfarpour, Mean shift-based preprocessing methodology for improved 3D buildings reconstruction, WASET Int. J. Civ. Environ. Struct. Constr. Architectural Eng, vol.9, issue.5, pp.575-580, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01295400

N. Vassillas, . Charou, . Petsa, and . Grammatikopoulos, Intelligent pattern recognition techniques for the development of multimodal representation of urban areas, 2013.

S. Villena, J. Abad, R. Molina, and A. Katsaggelos, Estimation of high resolution images and registration parameters from low resolution observations. Iberoamerican Congress on Pattern Recognition, 2004.

Y. Wang, R. Armstrong, and P. Mostaghimmi, Enhancing resolution of digital rock images with Super Resolution Convolutional Neural Networks, Journal of Petroleum Science and Engineering, p.106261, 2019.

P. J. Werbos, Applications of advances in nonlinear sensitivity analysis. System modeling and optimization, pp.762-770, 1982.

A. West and D. Saad, Adaptive back-propagation in on-line learning of multilayer networks, Advances in Neural Information Processing Systems, pp.323-329, 1996.

J. Yang, J. Wright, T. Huang, and Y. Mia, Image super-resolution via sparse representation, IEEE transactions on image processing, vol.19, issue.11, pp.2861-2873, 2010.

J. Yuan, Learning building extraction in aerial scenes with convolutional networks, IEEE transactions on pattern analysis and machine intelligence, vol.40, pp.2793-2798, 2017.