Cellular Neural Networks Survey of Techniques and Applications Max Pflueger CS 152: Neural Networks December 12, 2006

Cellular Neural Networks Cells are given a spatial arrangement with connection between cells that are within a certain radius of each other All the cells within the radius of cell (i,j) are the neighborhood of cell (i,j) (a)neighborhood with r = 1 (b)r = 2

Templates Cell behavior is governed by the differential equation shown above A template specifies values for A, B, and z that will be used throughout the CNN to achieve some effect A, and B, are typically matrices of weights associated with the relative position of neighbors

The CNN Universal Machine CNN with the ability to change templates during operation Templates can be strung together, creating a programmable CNN –Instructions are similar to traditional microprocessor Turing complete

Application of CNNs and the CNN-UM Ocean modeling 10,000 fps image recognition Bionic eye Face and eye detection Template learning

Ocean Modeling Exact solutions to fluid mechanics problems require solving systems of partial differential equations Analytical solutions do not exist in most cases Numerical solutions are very computationally intensive

Ocean Modeling Nagy and Szolgay designed a simulation of a CNN-UM with modified cell architecture to model ocean currents Simulation was run on a mid- size FPGA and an Athlon XP for comparison –Athlon XP 1800+: 56 min –FPGA: 41 s A larger FPGA could do the calculation in ~1 sec

Template Learning It would be nice to use learning techniques to find useful templates for CNNs Gradient descent is promising, except that it is difficult to compute the gradient for a CNN

Template Learning Brendel, Roska, and Bartfai presented the equations for calculating the gradient of a CNN They also showed that these equations have the same neighborhood and connectivity as the original CNN Therefore, a CNN-UM can be used to compute the gradients for templates, making it possible to do fast on-line training with a CNN-UM

Face and Eye Detection Detecting faces in images is a classic problem in computer science Balya and Roska designed a CNN algorithm for recognizing and normalizing faces from color images. –Accurate –Runs in hardware, so it is very fast

References Chua, Leon O. and Tamás Roska. Cellular Neural Networks and Visual Computing. Cambridge: Cambridge University Press, Nagy, Z.; Szolgay, P., "Emulated digital CNN-UM implementation of a barotropic ocean model," Neural Networks, Proceedings IEEE International Joint Conference on, vol.4, no.pp vol.4, July 2004 Brendel, M., Roska, T., and Bártfai, G Gradient Computation of Continuous-Time Cellular Neural/Nonlinear Networks with Linear Templates via the CNN Universal Machine. Neural Process. Lett. 16, 2 (Oct. 2002), Balya, D. and Roska, T Face and Eye Detection by CNN Algorithms. J. VLSI Signal Process. Syst. 23, 2-3 (Nov. 1999),