In this paper we develop a method for the simultaneous restoration and halftoning of scanned fingerprint images using a novel non-linear dynamical system, called the "M-lattice system". This system is rooted in the reactiondiffusion model, first proposed by Turing in 1952 to explain the formation of animal patterns such as zebra stripes and leopard spots. A typical reaction-diffusion system is a set of heat equations, coupled by non-linear reaction terms. The new M-lattice system is closely related to the analog Hopfield network and the cellular neural network, but has more flexibility in how its variables interact. Furthermore, the state variables of an M-lattice system are guaranteed to be bounded, which is not the case with many reaction-diffusion systems. Due to this large-signal boundedness, the M-lattice system possesses desirable numerical properties that make it useful in engineering applications. Our new method for enhancing fingerprints explores the ability of the M-lattice ...

This research begins with reaction-diffusion, first proposed by Alan Turing in 1952 to account for morphogenesis -- the formation of hydranth tentacles, leopard spots, zebra stripes, etc. Reaction-diffusion systems have been researched primarily by biologists working on theories of natural pattern formation and by chemists modeling dynamics of oscillating reactions. The past few years have seen a new interest in reaction-diffusion spring up within the computer graphics and image processing communities. However, reaction-diffusion systems are generally unbounded, making them impractical for many applications. In this thesis we introduce a bounded and more flexible non-linear system, the "M-lattice", which preserves the natural pattern-formation properties of reaction-diffusion. On the theoretical front, we establish relationships between reaction-diffusion systems and paradigms in linear systems theory and certain types of artificial "neurally-inspired" systems. The M-lattice is closel...

In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

Abstract — Time encoding is a novel real-time asynchronous mechanism for encoding amplitude information into a time sequence. The analog bandlimited input is fed into a simple nonlinear neuron-like circuit that generates a strictly increasing time sequence based on which the signal can be reconstructed. The heart of the reconstruction is solving a system of illconditioned linear equations. This contribution shows that the equations can be manipulated so that the reconstruction becomes feasible using a Cellular Neural Network (CNN) with a banded system matrix. In particular, the system is first transformed into a well-conditioned smaller system; and then, the Lanczos process is used to lay it out into a set of even smaller systems characterized by a set of tridiagonal matrices. Each of these systems can directly be solved by CNNs, whereas the preprocessing (transformation and Lanczos algorithm) and simple postprocessing phases can be partly or fully implemented by using the digital capabilities of the CNN Universal Machine (CNN-UM). Each step of the proposed formulation is confirmed by numerical (digital) simulations 1. I.

CNN’s fast image processing technology helps us to run high-speed filtering tasks for image enhancement, recognition or segmentation. Texture analysis is a specific task, since the whole image is processed massively parallel while we have a limited number of texture-specific filtering and evaluation steps. Former results of simulations and recognition results of simple CNN chips show that the CNN is an appropriate tool for this image-processing task. Now we see what the gray-scale image processor CNN chip at its limited memory capability and data-handling/-processing accuracy can complete for multi-texture images. We demonstrate and compare some of our earlier CNNrelated texture analysis methods. Some methods to improve CNN configuration are proposed. 1 Introduction: CNN for texture recognition Texture recognition and segmentation ask for a massively parallel computation, based on a series of simple-like (mostly early-vision effects) image processing steps. These steps are usually robust filtering and statistical evaluation effects. It is just a good role for the CNN applications. In [7,12] we see how the kernel matrices of a feedback & feed-forward

We have found a formalism that lets us present generalizations of several stability theorems to Multi-Layer Cellular Neural/Non-linear Networks (MLCNN) formerly claimed for Single-Layer Cellular Neural/Non-linear Networks (CNN). The theorems were selected with special regard to usefulness in engineering applications. Hence, in contrast to many works considering stability on recurrent neural networks, the criteria of the new theorems have clear indications that are easy to verify directly on the template values. Proofs of six new theorems on 2-Layer CNNs (2LCNN) related to symmetric, τ -symmetric, non-symmetric, τ -non-symmetric, and sign-symmetric cases are given. Furthermore, a theorem with a proof on a MLCNN with arbitrary template size and arbitrary layer number in relation to the sign-symmetric theorem is given, along with a conjecture for the one-dimensional, two-layer, non-reciprocal case.

Abstract—An important property of cellular neural networks (CNN’s) is the binary output property, that, when the self-feedback is greater than one, the final activations are 61. This brief considers the generalization of this property to networks with sigmoidal output functions. It is shown that in this case the property cannot be stated without reference to the cross feedback, and conditions are found under which the property remains valid. I.