Present Research Activities
- Circuit Models of Nano-Devices
- Global Dynamics of Arrays of Nonlinear Circuits
- Nonlinear Dynamics in Networks with Complex Topologies
- Approximation of Networks of Bio-Inspired Neurons
and Their Emulation Via Parallel Circuits
Past Research Activities
- CNN Application to Real Time Processing of Ophthalmic
Images as Medical Diagnosis Support - Nonlinear Dynamic Networks: Analysis and Applications
- Cellular Neural Network Models, Based on Nolinear
Partial Differential Equations, for Real Time Image Processing
Present Research Activities
Circuit Models of Nano-Devices
Microelectronics and the newly emerging nanotechnology enable engineers to build systems with macroscopic input and output access, and at the same time composed of microscale and nanoscale components as well. It has been shown that when elementary components are contacted with macroscopic metal electrodes, traditional linear and nonlinear circuits can be used to model the behaviour of the whole nanoscale device. The validity of classical circuit models has been extended to systems composed of classically coupled quantum subsystems, showing the potential of equivalent circuits for modeling and design purposes
June 2, 2008
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Global Dynamics of Arrays of Nonlinear Circuits
The analysis of the global dynamics of arrays of nonlinear circuits is a difficult task because they are described by a large set of nonlinear differential equations. Furthermore, it is essential for developing rigorous design algorithms, both in case of stationary behaviour (classical image processing applications) and in case of non-stationary behaviour (topographic wave computing). We obtained some significant contributions on: (a) the study of the stability of the dynamic behavior (including chaos and bifurcations) and of the applications of cellular neural/nonlinear networks, with particular reference to image processing; (b) the study of the dynamics of nonlinear circuits and oscillators and of nonlinear dynamic arrays, through time-domain and frequency domain techniques (harmonic-balance) methods.
June 2, 2008
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Nonlinear Dynamics in Networks with Complex Topologies
Networks consist of nodes, interconnected by a mesh of links. Their macroscopic behaviour is determined by both the dynamical rules governing the nodes and the flow occurring along the links. Real networks of interacting dynamical systems – be they neurons, power stations, lasers, or computers – are complex. Complexity may come from different sources: topological structure, network evolution, connection and node diversity, and/or dynamical evolution. Most networks offer support for various dynamical processes. In this research we propose to study dynamical processes in non-trivial complex network topologies, developing theoretical and computational methods for modeling dynamics of networks and flows on networks.
June 2, 2008
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Approximation of Networks of Bio-Inspired Neurons and Their Emulation Via Parallel Circuits
The simulation of large networks of dynamical systems is one of the most ambitious challenges taken up by the international scientific community. This research project concerns approximation/identification and synthesis of complex systems made up of a large amount of elementary units exhibiting a similar (not necessarily identical) structure. Such elementary units mutually interact and are modeled by means of ordinary differential equations (ODE).
Of course, the dynamical features of the elementary units influence the collective behaviour. However, the whole network is intrinsically complex, meaning that its behaviour is characterized by emerging collective phenomena. Generally speaking, such phenomena cannot be ascribed uniquely to the properties of each elementary unit, but are a consequence of their interactions.
The focus of this research program is on neuron networks and on their emulation by means of both computer simulations and circuits.
June 2, 2008
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Past Research Activity
CNN Application to Real Time Processing of Ophthalmic Images as Medical Diagnosis Support
Medical images provided by most practical devices (i.e. photo, video and IR images) contain a great deal of information that is not accessible to a human observer; moreover they are often degraded by environmental factors, copying, etc.
For this reason image analysis often requires a preliminary step (pre-processing). This step consists in transforming the original picture/image into a smooth version of it that contains the most significant information. The main parameter of such a
transformation is the “scale”: it measures the size of the neighbourhoods that are exploited for estimating the brightness of a picture at a given point. In image processing theory this operation is often called “multiscale analysis” and is considered a necessary step for all the tasks that require an understanding of a picture, as for example, to identify some objects or particular configurations in a picture.
Due to these considerations, the “multiscale analysis” is a necessary preliminary step for the realization of the proposed research program, whose main objective is the extraction of information from ophthalmic images as medical diagnosis support.
The main operations requested to a “multiscale analysis” can be briefly synthesized as follows: a) contrast enhancement, which improves the image quality for the viewer by modifying the grey scale; b) restoration techniques, that include removal of noise and blur; c) segmentation, which is basically a process of pixel classification into classes, including dark and light or more commonly edges and non-edges.
In the recent years it has been found that “multiscale” image processing can be afforded through a Partial Differential Equation (PDE) based approach [1,2]. In particular, it was shown that the techniques originating in the field of computational fluid dynamics
(and the related PDE models) have an important and direct relevance to image and video processing.
As an example of the effectiveness of this approach, we mention the non-linear PDEs exploited for modelling discontinuities in fluid dynamics; they were found to be suitable for developing methods, able to detect discontinuity (i.e. edges) in images.
The PDE based techniques and the related algorithms for “multiscale analysis” are based on the following fundamental steps: a) the image processing problem is formulated as a variational problem; b) such a problem is faced by writing down the Euler-Lagrange equations and by interpreting them as non-linear PDEs; c) if the PDEs satisfy some key properties (that were widely investigated by the researchers [1]), then they describe a dynamical system, that converges to an equilibrium point, representing the solution of the variational problem and, hence, of the image processing task.
PDE based approaches appear to be superior with respect conventional image processing techniques for a number of reasons: a) they provide a systematic theory and an effective
mathematical language for image processing; b) they do not act as a black box, but allow one to see in which way the original image is modified by the algorithm and therefore to change the algorithm parameters.
As already mentioned, it is important to know which are the properties, that should be satisfied by a non-linear PDE in order to be suitable for “multiscale analysis”. This question was answered by Pierre-Louis Lions (Fields medal in mathematics) and his collaborators in [1]: there it was proved that PDEs for “multiscale analysis” must satisfy a list of formal requirements (properties).
Simultaneously with the mathematical studies on the application of non-linear PDEs to image processing, in the electrical engineering community a new paradigm of neural network, called Cellular Neural Network (CNN) [3] was introduced and shown to be able to solve several complex computational problems. Cellular neural networks (CNNs) are analog dynamic processors,
described as a 2-dimensional array of non-linear dynamical systems (called cells), that are locally interconnected.
From a mathematical point of view, a CNN is described by a large set of locally coupled non-linear differential equations, that may exhibit a rich variety of attractors: stable equilibrium points, limit cycles, non-periodic and even chaotic attractors.
The relationship between PDEs and CNNs can be stated as follows; the space discretization of a PDE yields a system of ordinary differential equations (ODEs), that can be seen as the description of a suitable CNN, i.e. an array of analog circuits, with local interconnections. Therefore to each PDE corresponds a system of ODEs and therefore a possible CNN. On the other hand it is easily seen that there exist CNNs, (and therefore ODE systems) that do not correspond to any PDEs.
The research activity has been developed in the framework of a national project, devoted to the processing of ophthalmic images as medical diagnosis support and has focused on two main objectives: 1) to identify which classes of CNNs (derived from PDE with time-invariant parameters) are suitable for image pre-processing, through “multiscale analysis” of
static ophthalmic images of the eyeball; 2) to identify which classes of CNNs (possibly derived from PDE with time-variant parameters) are suitable for image pre-processing, through “multiscale analysis” of video-image sequences, in order to evaluate the reagent diffusion inside retinal blood-vessels.
References
[1] J. Wieckert, “A review of nonlinear diffusion filtering”, Lecture Notes in Computer Science, vol. 1252, Springer, Berlin, pp. 3-28, 1997.
[2] L. Alvarez, F. Guichard, P. L. Lions, J. M. Morel, “Axioms and Fundamentalequations of image processing”, Arch. Rational Mech. Anal. 123, pp. 199-257, 1993.
[3] L. O. Chua, and T. Roska, “The CNN paradigm”, IEEE Transactions on Circuits and Systems: Part I, vol. 40, no. 3, pp. 147-156, March 1993.
June 5, 2008
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Nonlinear Dynamic Networks: Analysis and Applications
This research project was devoted to the analysis and applications of networks composed of nonlinear units (cells), interconnected in various ways. We assumed each cell to be described by a low order differential model: either a system of ordinary (possibly functional) differential equations or a system of differential inclusions. The main objectives of the research project were the development of innovative methodologies and techniques for analyzing and classifying the global dynamic behaviors of nonlinear dynamic networks. The obtained results covered two classes of applications: biological system modeling (with particular emphasis on eco-system and neuroscience modeling) and bio-inspired neuromorphic information and image processing.
June 2, 2008
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Cellular Neural Network Models, Based on Nolinear Partial Differential Equations, for Real Time Image Processing
Recent studies have found that “multiscale“ image processing can be afforded through a Partial Differential Equation (PDE) based approach. On the other hand, in the electrical engineering community a new paradigm of neural network, called Cellular Neural Network (CNN) was introduced and shown to be able to solve several complex computational problems. The main objective of the research program was to identify which classes of CNNs are suitable for real time image preprocessing, through “multiscale analysis“ and to study the circuit model of such CNNs. The CNNs, matching the characteristic of being realizable as a VLSI circuits, have been simulated on a digital accelerator based on DSPsd. Recent studies have found that “multiscale“ image processing can be afforded through a Partial Differential Equation (PDE) based approach. On the other hand, in the electrical engineering community a new paradigm of neural network, called Cellular Neural Network (CNN) was introduced and shown to be able to solve several complex computational problems. The main objective of the research program was to identify which classes of CNNs are suitable for real time image preprocessing, through “multiscale analysis” and to study the circuit model of such CNNs. The CNNs, matching the characteristic of being realizable as a VLSI circuits, have been simulated on a digital accelerator based on DSPs.
June 2, 2008
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