23-04-2011, 04:40 PM
Presented by
DEEPA RANI PATRO
techsem_ppt_191.ppt (Size: 464.5 KB / Downloads: 62)
CELLULAR NEURAL NETWORK
INTRODUCTION
Cellular Neural Networks (CNNs) is a paradigm of mostly locally connected networks of simple non-linear processors in discrete N-dimensional spaces.
Cells are multiple input-single output processors, all described by one or just some few parametric functionals which control the cell inter-connection strength.
Cell interconnect is local, meaning that all connections between cells are within a specified radius, where distance is measured topologically which allows also to obtain global processing.
Connections can also be time-delayed to allow for processing in the temporal domain.
This exhibits space-invariance property.
Dynamics are usually
• Continuous-Time CNN (CT-CNN) processors
Discrete-Time CNN (DT-CNN) processors
FEATURES OF CNN
The CNN can be defined as an M x N type array of identical cell arranged in a rectangular grid.Each cell is locally connec-ted to its 8 nearest surrounding neighbors.
Each cell is characterised by uij, vij and xij being the input,
The output and the state variable of the cell respectively.
The output is related to the state by the nonlinear equation:
vij = f(xij) =o.5(| xij + 1| - | xij - 1|)
The state transition of the cell C(i,j) is governed by the following differential equation:
The coefficients are known as cloning templates which are generally non-linear and time and space variant operators.
Structure of single CNN cell
The node voltage Vxij is called the state of the cell .
The node voltage Vuij is called the input of c(i,j) .
The node voltage Vyij is called the output.
DISCRETE TIME-CNN
A DT-CNN poses a regular grid of locally connected cells.
The DT-CNN is a clocked system; whose dynamics are described by a set of discrete equations.
A cell ‘C’ is identified by the coordinate of its position in the grid, i.e. row Ci and column Cj and communicates directly with all the neighbor cells belonging to the r-neighborhood. The character d represents any cell belonging to the neighborhood of cell C, including C itself.
Equation below depicts the dependencies of state of a cell C, denoted xc on input ud and the time-variant output yd at a discrete time k.
The functionality of DT-CNN cell is depicted by
CNN-UNIVERSAL MACHINE
It is the first spatiotemporal analogic array computer.
The two different operations are
• continuous-time, continuous valued spatio-temporal nonlinear array dynamics (2-d$3-darrays) local &
• global logic
• As both analog & logic operations are mixed and embedded in array computer, this type of computing is called analogic.
DEEPA RANI PATRO
techsem_ppt_191.ppt (Size: 464.5 KB / Downloads: 62)
CELLULAR NEURAL NETWORK
INTRODUCTION
Cellular Neural Networks (CNNs) is a paradigm of mostly locally connected networks of simple non-linear processors in discrete N-dimensional spaces.
Cells are multiple input-single output processors, all described by one or just some few parametric functionals which control the cell inter-connection strength.
Cell interconnect is local, meaning that all connections between cells are within a specified radius, where distance is measured topologically which allows also to obtain global processing.
Connections can also be time-delayed to allow for processing in the temporal domain.
This exhibits space-invariance property.
Dynamics are usually
• Continuous-Time CNN (CT-CNN) processors
Discrete-Time CNN (DT-CNN) processors
FEATURES OF CNN
The CNN can be defined as an M x N type array of identical cell arranged in a rectangular grid.Each cell is locally connec-ted to its 8 nearest surrounding neighbors.
Each cell is characterised by uij, vij and xij being the input,
The output and the state variable of the cell respectively.
The output is related to the state by the nonlinear equation:
vij = f(xij) =o.5(| xij + 1| - | xij - 1|)
The state transition of the cell C(i,j) is governed by the following differential equation:
The coefficients are known as cloning templates which are generally non-linear and time and space variant operators.
Structure of single CNN cell
The node voltage Vxij is called the state of the cell .
The node voltage Vuij is called the input of c(i,j) .
The node voltage Vyij is called the output.
DISCRETE TIME-CNN
A DT-CNN poses a regular grid of locally connected cells.
The DT-CNN is a clocked system; whose dynamics are described by a set of discrete equations.
A cell ‘C’ is identified by the coordinate of its position in the grid, i.e. row Ci and column Cj and communicates directly with all the neighbor cells belonging to the r-neighborhood. The character d represents any cell belonging to the neighborhood of cell C, including C itself.
Equation below depicts the dependencies of state of a cell C, denoted xc on input ud and the time-variant output yd at a discrete time k.
The functionality of DT-CNN cell is depicted by
CNN-UNIVERSAL MACHINE
It is the first spatiotemporal analogic array computer.
The two different operations are
• continuous-time, continuous valued spatio-temporal nonlinear array dynamics (2-d$3-darrays) local &
• global logic
• As both analog & logic operations are mixed and embedded in array computer, this type of computing is called analogic.