A Low-Power CMOS Implementation of a Cellular Neural Network for Connected Component Detection by ijcsiseditor


									                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 9, No. 6, June 2011

 A Low-Power CMOS Implementation of a Cellular
Neural Network for Connected Component Detection.
                                                                                                                     M. El-Sayed Ragab
        S. El-Din, A. K. Abol Seoud, and A. El-Fahar                                School of Electronics, Comm. and Computer Eng.
               Electrical Engineering Department                                                        E-JUST.
                    University of Alexandria                                                       Alexandria, Egypt.
                       Alexandria, Egypt.                                                    E-mail: m.ragab@ejust.edu.eg
             E-mail: eng_salah_alx@yahoo.com

                                                                         in the ( i , j ) position of a two-dimensional regular array of
ABSTRACT- In this paper, we describe an analog VISI
implementation of a Cellular Neural Network (CNN) for
                                                                         M  N cells. The r-neighborhood                                                   N i, j 
                                                                                                                                                                       of a typical
Connected Component Detector (CCD) applications. In this                 cell    C i, j  is defined as:
                                                                         N i, j    Ck , l , max  k  i , l  j   r (integer )
implementation, a novel compact network architecture based on
a low-power CMOS realization has been employed. The                          r
functionality of the proposed network has been verified through          An r =1 neighborhood of a cell within a cell array consists of
SPICE simulations for 1-D vectors of arbitrary black-and-white
                                                                         all those cells shown shaded in Fig.1(c).

Keywords: Cellular Neural Network, Low-power CMOS, Connected
Component Detector.

                     I. INTRODUCTION
   The connected component detector (CCD) (alternatively
called connected component analysis, blob extraction, blob
discovery, region labeling, or region extraction) is an
algorithmic application of graph theory, where subsets of
connected components are uniquely labeled based on a given                                                                                (a)
heuristic. The CCD is used in computer vision to detect
connected regions in binary digital images, although color
images and data with higher-dimensionality can also be
processed [1, 2]. When integrated into an image recognition
system or human-computer interaction interface, the CCD can
operate on a variety of information [3, 4]. Blob extraction is
generally performed on the resulting binary image from a
threshold step. Blobs may be counted, filtered, and tracked.             (b)                                    (c)
Blob extraction is related to but distinct from blob detection           Figure 1. The cell circuit model and its neighborhood in a cell array. (a) The
[5]. In this paper, starting from the function of Connected              cell circuit model (b) The characteristics of the single nonlinear element of the
Component Detection [6], and through the proposed low-                   cell (a voltage-controlled current source). (c) An r =1 neighborhood in a part
                                                                         of a cell array.
power CNN cell circuit with opposite-sign templates [7, 8], we
can realize a complete pattern for VLSI CCD. By using a                  The dynamical system equations describing the Chua-Yang
bipolar pattern [9], we can represent the transient behavior.            CNN model shown in Fig. 1, are expressed as:
Performance of the transient behavior is evaluated using                 1) State equation:
PSPICE simulation.
                                                                             dV                        1
                                                                                                                          (t )            
                                                                         C                             V              xij
                                                                                                                                                         A(i, j; k , l ) V ykl (t )
        II. CONNECTED COMPONENT DETECTION                                          dt                R     x                         C ( k ,l )
                                                                                                                                            N r (i , j )                            (2)
For VLSI implementation of CNNs, it is usual to consider                                             
                                                                                                  C ( k ,l )
                                                                                                                               B(i, j; k , l )V ukl (t )  I
simplified versions of the Chua-Yang model in order to reduce                                                   N r (i , j )
circuit complexity [10]. A cellular system was defined as a              where                      1  i  M;                              1  j  N.
structured collection of identical elements called cells.
Consider the analog processing cell circuit, henceforth called a         2) Output equation:
cell, as shown in Fig.1(a), with only one nonlinear element
whose characteristics is shown in Fig.1(b). This cell is located         V         (t )  0.5 
                                                                                                          V                (t )  1           V         (t )  1 
                                                                                                                                                                                   (3)
                                                                                                                    xij                            xij            

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                                                                                                                                   ISSN 1947-5500
                                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                 Vol. 9, No. 6, June 2011

3) Constraint conditions:
                                                                                                   initial pattern
        V         (0)  1;               and                V          1.
            xij                                                 uij

where u, x and y refer to the input, state, and output,                                            final pattern
respectively.                                                                                                                                      (a)
It is noted that the network defined by the above set of
equations is completely stable if the self-feedback coefficient
 A (i, j )  1    and      the       symmetry       conditions                                 nitial pattern
 A (i, j; k , l )  A (k , l; i, j ) are satisfied [10]. However, from
an applications point of view, nonsymmetrical templates are                                    final pattern
also of interest and the associated stability properties have to                                                                             (b)
be considered. An interesting class of CNN with opposite-sign                                                   Figure 2. The initial states and final states of a CCD

                                                                                                               1, 1                                1, 1
templates is defined by the A-template values satisfying the                                                                12                                 25
following structures and sign conditions:                                                            (a) for                     cell chain.(b) for                 cell chain.

     0 0 0 
 A  s p  s
                                               (4)                                               III. Low-Power CMOS Implementation of a CNN cell.
                                                                                               In this section, a practical low power VLSI implementation of
     0 0 0 
                                                                                             a simplified version of the CNN model is presented, together
where p  1 and s  0 . Moreover, because the stability of                                     with simulation results. Fig. 3 shows a block diagram for the
                                                                                               CNN cell model.
the network is controlled by matrix A, the part of state
equation (2), given by                 
                                B (i, j; k , l ) ukl(t )  I , is
                               c ( k ,l )
                                             N r (i , j )
not of interest and can be taken equal to zero. In such a type of
networks, three important sub-classes have been investigated
depending on the relationship between the coefficients p and s
i) If s > p-1, the network will have no stable equilibrium
ii) If s < (p-1)/2, the network is completely stable.
iii) If s is in the interval ((p-1)/2,(p-1)), the complete stability
is strongly conjectured because in some saturation regions, in
which   V   xij
                    1, there exists no equilibrium states.                                                            Figure 3. Block diagram of CNN cell.

The network sub-class (iii) has led to an interesting application                              It includes an integrator that has as inputs weighted
in digital image processing, the connected component                                           contributions of the outputs and inputs of the set of m cells in a
detection (CCD), in which the dynamics of a cell chain                                         neighborhood of cell c. Vxij is the state of cell Cij, with an
consisting of black          (V xi  1) and white (V xi   1)                                 initial condition Vxij(0), RxC conforms the integration time
                                                                                               constant of the system. The cell output is Vyij (t) = f (Vxij (t)),
pixels, with an initial pattern, will converge to a final pattern                              where f can be any convenient non-linear function. The block
having the CCD properties. To be specific, we consider the                                     A can be implemented using a set of four quadrant multipliers
following two basic combinations in the cell chain:                                            whose inputs are the outputs of the cells within the assumed
  the combination                 tends toward               ; and                             neighborhood and the template A values. Similarly, block B
  the combination                 tends toward             .                                   can be implemented using a set of four quadrant multipliers
In fact, the natural results of this dynamical behavior have led                               whose inputs are the inputs of the cells within the assumed
to the functionality of the CCD, as follows                                                    neighborhood and the template B values. The outputs of
Each one-colored connected region of cells will be shifted to
the right and finally compressed into a single cell with this
                                                                                               blocks A and B are (in the current form)            xy
                                                                                                                                                       and xu , I             I
same color. Then these compressed cells will line up at the                                    respectively. Those currents are summed with the bias current
right hand end of the cell chain. Finally the one –colored                                     I of the cell and then integrated in the RxC circuit, to result in
leftmost region will expand to the alternating-colored cells at                                the cell state voltage Vxij. The output voltage of the cell Vyij is
the right.                                                                                     obtained through the limiting transfer function f(Vxij).
Fig. 2 shows two examples of two CCD operations in two                                         Alternatively, the nonlinear transfer function f(Vxij) can be
different cell chain    1,1 , and 1,1
                                       12                               25
                                                                                               incorporated in the multiplier circuits themselves, resulting in
                                                                                               a small area CNN cell. This can be realized using low-power

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                                                                                                                                      ISSN 1947-5500
                                                                                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                      Vol. 9, No. 6, June 2011

CMOS four quadrant multipliers operating in weak inversion
regime. The basic difference with respect to the original Chua-
Yang model is that a sigmoid-like function, instead of the
conventional piecewise-linear function, is used to generate the
cell output.
The proposed circuit of a programmable low-power CMOS
four quadrant multiplier and its circuit symbol are shown in
Fig. 4 [11]. It is composed of registers which store the weight
values, a linear DAC, and a tranconductance amplifier. The
cell has five bits. Each bit is controlled by a pass transistor.
Assuming weak inversion operation for all MOS devices in the
multiplier circuit, it can be shown that the output current Io is
expressed as:
                  I b tanh(k (
                                V 1  V 2 )) if                                                                         (5)
                                   2                               V   3
                                                                            is high and V 4 is low
I o  I1  I 2                    V 2
                  tanh(k (V 1                                                                                                                 Figure 5. The transfer function of the proposed circuit
                  Ib
                                   2
                                          )) if                     V   3
                                                                            is low and V 4 is high

where k  1                     , with n is a slope factor ( in practice it lies
                  nU        T
                                                                                                                                    Fig. 6 shows a complete implementation of a CNN cell using
between 1 and 2 and is close to 1 for high values of gate                                                                           the proposed multiplier circuit. The sets of multipliers in the
voltage), and UT is the thermal voltage whose value is 26mV                                                                         lower and upper parts of Fig.3 represent the second and third
at room temperature. Current switching logic controlled by V 3                                                                      terms in the left hand side of equation (2), respectively. Each
and V4 enables the output to change sign. It is noted that the                                                                      multiplier in the lower set accepts one of the cells' outputs
output current is linearly proportional to one of the multiplier                                                                    within the given neighborhood, as one input, and the
inputs, Ib, and varies nonlinearly with the other input, (V1-V2).                                                                   corresponding template value A () as the other input. The A-
The transfer characteristic of the multiplier circuit is shown in                                                                   template values are determined by the programmable tail
Fig. 5                                                                                                                              current sources Ib,y and their signs are controlled by the
                                 Vdd       Vdd
                                                                                                                                    multiplier control inputs V3's and V4's. On the other hand, each
                                                                                              I1       Io
                                                                                                                                    multiplier in the upper set accepts one of the cell's inputs
                  Vdd               Vdd
                                                                                                                                    within the given neighborhood as one input, and the
                                                                                                                                    corresponding template value B () as the other input. Also,
                                                          V3                                                V3
                                                                                                                                    those B- template values are determined by the programmable
   Va                                                                               V4
                                                                                                                                    tail current source, Ib,u and their signs are controlled by the
                                                                                                                                    corresponding multiplier control inputs V3's and V4's. The
                                                         V1                                                V2                      output currents of the two multiplier sets are summed together
                                                                                        Ib                                          and applied to the RxC current integrator. The resistor Rx is
                                B0              B1               B2                B3             B4
                                                                                                                                    implemented using the diode-connected transistor Mr.
                                I0         I0               I1                I2             I3                  I4
                                                                                                                                                                            V3,u1      V4,u1
                                                                                                                                                             Vu1                        Io,u1


                                                                                                                                             Cells’ inputs                  V3,u2      V4,u2
                                                                                                                                                u(Nr)                Vcom
                                                          (a)                                                                                                      Vcom                              Vdd
                                                     V3          V4
                                                                                                                                                             Vun                                               Vx

                                                                                                                                                                                                Mr         C
                       V1                                                      Io                                                                                           V3,y2      V4,y2
                                                                                                                                                             Vy2                        Io,y2
                       V2                                                                                                                   Cells’ outputs
                                                                                                                                                y(Nr)              Vcom
                                                               Ib                                                                                                                   Ib,y2

                                                                                                                                                                            V3,y1      V4,y1
                                                                                                                                                             Vy1                        Io,y1

   Figure 4. (a) circuit diagram of programmable low-power CMOS four
               quadrant multiplier and (b) its circuit symbol.                                                                                               Figure 6. Complete CNN cell.

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             IV. SIMULATION EXAMPLE:                                                                                   The network of Fig.8 has been employed to function as a
Fig. 7 shows three adjacent cells
CNN with opposite-sign templates.
                                  i 1
                                       , i,                         C C C                  i 1
                                                                                                  in a 1-D
                                                                                                                       CCD for the       1, 1          12
                                                                                                                                                               cell chain of Fig. 2(a). The

                                                                                                                       template        a , a and a values are taken as [6,12]:
                                                                                                                                        i 1   i               i 1

                                                                                                                        a  i 1
                                                                                                                                   ,   a , a    1 2 1 
                                                                                                                                         i         i 1
                                                                                                                       which correspond to the stability criterion (iii) discussed in
                                                                                                                       section 2. The initial state condition of each cell is set by
                                                                                                                       adjusting the initial voltage of the capacitor at the cell output.

    Figure 7. Three adjacent cells in a 1-D CNN with opposite-sign template.

The cells" inputs and their bias terms are set to zero. The state
equations of the cell C can be described by:

x  x  s f (x
   i        i                        i 1
                                          )  p f ( xi )  s f ( xi 1)                                    (5)
Fig 8. shows a complete implementation of 1-D opposite-sign
template CNN of 12 cells. Note that in such an architecture the
cell's state voltage                         V    xi1
                                                         ,V xi , and          V    xi 1
                                                                                            are directly
fedback               to               their             cells       and           the            nonlinear
functions         f ( xi 1), f ( xi ), and                       f ( xi 1)            are        already
embedded in the multipliers' transfer characteristics. As
previously stated, this would guarantee compact CNN design
architectures. The state equations resulting from such an
implementation are then expressed as:
  d V xi   1                                           (6)
C                       V   xi
                                    ai 1 I bo f (V xi 1)  ai I bo f (V xi )  ai 1 I bo f (V xi 1)
        dt        R   x

where,       R    x
                      is the resistance of the diode-connected transistor,
                                     KV x
 f (V x)  tanh (      ) , and i1 ,                         a a , and a  i                i 1
the template-A values of the network.
                                                                                                                          Figure 9. Transient Behavior of the         1,1  12
                                                                                                                                                                                   cell chain of Fig. 2 (a).

                                                                                                                       Note that a "High" voltage corresponds to a "black" pixel and
                                                                                                                       a "Low" voltage corresponds to a "white" pixel. Fig.9 shows
                                                                                                                       the transient response of the cells' states obtained from SPICE
                                                                                                                       simulations. It is clear that the steady state behavior of the
                                                                                                                       cells conforms the expected CCD behavior of the example
                                                                                                                       shown in Fig. 2(a).

                                                                                                                                               IV. Conclusion
                                                                                                                       Cellular neural networks (CNN's) with opposite-sign templates
                                                                                                                       have been successfully applied in connected component
                                                                                                                       detection (CCD). A novel circuit architecture based on low-
                                                                                                                       power CMOS four-quadrant multipliers has been employed to
                                                                                                                       realize such a type of networks. The proposed architecture has
                                                                                                                       been applied to the case of 1-D CNN functioning as a CCD.
                                                                                                                       The CCD functionality of the network has been verified
                                                                                                                       through SPICE simulations.

    Figure 8. Complete circuit of 12 cells 1-D opposite-sign template CNN.

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