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(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 r of a typical Connected Component Detector (CCD) applications. In this cell C i, j is defined as: N i, j Ck , 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 (1) 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). pixels. 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 ) xij 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) FUNCTIONALITY 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) yij xij xij 148 http://sites.google.com/site/ijcsis/ 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 ) V 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 [6]: i) If s > p-1, the network will have no stable equilibrium states. 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 149 http://sites.google.com/site/ijcsis/ 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 I2 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 B Ib and applied to the RxC current integrator. The resistor Rx is Vdd B0 B1 B2 B3 B4 implemented using the diode-connected transistor Mr. Vgg I0 I0 I1 I2 I3 I4 V3,u1 V4,u1 Vcom Vu1 Io,u1 Vcom Ib,u1 Cells’ inputs V3,u2 V4,u2 u(Nr) Vcom Io,u2 Vu2 (a) Vcom Vdd Ib,u2 I V3 V4 Vun Vx Vyn Mr C V1 Io V3,y2 V4,y2 Vcom Vy2 Io,y2 V2 Cells’ outputs y(Nr) Vcom Ib Ib,y2 V3,y1 V4,y1 Vcom Vy1 Io,y1 Vcom Ib,y1 (b) Figure 4. (a) circuit diagram of programmable low-power CMOS four quadrant multiplier and (b) its circuit symbol. Figure 6. Complete CNN cell. 150 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 6, June 2011 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 (7) 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: i 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 xi1 ,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 i1 , a a , and a i i 1 represent 2 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). 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