Electronic Implementation of Oscillators for Visual
Algorithms
Jordi Cosp, Jordi Madrenas
Department of Electronics Engineering, Universitat Politecnica de Catalunya, Spain
e-mail: jcosp@eel.upc.es
Abstract
In this paper we present an electronic oscillator model that can be used to
implement VLSI oscillatory networks for image segmentation. Oscillators can be
easily coupled to their nearest neighbours in a network. Although coupling being
local, we demonstrate that synchonization is global to all the network.
1 Introduction
Image segmentation is a key stage in image processing systems. Most efforts on this
topic have focused on implementing complex algorithms on standard digital computers
that require large electric power and area compared to dedicated analog VLSI systems
as neuromorphic implementations (Mead, 1975). Portable applications are benefited of
these characteristics.
However, few efforts have been done to implement segmentation algorithms on
analog microelectronics (Cosp and Madrenas, 2003) (Ando et al., 2001) (Andreou
and T.G.Edwards, 1994). A key element of some of these algorithms is oscillators.
However, oscillators used in the most common algorithms are oriented to a computer
implementation and they are difficult to implement using a VLSI technique.
In this paper we show an oscillator model that can be easily implemented using
analog electronics, it power consumption is low and it keeps synchronization properties
to segment images when implemented in a segmentation network (Wang and Terman,
1997)
2 Oscillator model
Non-linear electronic oscillators can be easily implemented by looping an hysteresis
comparator and an integrator. Both blocks consist of two or more current sources that
charge and discharge a capacitor. Thus, capacitor voltage is given by the well known
voltage-current relation:
(1)
where
is the capacitor voltage, the charge current, the discharge current and
the capacitance.
The hysteresis comparator consists of a subtraction of an input current to a variable
refence current that is responsible of the hysteresis. Then, the result is integrated to
the output node parasitic capacitance. As this output voltage is limited by the power
source and integration is relatively fast, the output node swings from ground to power
supply. When the output is high, the reference current (charge current) becomes high
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and the input current (discharge current) has to increase to lower the output voltage.
On the other hand, when the output is low, the reference current becomes low and the
input current has to decrease to increase the output voltage.
The integrator consists of a low and constant discharge current and a variable charge
current. These currents are integrated to a large capacitor, thus integrator time constant
is larger than comparator time constant. When comparator output is lower than a certain integrator threshold ( ), charge current
is null and the capacitor is discharged.
When comparator output is higher than , charge current is positive and larger than
discharge current, thus the integrator is charged. Finally, integrator voltage is converted
to current by a non-linear element (a MOS transistor) for Fast Threshold Modulation
(Somers and Kopell, 1993) when coupled to other oscillators. The output current of
the non-linear element is the input current to the comparator.
This oscillator can be easily coupled to other oscillators by adding current sources
to the hysteresis comparator. A charge current that is not null when the coupling oscillator output is high, synchronizes both oscillators. On the other hand, if a discharge
current is used, it desynchronizes oscillators and Selective Gating is obtained (Wang
and Terman, 1997) to segment images.
3 Simulations
The cell presented above has been simulated using adimensional parameters and results
are shown in Figure 1. Hysteresis comparator output – variable– shifts from 0 to 1 and
the integrator output – variable– moves from a hysteresis comparator high-threshold
to a low-threshold. Notice that these thresholds do not limit integrator range. When
these thresholds are reached, comparator
reference currents change but the output of
the comparator has to reach to change slow integrator charging current, thus,
integrator voltage output.
4 Experimental results
A network of 256 coupled oscillators have been implemented using a comercial CMOS
technology and experimentally tested (Cosp and Madrenas, 2003). In this section we
show some experimental results that demonstrate the oscillator capability to synchronize with other coupled oscillators.
In figure 2 we show the synchronization of two coupled oscillators as seen in the
oscilloscope. Oscillators start in a desynchronous state, then, coupling is established at
time . In less than one oscillation cycle both oscillators reach synchrony and it is
maintained.
Experiments show that chains of locally coupled oscillators also synchronize. Global
synchronization can be achieved with local couplings. Each oscillator is coupled to its
two nearest neighbours in the chain. Directly coupled oscillators synchronize and this
synchrony spreads throughout the chain, synchronizing all oscillators. This behaviour
has been experimentally tested with an logic analyzer and its result is depicted
in 3.
First, two chains coupled oscillators oscillate synchronously. Then, at time indicated
2
(a)
(b)
Figure 1: (a) Temporal evolution of oscillator. variable is the output of the hysteresis
comparator and variable is the slow integrator voltage. Thresholds of the hysteresis
comparator are depicted with dashed lines. (b) Oscillator orbit. Comparator thresholds are depicted with vertical dashed lines. Integrator charging current is null when
comparator output is lower that the horizontal dashed line.
Figure 2: Synchronization of two coupled oscillators. Coupling is established at T and
synchronization is reached in one cycle.
by a vertical dashed line, a positive coupling is established between the two extreme
oscillators of each chain. After a brief transient of one oscillation cycle, synchroniy is
achieved.
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Figure 3: Synchronization of a chain of coupled oacillators. First, two independent
chains are synchronous. Then coupling is established between an oscillator of each
small chain making up a larger synchronous chain.
5 Conclusions
In this paper we have introduced simple microelectronic oscillators with synchronization properties that can be used in oscillatory image segmentation systems. Synchronization is demonstrated above with experimental results. Simulations and experimental results presented in (Cosp and Madrenas, 2003) show that these oscillator have low
power requirements while maintaining their segmentation capabilities. This network
is focused to embbed a segmentation layer in a focal-plane parallel vision system that
incorporates optical sensors, a pre-processing stage to filter noise and extract visual
characteristics, a segmentation stage and a post-processing stages that analyzes results
and outputs data from the oscillation coded information.
References
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Cosp, J. and Madrenas, J. (2003). Scene segmenation using neuromorphic oscilatory networks.
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Mead, C. (1975). Analog VLSI and Neural Systems. Addison-Wesley, Reading, MA.
Somers, D. and Kopell, N. (1993). Rapid synchronization through fast threshold modulation.
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