Analog VLSI Cellular Implementation of the 
Boundary Contour System 
Gert Cauwenberghs and James Waskiewicz 
Department of Electrical and Computer Engineering 
Johns Hopkins University 
3400 North Charles Street 
Baltimore, MD 21218-2686 
E-mail: {gert, davros}@bach. ece. jhu. edu 
Abstract 
We present an analog VLSI cellular architecture implementing a simpli- 
-fled version of the Boundary Contour System (BCS) for real-time image 
processing. Inspired by neuromorphic models across several layers of 
visual cortex, the design integrates in each pixel the functions of sim- 
ple cells, complex cells, hyper-complex cells, and bipole cells, in three 
orientations interconnected on a hexagonal grid. Analog current-mode 
CMOS circuits are used throughout to perform edge detection, local inhi- 
bition, directionally selective long-range diffusive kernels, and renormal- 
izing global gain control. Experimental results from a fabricated 12 x 10 
pixel prototype in 1.2/zm CMOS technology demonstrate the robustness 
of the architecture in selecting image contours in a cluttered and noisy 
background. 
1 Introduction 
The Boundary Contour System (BCS) and Feature Contour System (FCS) combine models 
for processes of image segmentation, feature filling, and surface reconstruction in biolog- 
ical vision systems [1],[2]. They provide a powerful technique to recognize patterns and 
restore image quality under excessive fixed pattern noise, such as in SAR images [3]. A 
related model with similar functional and structural properties is presented in [4]. 
The motivation for implementing a relatively complex model such as BCS and FCS on 
the focal-plane is dual. First, as argued in [5], complex neuromorphic active pixel designs 
become viable engineering solutions as the feature size of the VLSI technology shrinks 
significantly below the optical diffraction limit, and more transistors can be stuffed in each 
pixel. The pixel design that we present contains 88 transistors, likely the most complex 
658 G. Cauwenberghs and J. Waskiewicz 
Bipole Cells 
(long-range orientational cooperation) 
Diffusive Network 
 Complex/Hypercomplex Cells 
{orientational/spatial competition) 
Local bthibition 
Focal-Plane Receptors; 
Random-Access Inputs 
BCS FCS 
Figure 1: Diagram of BCS/FCS model for image segmentation, feature filling, and surface 
reconstruction. Three layers represent simple, complex and bipole cells. 
active pixel imager ever put on silicon. Second, our motivation is to extend the functionality 
of previous work on analog VLSI neuromorphic image processors for image boundary 
segmentation, e.g. [6, 7, 5, 8, 9] which are based on simplified physical models that do not 
include directional selectivity and/or long-range signal aggregation for boundary formation 
in the presence of significant noise and clutter. The analog VLSI implementation of BCS 
reported here is a first step towards this goal, with the additional objectives of real-time, 
low-power operation as required for demanding target recognition applications. As an 
alternative to focal-plane optical input, the image can be loaded electronically through 
random-access pixel addressing. 
The BCS model encompasses visual processing at different levels, including several lay- 
ers of cells interacting through shunting inhibition, long-range cooperative excitation, and 
renormalization. The implementation architecture, shown schematically in Figure 1, parti- 
tions the BCS model into three levels: simple cells, complex and hypercomplex cells, and 
bipole cells. 
Simple cells compute unidirectional gradients of normalized intensity obtained from the 
photoreceptors. Complex (hyper-complex) cells perform spatial and directional compe- 
tition (inhibition) for edge formation. Bipole cells perform long-range cooperation for 
boundary contour enhancement, and exert positive feedback (excitation) onto the hyper- 
complex cells. Our present implementation does not include the FCS model, which com- 
pletes and fills features through diffusive spatial filtering of the image blocked by the edges 
formed in BCS. 
2 Modified BCS Algorithm and Implementation 
We adopted the BCS algorithm for analog continuous-time implementation on a hexagonal 
grid, extending in three directions u, v and w on the focal plane as indicated schematically 
in Figure 2. For notational convenience, let subscript 0 denote the center pixel and +u, +v 
and +w its six neighbors. Components of each complex cell "vector" Ci at grid location i, 
along three directions of edge selectivity, are indicated with superscript indices u, v and w. 
In the implemented circuit model, a pixel unit consists of a photosensor (or random-access 
analog memory) sourcing a current indicating light intensity, gradient computation and 
rectification circuits implementing simple cells in three directions, and one complex (hyper- 
Analog VLSI Cellular Implementation of the Boundary Contour System 659 
l.u 
Figure 2: Hexagonal arrangement of BCS pixels, at the level of simple and complex cells, 
extending in three directions u, v and w in the focal plane. 
complex) cell and one bipole cell for each of the three directions. 
The photosensors generate a current Ii that is proportional to intensity. Through current 
mirrors, the currents Ii propagate in the three directions u, v, and w as noted in Figure 
2. Rectified finite-difference gradient estimates of Ii are obtained for each of the three 
hexagonal directions. These gradients excite the complex cells 6'. 
Lateral inhibition among spatially (i) and directionally (j) adjacent complex cells imple- 
ment the function of hypercomplex cells for edge enhancement and noise reduction. The 
complex output (C'{) is inhibited by local complex cell outputs in the two competing direc- 
tions of j. Co is additionally inhibited by the complex cells of the four nearest neighbors 
in competing locations i with parallel orientation. 
A directionally selective interconnected diffusive network of bipole cells B, interacting 
with the complex cells C', provides long range cooperative feedback, and enhances smooth 
edge contours while reducing spurious edges due to image clutter. C' is excited by bipole 
interaction received from the bipole cell B on the line crossing i in the same direction j. 
The operation of the (hyper-)complex cells in the hexagonal arrangement is summarized in 
the following equation, for one of the three directions u: 
II(Iv + Lo) - Io - a(6' 
C=5 
where: 
+C ) - a'(C +C +C_v + C_w) +/3Bg (1) 
1. [ + Lo) - Io[ represents the rectified gradient input as approximated on the 
hexagonal grid; 
2. a(6' + 6' ) is the inhibition from locally opposing directions; 
3. a (6' + 6' + 6'_v + 6'_o) is inhibition from non-aligned neighbors in the same 
direction; and 
4. /3B is the excitation through long-range cooperation from the bipole cell. 
660 G. Cauwenberghs and d. Wasla'ewicz 
Figure 3: Network of bipole cells, implemented on a hexagonal resistive grid using orien- 
tationally tuned diffusors extending in three directions. ]lat/vert deteFmines the spatial 
extent of the dipole, whereas glat / Ocross sets the directional selectivity. 
The bipole cell resistive grid (Figure 3) implements a three-fold cross-coupled, direction- 
ally polarized, long-range diffusive kernel, formulated as follows: 
B  u u u v u w 
K.C 
Kv C + 
K, C + 
(2) 
where K, K, and K represent spatial convolutional kernels implementing bipole fields 
symmetrically polarized in the u, v and w directions. Diffusive kernels can be efficiently 
implemented with a distributed representation using resistive diffusive elements [7, 10]. 
Three linear networks of diffusor elements are used, complemented with cross-links of 
adjustable strength, to control the degree of direction selectivity and the spatial spread 
of the kernel. Finally, the result (2) is locally normalized, before it is fed back onto the 
complex cells. 
3 Analog VLSI Implementation 
The simplified circuit diagram of the BCS cell, including simple, complex and bipole cell 
functions on a hexagonal grid, is shown in Figure 4. 
The image is acquired either optically from phototransistors on the focal-plane, or in direct 
electronic format through random-access pixel addressing, Figure 4 (a). The simple cell 
portion in Figure 4 (b) combines the local intensity I0 with intensities Ivand Lo received 
from neighboring cells to compute the rectified gradient in (1), using distributed current 
mirrors and an absolute value circuit. A pMOS load converts the complex cell output into 
a voltage representation C' for distribution to neighboring nodes and complementary ori- 
entations: local inhibition for spatial and directional competition in Figure 4 (c), and long- 
range cooperation through the bipole layer in Figure 4 (d). The linear diffusive kernel is 
implemented in current-mode using ladder structures of subthreshold MOS transistors [7], 
three families extending in each direction with cross-links for directional dispersion as in- 
dicated in Figure 3. 
Voltage biases control the spatial extent and directional selectivity of the interactions, as 
Analog VLSI Cellular Implementation of the Boundary Contour System 661 
Vo 
i i WR . SELy 
(a) 
v+-( 
I++I+   
-Vo 
u 
CoU 
BoU 
' I Vc-ro s 
Vve [ 
B +uU 
Vbnorm'[ lnorm 
Vthres 5-- Vnorm 
(b) (d) (e) 
Figure 4: Simplified circuit schematic of one BCS cell in the hexagonal array, showing 
only one of three directions, the other directions being symmetrical in implementation. (a) 
Photosensor and random-access input selection circuit. (b) Simple cell rectified gradient 
calculation. (c) Complex cell spatial and orientational inhibition. (d) Bipole cell direc- 
tional long range cooperation. (e) Bipole global gain and threshold control. 
well as the relative strength of inhibition and excitation, and the level of renormalization, 
for the complex and bipole cells. The values for tIvert, tltat and t7c,-o88 controlling the 
bipole kernel are set externally by applying gate bias voltages Vvet, Vtat and Vcos,, re- 
spectively. Likewise, the constants a, a and/3 in (1) are set independently by the applied 
source voltages V, V, and Va. Global normalization and thresholding of the bipole re- 
sponse for improved stability of edge formation is achieved through an additional diffusive 
network that acts as a localized Gilbert-type current normalizer (only partially shown in 
Figure 4 (e)). 
4 Experimental Results 
A prototype 12 x 10 pixel array has been fabricated and tested. The pixel unit, illustrated in 
Figure 5 (a), has been designed for testability, and has not been optimized for density. The 
pixel contains 88 transistors including a phototransistor, a large sample-and-hold capacitor, 
and three networks of interconnections in each of the three directions, requiring a fan- 
in/fan-out of 18 node voltages across the interface of each pixel unit. A micrograph of the 
Tiny 2.2 x 2.2 sq. mm chip, fabricated through MOSIS in 1.2/m CMOS technology, is 
shown in Figure 5 (b). 
We have tested the BCS chip both under focal-plane optical inputs, and random-access 
direct electronic inputs. Input currents from optical input under ambient room lighting 
conditions are around 30 hA. The experimental results reported here are obtained by feed- 
ing test inputs electronically. The response of the BCS chip to two test images of interest 
are shown in Figures 6 and 7. 
662 G. Cauwenberghs and J. Wasla'ewicz 
(a) 
Figure 5: BCS processor. (a) Pixel layout. (b) Chip micrograph. 
Figure 6: Experimental response of the BC$ chip to a curved edge. (a) Reconstructed 
input image. (b) Complex field. (c) Bipole field. The thickness of the bars on the grid 
represent the measured components in the three directions. 
Figure 6 illustrates the interpolating directional response to a curved edge in the input, vary- 
ing in direction between two of the principal axes (u and w in the example). Interpolation 
between quantized directions is important since implementing more axes on the grid incurs 
a quadratic cost in complexity. The second example image contains a bar with two gaps of 
different diameter, for the purpose of testing BCS's capacity to extend contour boundaries 
across clutter. The response in Figure 7 illustrates a characteristic of bipole operation, in 
which short-range discontinuities are bridged but large ones are preserved. 
5 Conclusions 
An analog VLSI cellular architecture implementing the Boundary Contour System (BCS) 
on the focal plane has been presented. A diffusive kernel with distributed resistive networks 
has been used to implement long-range interactions of bipole cells without the need of 
excessive global interconnects across the array of pixels. The cellular model is fairly easy to 
implement, and succeeds in selecting boundary contours in images with significant clutter. 
Analog VLSI Cellular Implementation of the Boundary Contour System 663 
(a) () 
Figure 7: Experimental response of the BCS chip to a bar with two gaps of different size. 
(a) Reconstructed input image. (b) Complex field. (c) Bipole field. 
Experimental results from a 12 x 10 pixel prototype demonstrate expected BCS operation 
on simple examples. While this size is small for practical applications, the analog cellular 
architecture is fully scalable towards higher resolutions. Based on the current design, a 
10,000-pixel array in 0.5/m CMOS technology would fit a 1 cm 2 die. 
Acknowledgments 
This research was supported by DARPA and ONR under MURI grant N00014-95-1-0409. 
Chip fabrication was provided through the MOSIS service. 
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