Biomimetic model of the outer plexiform layer by incorporating memristive devices

In this paper we present a biorealistic model for the first part of the early vision of processing by incorporating memristive nanodevices. The architecture of the proposed network is based on the organization and functioning of the outer plexiform layer (OPL) in the vertebrate retina. We demonstrate that memristive devices are indeed a valuable building block for neuromorphic architectures, as their highly nonlinear and adaptive response could be exploited for establishing ultradense networks with dynamics similar to that of their biological counterparts. We particularly show that hexagonal memristive grids can be employed for faithfully emulating the smoothing effect occurring in the OPL to enhance the dynamic range of the system. In addition, we employ a memristor-based thresholding scheme for detecting the edges of grayscale images, while the proposed system is also evaluated for its adaptation and fault tolerance capacity against different light or noise conditions as well as its distinct device yields.

Figure 1

Conceptual representation of the mammalian retina. To avoid confusion, only five major cell types are depicted, with the main interconnection between them organized across the seven layers. The visual information flows through the retina via bipolar cells and travels to the thalamus via the axons of ganglion cells. Lateral interconnections also exist between the bipolar and the horizontal cells in the OPL and the bipolar and the amacrine cells in the IPL.

Figure 2

(a) Illustration of the OPL architecture, with on and off bipolar cells contracted for simplicity. In the OPL, photoreceptor, horizontal, and bipolar cells are interconnected through so-called triads. Horizontal cells are interlinked through gap junctions, forming an extended lateral network. (b) A triad from the OPL is formed by the cone pedicle, on and off bipolar cell dendrites, and horizontal cell dendrites or axons. The incoming visual signal is modulated at these nodes through the interconnecting neurons, essentially establishing the first layer of visual processing.

Figure 3

Schematic illustration of the memristive fuse. Two identical memristors of opposing polarities are connected serially.

Figure 4

Closeup view of a single node of the proposed grid. Voltage sources and serial resistors are representations of the output signals of photoreceptors, when subjected to an optical stimulus. Every node establishes a triad through hexagonally interconnected memristive fuses for imitating the dendrites or axons of horizontal cells, one memristor that represents the dendrite of bipolar cells, and bias sources and resistors at the input stage that denote the cone pedicle.

Figure 5

Effect of single-node biasing with a large contrast. (a) Static voltage distribution across center-surrounding nodes of the OPL network after $t=30$ s. Inset: Biasing scheme. (b) Memristance transient of OPL memristive fuses. Time evolution of all memristive fuse states affiliated with this node. Inset: Distinct colors and marks correspond to the neighboring devices to the center node.

Figure 6

Mapping mechanisms between the input image and the OPL model. (a) Simulated photoreceptor depolarization due to distinct grayscale levels. Every pixel of an input image is represented by a corresponding voltage level. (b) Mapping between rectangular image and the hexagonal grid. All images were handled as pseudohexagonals to assign every pixel to a node of the grid.

Figure 7

Demonstration of local Gaussian filtering with our proposed OPL model. (a) The original input image. (b) The extrapolated smoothed version of (a) after $t=30$ s. (c) A distorted version of (a); (d) the corresponding smoothed output after $t=30$ s. (e) The accentuated intensity mismatch of the smoothed outputs with versus without distortion.

Figure 8

Detection of the edges of the utilized input image shown in (a). Edge detection was achieved via (b) a bipolar threshold scheme at the output of the OPL nodes, with $600\Omega \le M_T\le 2$ k$\Omega$, and (c) a thresholding scheme at the memristive fuses with $M_T=1.6$ k$\Omega$. These results are compared with conventional edge-detection algorithms: (d) Prewitt, (e) Sobel, and (f) Canny.

Figure 9

Detection of the edges of the utilized input image shown in (a). (b) The corresponding smoothed output after $t=30$ s. (c) Edge detection was achieved by applying a thresholding scheme with $M_T=3$ k$\Omega$. This result is also compared against conventional edge-detection algorithms: (d) Prewitt, (e) Sobel, and (f) Canny.

Figure 10

Evaluation of the memristive platform against distinct light conditions. (a, d) Representations of the employed input image [Fig. 9a] in brighter and lighter tones. The detected edges for both conditions when corresponding memristive thresholds are utilized: (b) $M_{TL}=6.35$ k$\Omega$ and (e) $M_{TD}=1.2$ k$\Omega$. Corresponding results when $M_{TL}=3$ k$\Omega$ is the same for both cases, after the system has evolved for (c) $t_L=21.8$ s and (f) $t_D=44.7$ s.

Figure 11

Test conditions for evaluating the fault tolerance capacity of this model. The distribution of memristive elements whose initial state ($M_{\mathrm{init}}$) was altered by (a) 25$\%$ and (b) 50$\%$ of the total memristors in the network is shown.

Figure 12

Smoothing and edge-detection performance for varying memristor yields: (a) ideal scenario, (b) 75$\%$ yield, and (c) 50$\%$ yield. (d, e) The accentuated difference between the ideal and the randomly affected networks. The corresponding detected edges are illustrated for yields of (f) 100$\%$, (g) 75$\%$, and (h) 50$\%$.