Adaptive Neuromorphic Circuit for Stereoscopic Disparity Using Ocular Dominance Map

Stereopsis or depth perception is a critical aspect of information processing in the brain and is computed from the positional shift or disparity between the images seen by the two eyes. Various algorithms and their hardware implementation that compute disparity in real time have been proposed; however, most of them compute disparity through complex mathematical calculations that are difficult to realize in hardware and are biologically unrealistic. The brain presumably uses simpler methods to extract depth information from the environment and hence newer methodologies that could perform stereopsis with brain like elegance need to be explored. This paper proposes an innovative aVLSI design that leverages the columnar organization of ocular dominance in the brain and uses time-staggered Winner Take All (ts-WTA) to adaptively create disparity tuned cells. Physiological findings support the presence of disparity cells in the visual cortex and show that these cells surface as a result of binocular stimulation received after birth. Therefore, creating in hardware cells that can learn different disparities with experience not only is novel but also is biologically more realistic. These disparity cells, when allowed to interact diffusively on a larger scale, can be used to adaptively create stable topological disparity maps in silicon.


Temperature Analysis
To test the robustness of the ts-WTA cell and the Disparity Selective Cell under temperature variation, simulations were performed for different temperatures in the range -45 to 85 o C. It was found that the ts-WTA worked well between -45 o C and 65 o C, however with an increase in temperature there was an increase in the learning time. This delayed learning time in the ts-WTA at high temperatures seemed to be affecting the Disparity Cells performance. It appears that the increased learning time increases the diffusion or the neighborhood influence on each cell, as a result of which the pattern that the disparity cell learns is a not a unique pattern but a reflection of many input patterns. This can be adjusted by changing the diffusion resistances, however this aspect has not been taken into account in the current circuit.
During the detection phase, the circuit's performance remains unaltered for low temperatures. However for higher temperatures, although the detection of disparity happens correctly, there is a reduction in the output voltage range.

Monte Carlo Analysis of Disparity Selective Cell
To test the robustness of our Disparity Selective Cell, Monte Carlo Analysis with random parameter value variations was performed. The Disparity Selective Cell's performance heavily depends on the injection and tunnel currents. Any variation in these currents can affect the equilibrium of the circuit and affect the circuit's learning and response behavior. Our models for injection and tunnel currents are based on the equations described in [Rahimi et.al, 2001] also described below.
The tunnel current varies according to the below equation and depends on the floating gate voltage, the tunnel voltage and a factor Vf that depends on the oxide thickness. Our model assumes an oxide thickness of 70A o . I to is a pre-exponential current. The typical values of these parameters are listed in table I.  To test the robustness of our design under these two situations we performed Monte-Carlo analysis at two levels. First, by randomly varying the base values of all the parameters and applying the same (randomly generated parameters ) to all the 9x9 ts-WTA cells and second, by randomly varying the base values and applying different parameter values to all 9x9 ts-WTA cells. The first analysis determines the extent to which the disparity cell is resilient to changes in the base values of parameters and the second analysis checks for how resilient the circuit is to variations in parameters across the 9x9 ts-WTA cells over the same IC. The following sections describe the detailed analysis.

Performance under parameter base value variation
To check for the first case, a MATLAB code was written to generate random values of all the parameters. The parameters were varied by 10%, 5% and 3% from the base values listed in table I. Some sample values of the parameters are listed in tables 2a, 2c and 2e.

Performance under 10% parameter variation
Multiple simulations were performed on the Disparity cell keeping the inputs and initial conditions the same but varying the parameters and applying the same to all the 9x9 ts-WTA cells.  (1), even when Vf changes, the overall effect of the exponential term in the tunnel current can be kept constant by changing the tunnel voltage(Vtun) appropriately. By modifying Vtun, for all the cases except for case 4, the response of the cell could be made normal.Therefore, it seems that the circuit is not very stable to 10% variation in Vf. However, in 90% of the cases, we can recover from this unstable response by adjusting Vtun. The exact variation in Vtun can be seen in table 2b.

Performance under 5% parameter variation
To check the if the performance of the disparity cell improves with a lower percentage parameter variation, we varied the parameters by 5%. Some of the sample parameter values used in the simulations are recorded in table 2c.

Performance under 3% parameter variation
To find the range of parameter variation within which the cell works perfectly (without having to change Vtun) we then varied the parameters by 3%. Some sample values are listed in table 2e. Analysis: It was found that in all the cases the cell's behavior was as expected. For case 3, the learning took slightly longer, however the output or receptive field did converge to the expected pattern. For all other cases the learning was normal.

Performance under parameter variation across the same IC
To test how robust our circuit is to parameter variations between the different 9x9 ts-WTA cells a MATLAB code was written to generate random parameters for all the 81 ts-WTAs. The parameter variation range was varied from ±2% to ±10%. It was found that when the parameters varied within ±3% of the base values, the cell performed normally, however, for larger limits the cell's performance deteriorated. Sample values with a ±3% random parameter variation across all 9x9 ts-WTA cells are listed in table 3.

Conclusions
i) The cell is fairly robust to noise ii) Works well between -45 o C and 65 o C iii) The two stage Monte-Carlo analysis performed on the Disparity Selective Cell brings forth the following conclusions a. The cell is fairly stable under a ±3% variation in parameter base values.
b. For a variation greater than 3% but less than 10%, the response of the cell gets altered but it can easily be recovered by changing the tunnel voltage Vtun appropriately. c. The cell is also resilient upto a ±3% parameter mismatch between the 9x9 ts-WTA cells forming the disparity cell.