A Comparison of Deterministic and Stochastic Logic for Image Processing Applications

Under the guidance ofDr. Kewal Saluja

Presented ByRakesh Roshan Amalraj

Rasika JoshiGayatri Vishwanathan

University of Wisconsin - MadisonDept. of Electrical & Computer Engineering

ECE 753 PROJECT

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Outline

• Motivation• Introduction to Stochastic Logic • Relevance in Real Time Signal Processing• Stochastic Architecture• Analysis for Gamma Correction• Analysis for Edge detection• Architecture for Mean filter• Fault Injection Methods• Results and Discussion• Conclusion and Future Work

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Motivation

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Progressive scalingNecessity for Fault tolerance especially in Real-Time

applications Continuing downscaling of IC design calls for power

efficiency Need for hardware with smaller area Increasing need to meet timing requirements at a high

rate of accuracy Existing methods -> ECC and hardware redundancy

Why Stochastic Computing???

Randomness->valuable resource Convert probability values into another - statistical bit

stream Compared to Deterministic computing, lacks place

value -> no MSB and LSB Computation is robust

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SC and real time image processing can handle image intensities and probabilities with good noise tolerance.

SC supports massive parallelism. Hardware cost is less Outperforms binary computing in processing tasks

involving stored images. High fault tolerance

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Stochastic for Image Processing Applications

How does it work really?

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The interpretation of Digital logic Blocks is considered differently: Egs- A mux can be a scaled adder, an AND gate can be a multiplier, OR gate an adder and so on

Not every input can be represented in a probabilistic bit sequence The range of inputs should be within [0,1] and the outputs should fall in same

interval To accommodate inputs greater than 1, they are generally scaled by a factor to

bring them within [0,1] interval.

Any polynomial function can be represented in Stochastic logic-only if coefficients lie between [0,1] or else they are converted to Bernstein Polynomials:

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Continued…

Non polynomial functions such as trigonometric functions etc. can be converted using the Bernstein Approximation:

But for our designs we merely use approximated versions of the Bernstein Coefficients to suit the application.

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Stochastic Architecture

RANDOMIZE

R

PROCESSING UNIT

DERANDOMIZER

Generate input Stochastic bit stream using LFSRs

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Schematic Diagram

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Modus operandi:

MATLAB •Image procured was converted into N*N matrix •Values were converted to Binary ,scaled and bit-widths adjusted

VERILOG •Design of Stochastic and Deterministic Modules •Implementation of TestBench for input extraction and feeding through Processing units

MATLAB •Processing output file and converting it to Image•Derive results based on PSNR and SSIM

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Gamma Correction• A popular image processing Technique used to

apply contrast to images.• The operation applied: Vout=A*Vin^(ϒ). Factor

used is usually 0.45• Generally Complex floating point number

Crunching Involved• Hefty N-bit adders, Multipliers, Subtractors

shown in Fig.(b)

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Results for Gamma Correction

• 4-BIT IMAGE (Bird)

• 8-BIT IMAGE (Lena)

A1 A2 B1 B2

A1 and B1 are deterministic gamma corrected ImagesA2 and B2 are Stochastic Gamma Corrected Images

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Edge Detection

An edge in an image is a significant local change in the image intensity.

Typically occurs on the boundary between two regions in an image.

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What Causes Intensity Changes?Geometric events

• Surface orientation (boundary) discontinuities• Depth discontinuities• Color and texture discontinuities

Non-geometric events• Illumination changes• Specularities• Shadows• Inter-reflections

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Image to Edge map

Important features can be extracted from the edges of an image (e.g., corners, lines, curves).

These features are used by higher-level computer vision algorithms (e.g., recognition).

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Stochastic Implementation

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The edge detection implementation is based on the Robert Cross Algorithm.

Uses Parallel Processing to deal with the every pixel of the input matrix.

Deterministic Implementation

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Synthesis shows that stochastic design has less area-delay and power dissipation.

Stochastic design Provides maximum parallelism .

Mean Filter or Smoothing Filter ‘MEAN filter’ computes the average of the neighboring pixels

of every pixel in the image matrix and performs a smoothing effect that would render certain types of noises ineffective.

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Mean Filter Architecture

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Deterministic Implementation would require many adders and a multiplier

In stochastic domain MUXes can function as a scaled adders as shown beforeCases to be considered:a) Image pixels in the four corners were given only 3 neighbors.b) Image pixels in the last row were given an accommodation of 4neighbors.c) Image pixels well into the matrix were given a maximum of 8 neighbors.d) Image pixels in the last column of each row of the matrix were assigned 4 neighbors.

Inputs would be 8 pixel neighboursSelect Lines:A=B=C=0.5

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Fault Injection Methods

Fault injection was done for all three applications Gamma Correction, Edge Detection and Mean Filtering to compare the fault tolerance capabilities of  the Deterministic and Stochastic logic

Two types of Faults were introduced:• Soft Errors (Random Bit Flips )• Salt & Pepper Noise in Images

Fault Injection

GA MMA CO RRE CT ION

Deterministic Logic

Bit flips in the pixel using XOR

6.25% 12.5% 25%

Stochastic Logic

Bit flips introduced in the randomized bit sequence

6.25% 12.5% 25%

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Fault Injection (contd.)

Edge Detection and Mean Filtering

Salt and Pepper noises

5%

10%

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Problems faced IMPLEMENTATION DETAILS: ■ Implemented of hardware modules : Verilog HDL■ Simulations and Introduction of Bit Flip Faults : ModelSim ■ Synthesis : DesignVision■ Pre-processing of input images, Processing of the simulation outputs to Images,

Salt & Pepper fault-injection and obtaining PSNR and SSIM Index : MATLAB

❖ METRICS USED TO ASSESS FAULT-TOLERANCE :■ PSNR: Peak Signal to Noise Ratio value is in dB and a PSNR of 50-70dB is

considered a good image. ■ SSIM: Structural SIMilarity index measures the similarity between two images.

It is a quality measure of one of the images being compared, with the other image as reference. An SSIM index of 1 implies the two images are equal and any value above 0.7 is considered a decent quality image.

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Results and Discussion

Problems faced

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Results and Discussion (contd.)

GAMMA SSIM PSNRBird (4-bit) Deterministic Stochastic Deterministic Stochasticno fault 0.8797 0.7229 69.8069 66.57786.25% fault 0.8564 0.6783 63.411 64.252512.5% fault 0.8564 0.6891 63.411 63.429820% fault 0.7678 0.6574 60.2854 62.132625% fault 0.7377 0.6574 59.6453 62.1326

Gamma Correction

(c) (d) (e) (f)

Problems faced

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Results and Discussion (contd.)

a) Original Lena (8 bit Image) and b) Gamma Corrected through Matlab

(c)

(d)

(e)

(f) (g)

Stochastic Gamma Correction

Deterministic Gamma Correction

(a)

(b)

Figure 10: 4bit ‘Bird’ Image Gamma Corrected: (c) No Fault (d) 6.25% fault (e) 12.5% fault (f) 20% fault (g) 25% fault

GAMMA SSIM PSNR LENA (8-bit) Deterministic Stochastic Deterministic Stochasticno fault 0.9897 0.9605 71.5971 75.77346.25% fault 0.9396 0.9619 66.8139 76.307412.5% fault 0.8544 0.9443 63.311 71.693120% fault 0.8458 0.8949 63.0776 68.585525% fault 0.8099 0.8428 62.2828 69.1365

Table 2: Comparison of SSIM and PSNR for Stochastic and Deterministic Implementations of Gamma Correction for 8bit Image and below, graphs

representing the data given above.

Results and Discussion (contd.)

b) 8-bit Image

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Results and Discussion (contd.)

Stochastic Edge Detection

Deterministic Edge Detection

(a) No Fault (b) 5% Salt&Pepper (c) 10% Salt&Pepper

Figure 12: Edge Detection for Lena 8bit Image

Edge Detection

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Results and Discussion (contd.)

(a) No Fault (b) 5% Error (c) 10% Error

Mean Filter SSIM PSNRLena Deterministic Stochastic Deterministic Stochasticno fault 0.9956 0.9684 86.3756 73.59255% fault 0.6826 0.6361 75.226 71.278110% fault 0.4849 0.5324 69.7837 72.297815% fault 0.384 0.4288 68.4122 70.2399

Stochastic Mean Filter

Deterministic Mean Filter

Mean Filtering

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Results and Discussion (contd.)

ApplicationStochastic Deterministic

  AreaPower (mW)

Timing (Slack:

2ns Clk) Delay AreaPower (mW)

Timing (Slack:

2ns Clk) Delay

GAMMA 113.95 7.22e-02 0.8 2^N 505.91 0.5368 -0.18 0

EdgeDetection 66.856 2.5559e-02 1.52 2^N 396.37 0.2093 0 0Mean Filtering 12.348 2.1283e-05 1.13 2^N 230.73 8.9428e-02 0.87 0

*N=BitDepth

Hardware Statistics

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Conclusion (Summary)

❖ We have studied the functioning, advantages and disadvantages of Stochastic Logic versus Deterministic Logic

❖ Carried out hardware implementation of Image Processing applications, such as Gamma Correction, and Edge Detection in Stochastic and Deterministic Logic

❖ Proposed a simple yet effective design for implementing an Averaging or Smoothing Filter in Stochastic Logic and compared its performance

❖ Injected Faults and compared the Fault tolerance capabilities for Image Processing applications using the SSIM and PSNR metrics

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Take Away

Table : Overall Comparison of Deterministic and Stochastic Implementation Logic

DETERMINISTIC LOGIC STOCHASTIC LOGIC

More hardware, Greater area Lesser hardware, Lesser Area, enabling parallelism

Not power efficient Power reduction is by the thousands

Clock and reset signals for combinational logic not required

Clock and Reset required for every logic block (due to Randomizer and Derandomizer (R&D))Hence, susceptible to clock jitter and skew

Comparatively slower Can be clocked at very high frequencies (critical path is very small), but Delay due to R&D

Widely used, easy to implement any functionality and well tested

Best suited for limited applications with bounded input -output ranges.Application to real time signal processing Speech/Control signals not yet explored

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Future Work

❖ Tackle the overhead of delay introduced by randomizing and derandomizing the input and output signals

❖ Efficient use of the randomizer and derandomizer modules to further reduce area are of top priority.

❖ Explore more critical applications such as control signals or avenues such as audio signal / speech processing, apart from Image Processing applications.

❖ Expand the possible range of functions that can be implemented through Stochastic Logic

❖ Stochastic Logic can offer a paradigm shift in digital circuit design and if not escape the power wall, at least delay it

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References

❖ Main References

■ Weikang Qian; Xin Li; Riedel, M.D.; Bazargan, K.; Lilja, D.J., "An Architecture for Fault-Tolerant Computation with Stochastic Logic," Computers, IEEE Transactions on , vol.60, no.1, pp.93,105, Jan. 2011

■ Alaghi, A.; Cheng Li; Hayes, J.P., "Stochastic Circuits for Real-Time Image-Processing Applications," Design Automation Conference (DAC), 2013 50th ACM / EDAC / IEEE , vol., no., pp.1,6, May 29 2013-June 7 2013

■ Li, Peng, and David J. Lilja. "Using Stochastic Computing to Implement Digital Image Processing Algorithms." Computer Design (ICCD), 2011 IEEE 29th International Conference on. IEEE, 2011.

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THANK YOU!

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