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A Comparison of Deterministic and Stochastic Logic for Image Processing Applications Under the guidance of Dr. Kewal Saluja Presented By Rakesh Roshan Amalraj Rasika Joshi Gayatri Vishwanathan University of Wisconsin - Madison Dept. of Electrical & Computer Engineering ECE 753 PROJECT 1

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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 2

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Motivation 3 Progressive scaling Necessity 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

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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 4

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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 5 Stochastic for Image Processing Applications

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How does it work really? 6 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

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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: 7

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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. 8

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Stochastic Architecture RANDOMIZERPROCESSING UNIT Processing in SPE- Stochastic Processing Element DERANDOMIZER Mapping bit sequence to output Generate input Stochastic bit stream using LFSRs 9

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Schematic Diagram 10

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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 11

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Gamma Correction A popular image processing Technique used to apply contrast to images. The operation applied: V out =A*V in ^( ). Factor used is usually 0.45 Generally Complex floating point number Crunching Involved Hefty N-bit adders, Multipliers, Subtractors shown in Fig.(b) 12

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Results for Gamma Correction 4-BIT IMAGE (Bird) 8-BIT IMAGE (Lena) A1 A2 B1B2 A1 and B1 are deterministic gamma corrected Images A2 and B2 are Stochastic Gamma Corrected Images 13

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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. 14

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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 15

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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). 16

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Stochastic Implementation 17 The edge detection implementation is based on the Robert Cross Algorithm. Uses Parallel Processing to deal with the every pixel of the input matrix.

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Deterministic Implementation 18 Synthesis shows that stochastic design has less area-delay and power dissipation. Stochastic design Provides maximum parallelism.

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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. 19

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Mean Filter Architecture 20 Deterministic Implementation would require many adders and a multiplier In stochastic domain MUXes can function as a scaled adders as shown before Cases 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 neighbours Select Lines: A=B=C=0.5

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21 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

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Fault Injection GAMMA CORRECTION 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% 22

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Fault Injection (contd.) Edge Detection and Mean Filtering 5% 10% Salt and Pepper noises 23

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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. 24 Results and Discussion

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Problems faced 25 Results and Discussion (contd.) GAMMASSIMPSNR Bird (4-bit)DeterministicStochasticDeterministicStochastic no fault0.87970.722969.806966.5778 6.25% fault0.85640.678363.41164.2525 12.5% fault0.85640.689163.41163.4298 20% fault0.76780.657460.285462.1326 25% fault0.73770.657459.645362.1326 (c) (d)(e)(f)

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Problems faced 26 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 GAMMASSIMPSNR LENA (8-bit)DeterministicStochasticDeterministicStochastic no fault0.98970.960571.597175.7734 6.25% fault0.93960.961966.813976.3074 12.5% fault0.85440.944363.31171.6931 20% fault0.84580.894963.077668.5855 25% fault0.80990.842862.282869.1365 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.

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Results and Discussion (contd.) b) 8-bit Image 27

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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 28

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Results and Discussion (contd.) (a) No Fault (b) 5% Error (c) 10% Error Mean FilterSSIMPSNR LenaDeterministicStochasticDeterministicStochastic no fault0.99560.968486.375673.5925 5% fault0.68260.636175.22671.2781 10% fault0.48490.532469.783772.2978 15% fault0.3840.428868.412270.2399 Stochastic Mean Filter Deterministic Mean Filter 29

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Results and Discussion (contd.) Application StochasticDeterministic Area Power (mW) Timing (Slack: 2ns Clk)DelayArea Power (mW) Timing (Slack: 2ns Clk)Delay GAMMA113.957.22e-020.82^N505.910.5368-0.180 EdgeDetection66.8562.5559e-021.522^N396.370.209300 Mean Filtering12.3482.1283e-051.132^N230.738.9428e-020.870 *N=BitDepth 30

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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 31

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Take Away Table : Overall Comparison of Deterministic and Stochastic Implementation Logic DETERMINISTIC LOGICSTOCHASTIC LOGIC More hardware, Greater areaLesser hardware, Lesser Area, enabling parallelism Not power efficientPower 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 32

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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 33

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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. 34

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THANK YOU! 35