Abstract
Sets-Of-Real-Numbers (SORN) Arithmetic derives from the type-II unums and realizes a low-complexity and low-precision digital number format. The interval-based SORNs are especially well-suited for preprocessing large datasets or replacing particular parts of threshold-based algorithms, in order to achieve a significant reduction of runtime, complexity and/or power consumption for the respective circuit.
In this work, the advantages and challenges of SORN arithmetic are evaluated and discussed for a SORN-based edge detection algorithm for image processing. In particular, different SORN implementations of the Sobel Operator for edge filtering are presented, consisting of matrix convolution and a hypot function. The implemented designs are evaluated for different algorithmic and hardware performance measures. Comparisons to a reference Integer implementation show promising results towards a lower error w.r.t. ground truth solutions for the SORN implementation. Syntheses for FPGA and CMOS target platforms show a reduction of area utilization and power consumption of up to \(68\%\) and \(80\%\), respectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011). https://doi.org/10.1109/TPAMI.2010.161
Bärthel, M., Rust, J., Paul, S.: Hardware implementation of basic arithmetics and elementary functions for unum computing. In: 2018 52nd Asilomar Conference on Signals, Systems, and Computers, pp. 125–129, October 2018. https://doi.org/10.1109/ACSSC.2018.8645453
Bärthel, M., Rust, J., Paul, S.: Application-specific analysis of different SORN datatypes for unum type-2-based arithmetic. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9181182
Bärthel, M., Knobbe, S., Rust, J., Paul, S.: Hardware implementation of a latency-reduced sphere decoder With SORN preprocessing. IEEE Access 9, 91387–91401 (2021). https://doi.org/10.1109/ACCESS.2021.3091778
Bocco, A., Durand, Y., De Dinechin, F.: SMURF: scalar multiple-precision unum Risc-V floating-point accelerator for scientific computing. In: Proceedings of the Conference for Next Generation Arithmetic 2019, pp. 1–8 (2019)
Bounini, F., Gingras, D., Lapointe, V., Pollart, H.: Autonomous vehicle and real time road lanes detection and tracking. In: 2015 IEEE Vehicle Power and Propulsion Conference (VPPC), pp. 1–6 (2015). https://doi.org/10.1109/VPPC.2015.7352903
Cui, W., Wu, G., Hua, R., Yang, H.: The research of edge detection algorithm for Fingerprint images. In: 2008 World Automation Congress, pp. 1–5. IEEE (2008)
Dim, J.R., Takamura, T.: Alternative approach for satellite cloud classification: edge gradient application. Adv. Meteorol. 2013 (2013)
Gatopoulos, I.: Line detection: make an autonomous car see road lines. Towards Data Sci. (2019). https://towardsdatascience.com/line-detection-make-an-autonomous-car-see-road-lines-e3ed984952c
Glaser, F., Mach, S., Rahimi, A., Gurkaynak, F.K., Huang, Q., Benini, L.: An 826 MOPS, 210uW/MHz Unum ALU in 65 nm. In: 2018 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5. IEEE (2018). https://doi.org/10.1109/ISCAS.2018.8351546
Gustafson, J.L.: A Radical Approach to Computation with Real Numbers. Supercomput. Front. Innov. 3(2) (2016). https://doi.org/10.14529/jsfi160203
Gustafson, J.L.: The end of error: Unum computing. CRC Press, Boca Raton, Chapman & Hall/CRC Computational Science Series (2015)
Gustafson, J.L., Yonemoto, I.T.: Beating floating point at its own game: posit arithmetic. Supercomput. Front. Innov. 4(2) (2017). https://doi.org/10.14529/jsfi170206
Hülsmeier, N., Bärthel, M., Rust, J., Paul, S.: SORN-based cascade support vector machine. In: 2020 28th European Signal Processing Conference (EUSIPCO), pp. 1507–1511. IEEE (2021)
Lopez-Molina, C., De Baets, B., Bustince, H.: Quantitative error measures for edge detection. Pattern Recogn. 46(4), 1125–1139 (2013)
Microprocessor Standards Committee of the IEEE Computer Society: IEEE Standard for Floating-Point Arithmetic. IEEE Std. 754–2008, 1–70 (2008). https://doi.org/10.1109/IEEESTD.2008.4610935
Rust, J., Bärthel, M., Seidel, P., Paul, S.: A hardware generator for SORN arithmetic. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 39(12), 4842–4853 (2020). https://doi.org/10.1109/TCAD.2020.2983709
Sobel, I.: An Isotropic 3x3 Image Gradient Operator. Presentation at Stanford A.I. Project 1968 (2014)
Solomon, C., Breckon, T.: Fundamentals of Digital Image Processing: A practical approach with examples in Matlab. Wiley, Hoboken (2011)
Yang, X., Yang, T.A., Wu, L.: An edge detection IP of low-cost system on chip for autonomous vehicles. In: Arabnia, H.R., Ferens, K., de la Fuente, D., Kozerenko, E.B., Olivas Varela, J.A., Tinetti, F.G. (eds.) Advances in Artificial Intelligence and Applied Cognitive Computing. TCSCI, pp. 775–786. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-70296-0_56
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bärthel, M., Hülsmeier, N., Rust, J., Paul, S. (2022). On the Implementation of Edge Detection Algorithms with SORN Arithmetic. In: Gustafson, J., Dimitrov, V. (eds) Next Generation Arithmetic. CoNGA 2022. Lecture Notes in Computer Science, vol 13253. Springer, Cham. https://doi.org/10.1007/978-3-031-09779-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-031-09779-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-09778-2
Online ISBN: 978-3-031-09779-9
eBook Packages: Computer ScienceComputer Science (R0)