Daniel Cheok Kiang Kho, Mohammad Faizal Ahmad Fauzi, Sin Liang Lim

Corresponding email: lim.sin.liang@mmu.edu.my

Corresponding email: lim.sin.liang@mmu.edu.my

**Published at : ** 29 Nov 2019

**IJtech :** IJtech
Vol 10, No 7 (2019)

**DOI :** https://doi.org/10.14716/ijtech.v10i7.3263

Kho, D.C.K., Fauzi, M.F.A. Lim, S.L., 2019. Hardware-Based Sobel Gradient Computations for Sharpness Enhancement.

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Daniel Cheok Kiang Kho | Faculty of Engineering, Multimedia University, Persiaran Multimedia, 63100 Cyberjaya, Selangor, Malaysia |

Mohammad Faizal Ahmad Fauzi | Faculty of Engineering, Multimedia University, Persiaran Multimedia, 63100 Cyberjaya, Selangor, Malaysia |

Sin Liang Lim | Faculty of Engineering, Multimedia University, Persiaran Multimedia, 63100 Cyberjaya, Selangor, Malaysia |

Abstract

The majority of imaging systems are software based; they require some
kind of microprocessor or microcontroller for the imaging algorithms to run. As
the speed requirements of imaging and communications systems increase, the need
for more hardware-based imaging systems arises. These fully hardware systems
solve the fundamental problem inherent in software-based solutions, in which
the speed of the algorithms depend on the instruction cycle speed of the
processor. Once an algorithm is designed directly on hardware, the speed of the
algorithm depends on the system clock frequency and the propagation delays of
the logic cells (or standard cells) used in the design, usually measured in
nanoseconds per cell. Therefore, such systems no longer depend on any instruction
cycle delays, as there is no microprocessor involved. Most modern imaging and
communications systems rely on digital signal processing (DSP) to compute
complex mathematical operations. The emergence of powerful and low-cost
field-programmable gate array (FPGA) devices with hundreds of arithmetic
multipliers has enabled the development of many such DSP hardware applications,
traditionally implemented only as software solutions.

Digital signal processing; Edge detection; Gradient; Sobel; VHDL

Introduction

Lately, there have
been several texts (Li & Chu, 1997; Nelson, 2000; Yasri et al., 2009; Mehra & Verma, 2012; Nosrat &
Kavian, 2012; Sanduja & Patial, 2012; Singh et al., 2012; Umar et al., 2012; Bhagat et al., 2015) written on
hardware-based Sobel implementations on FPGAs using VHDL (Ashenden, 2008) or
Verilog. However, nearly all of these advocate the use of calculating the
gradient magnitude by obtaining the sum of the absolute values of the gradient in
both the horizontal and vertical directions. Implementing gross
approximations of many such nonlinear imaging algorithms (Arce et al., 2000; Aubert & Kornprobst, 2006; Bertalm?o et al., 2001; Chambolle, 1994; Kokkinos, 2013; Kornprobst et al., 1999; Mitra & Sicuranza, 2001; Xu & Mueller, 2010) on
hardware has become common practice.Although this
approach simplifies the hardware implementation by avoiding the more
computationally intensive square root calculations, the resulting gradient
magnitude suffers from having more errors than a gradient magnitude calculated
using the Pythagorean theorem of square-rooting the sum of squares of the
gradients in each horizontal and vertical direction.

Before other algorithms are performed, usually, an image filter is applied. This preprocessing filter helps ease the computation of further downstream algorithms, such as those used in optical character recognition systems (Pangestu et al., 2017), or the K-NN algorithms (Naik & Metkewar, 2015) used in artificial intelligence. Either a spatial filter, such as a Sobel edge detector, or a histogram equalizer frequency domain filter may be used as the prefilter, depending on the type of further processing required.

This paper introduces a computationally efficient technique
of preserving the precision of the gradient magnitude by using an efficient and
fast square root algorithm in the computation of the gradient magnitude.
Although we also introduce a different kernel processing scheme that computes
kernels in parallel, this paper focuses its discussion on the use of the fast
reciprocal square root (FRSR) algorithm for hardware-based Sobel edge
detection.

Conclusion

The Sobel algorithm, used frequently in many edge detection algorithms,
has been shown to be feasibly implemented on digital hardware. However, the
gradient magnitude of these implementations used the summation of the absolute
values of the g_{x } and g_{x} gradients as its
estimate , whereas in our implementation, we used the actual square
root operator to compute the gradient magnitude. Using the FRSR algorithm gives
a more accurate estimate of the gradient magnitude as computed from the square
root of the square of the gradients in both the horizontal and vertical
directions

Acknowledgement

The authors are thankful to the Ministry of Higher
Education of Malaysia for the award of the Fundamental Research Grant Scheme
FRGS/1/2015/TK04/MMU/02/10 to support this project. We are also thankful to
Jeannie Lau and Ang Boon Chong for the many technical discussions that helped
us complete this project.

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