# Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments

^{*}

## Abstract

**:**

## 1. Introduction

## 2. ERT Imaging

#### 2.1. Modeling and Simulation Studies in ERT

#### 2.2. Reconstruction Methods

^{N X LK}, where K is the number of current patterns, L is the number of electrodes, and N is the number of parameters to be estimated. The normalized changes in the electrical conductivities can be computed as

_{n}= diag (V

_{1}

^{1}, V

_{2}

^{1}, V

_{3}

^{1}, …, V

_{L}

^{K})J,

#### 2.3. ERT and Quantitative Spatial Evaluations

## 3. Experimental Design

#### 3.1. Experimental Setup and Sensor Design

^{2}. Reactor measurement sizes are shown in Table 2.

#### 3.2. Phantom Design and 3D Printing

#### 3.3. Sucrose Crystal Agglomerate Assesments, Experimental Progression, and Test Objectives

## 4. Results

#### 4.1. Differences Due to Reconstruction Methods

#### 4.2. Varying the Iterations in the TV Reconstruction

#### 4.3. Analysing Segmentation Methods and Morphological Image Processing

_{P}) with phantom diameters (PD) and the expected percentage area of phantoms are shown in Table A1 in the Appendix A. The effect of applying erosion as morphological processing to obtain is shown in Figure A2a–e in the Appendix A. The E0 to E30 signifies the morphological image processing erosion applied. E0 stands for no erosion applied, and E10, E20, and E30 stands for incremental erosion applied using ‘disk’ operation in MATLAB image processing toolbox with 10, 20, and 30 as the radius, respectively.

#### 4.4. Towards Quantitative Estimations Using a Combination of Image Processing Methods to Achieve the Expected Area Estimation

#### 4.4.1. Contrast Profile Assessment at Various Iteration Levels

#### 4.4.2. Evaluation of the Area Covered by Phantoms at Various Iterations

#### 4.4.3. Evaluation of the Area Covered by Phantoms at Various Threshold Levels

#### 4.5. Experimental Industrial Application in Assessment of Sucrose Crystals in Demineralized Water

_{C}. It was observed that the G-Channel segmentation provides better results compared to the Otsu method. The area of the 2D region visualized inside the reactor is compared.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**a**) Contrast profile plot for 50 mm phantom R1, reconstruction: TV, iterations: 2–12; channel: green. (

**b**) Contrast profile plot for 40 mm phantom R2, reconstruction: TV, iterations: 2–12; channel: green. (

**c**) Contrast profile plot for 30 mm phantom R3, reconstruction: TV, iterations: 2–12; channel: green. (

**d**) Contrast profile plot for 20 mm phantom R4, reconstruction: TV, iterations: 2–12; channel: green. (

**e**) Contrast profile plot for 10 mm phantom R5, reconstruction: TV, iterations: 2–12; channel: green. (

**f**) Contrast profile plot for phantom R6-L1 (2 × 10 mm), reconstruction: TV, iterations: 2–12; channel: green, location: 1.

**Figure A2.**Comparison of the area percentage for Otsu and G-Channel segmentation using TV, LBP, and GN reconstruct (

**a**) R1 (

**b**) R2, (

**c**) R3, (

**d**) R4, and (

**e**) R5.

**Table A1.**Table showing correlation coefficient of the evaluated percentage area with the phantom diameter and expected area.

Corr. PD | Corr. A_{P} | |||||||
---|---|---|---|---|---|---|---|---|

Phantom diameter (PD) | 10 | 20 | 30 | 40 | 50 | 0.9811 | ||

Expected area (A_{P}) | 1.45 | 5.81 | 13.06 | 23.23 | 36.29 | 0.9811 | ||

TV | G-Channel | 14.99 | 17.44 | 22.10 | 26.48 | 38.38 | 0.9563 | 0.9904 |

Otsu | 13.06 | 17.44 | 20.69 | 25.23 | 35.39 | 0.9714 | 0.9920 | |

LBP | G-Channel | 16.76 | 18.53 | 19.66 | 21.21 | 26.16 | 0.9499 | 0.9811 |

Otsu | 10.29 | 12.22 | 12.13 | 13.90 | 17.76 | 0.9314 | 0.9662 | |

GN | G-Channel | 7.44 | 8.28 | 9.34 | 10.71 | 15.38 | 0.9255 | 0.9740 |

Otsu | 4.60 | 4.70 | 5.57 | 6.49 | 9.23 | 0.9196 | 0.9748 | |

stdevA | 4.63 | 5.69 | 6.84 | 8.18 | 11.59 | |||

˄ (%) | 319.14 | 97.95 | 52.33 | 35.20 | 31.95 |

_{P}with the phantom diameters. Corr. EA shows the correlation coefficient of the evaluated percentage area with the expected percentage area. The correlation coefficient was computed using MATLAB function corrcoef(). Factor ˄ was evaluated using the following Equation (A1). Higher ˄ signifies the higher deviations from the expected percentage area A

_{P}.

## References

- Chakraborty, J.; Sarkar, D.; Singh, A.; Bharti, A.K. Measuring the three-dimensional morphology of crystals using regular reflection of light. Cryst. Growth Des.
**2012**, 12, 6042–6049. [Google Scholar] [CrossRef] - Singh, M.R.; Chakraborty, J.; Nere, N.; Tung, H.-H.; Bordawekar, S.; Ramkrishna, D. Image-analysis-based method for 3D crystal morphology measurement and polymorph identification using confocal microscopy. Cryst. Growth Des.
**2012**, 12, 3735–3748. [Google Scholar] [CrossRef] - De Sena, R.C.; Soares, M.; Pereira, M.L.O.; da Silva, R.C.D.; do Rosário, F.F.; da Silva, J.F.C. A simple method based on the application of a CCD camera as a sensor to detect low concentrations of barium sulfate in suspension. Sensors
**2011**, 11, 864–875. [Google Scholar] [CrossRef] [PubMed][Green Version] - Abu Bakar, M.; Nagy, Z.; Rielly, C. A combined approach of differential scanning calorimetry and hot-stage microscopy with image analysis in the investigation of sulfathiazole polymorphism. J. Therm. Anal. Calorim.
**2010**, 99, 609–619. [Google Scholar] [CrossRef][Green Version] - Soppela, I.; Airaksinen, S.; Hatara, J.; Räikkönen, H.; Antikainen, O.; Yliruusi, J.; Sandler, N. Rapid particle size measurement using 3D surface imaging. Aaps Pharmscitech
**2011**, 12, 476–484. [Google Scholar] [CrossRef][Green Version] - Simone, E.; Saleemi, A.N.; Nagy, Z.K. Raman, UV, NIR, and Mid-IR spectroscopy with focused beam reflectance measurement in monitoring polymorphic transformations. Chem. Eng. Technol.
**2014**, 37, 1305–1313. [Google Scholar] [CrossRef] - Verma, S.; Shlichta, P.J. Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution. Prog. Cryst. Growth Charact. Mater.
**2008**, 54, 1–120. [Google Scholar] [CrossRef] - Simon, L.L.; Simone, E.; Oucherif, K.A. Crystallization process monitoring and control using process analytical technology. In Computer Aided Chemical Engineering; Elsevier: Amsterdam, The Netherlands, 2018; Volume 41, pp. 215–242. [Google Scholar]
- De Anda, J.C.; Wang, X.; Lai, X.; Roberts, K.; Jennings, K.; Wilkinson, M.; Watson, D.; Roberts, D. Real-time product morphology monitoring in crystallization using imaging technique. Aiche J.
**2005**, 51, 1406–1414. [Google Scholar] [CrossRef] - Sankowski, D.; Sikora, J. Electrical Capacitance Tomography: Theoretical Basis and Applications; Wydawnictwo Książkowe Instytutu Elektrotechniki: Warsaw, Poland, 2010. [Google Scholar]
- Sattar, M.A.; Wrasse, A.D.N.; Morales, R.E.; Pipa, D.R.; Banasiak, R.; Da Silva, M.J.; Babout, L. Multichannel Capacitive Imaging of Gas Vortex in Swirling Two-Phase Flows Using Parametric Reconstruction. IEEE Access
**2020**, 8, 69557–69565. [Google Scholar] [CrossRef] - Wajman, R.; Banasiak, R.; Babout, L. On the Use of a Rotatable ECT Sensor to Investigate Dense Phase Flow: A Feasibility Study. Sensors
**2020**, 20, 4854. [Google Scholar] [CrossRef] - Kowalska, A.; Banasiak, R.; Romanowski, A.; Sankowski, D. 3D-printed multilayer sensor structure for electrical capacitance tomography. Sensors
**2019**, 19, 3416. [Google Scholar] [CrossRef][Green Version] - Koulountzios, P.; Rymarczyk, T.; Soleimani, M. A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes. Sensors
**2019**, 19, 5117. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rymarczyk, T.; Polakowski, K.; Sikora, J. A new concept of discretisation model for imaging improving in ultrasound transmission tomography. Inform. Autom. Pomiary Gospod. Ochr. Sr.
**2019**, 9. [Google Scholar] [CrossRef] - Saad, R.; Nawawi, M.N.M.; Mohamad, E.T. Groundwater detection in alluvium using 2-D electrical resistivity tomography (ERT). Electron. J. Geotech. Eng.
**2012**, 17, 369–376. [Google Scholar] - Rymarczyk, T.; Adamkiewicz, P.; Duda, K.; Szumowski, J.; Sikora, J. New electrical tomographic method to determine dampness in historical buildings. Arch. Electr. Eng.
**2016**, 65, 273–283. [Google Scholar] [CrossRef] - Kemna, A.; Vanderborght, J.; Kulessa, B.; Vereecken, H. Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models. J. Hydrol.
**2002**, 267, 125–146. [Google Scholar] [CrossRef] - Koestel, J.; Kemna, A.; Javaux, M.; Binley, A.; Vereecken, H. Quantitative imaging of solute transport in an unsaturated and undisturbed soil monolith with 3-D ERT and TDR. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef][Green Version] - Woo, E.J.; Hua, P.; Webster, J.G.; Tompkins, W.J. Measuring lung resistivity using electrical impedance tomography. IEEE Trans. Biomed. Eng.
**1992**, 39, 756–760. [Google Scholar] [CrossRef] - Sharifi, M.; Young, B. Electrical resistance tomography (ERT) applications to chemical engineering. Chem. Eng. Res. Des.
**2013**, 91, 1625–1645. [Google Scholar] [CrossRef] - Rao, G.; Aghajanian, S.; Koiranen, T.; Wajman, R.; Jackowska-Strumiłło, L. Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography. Appl. Sci.
**2020**, 10, 3903. [Google Scholar] [CrossRef] - Yang, Z.; Yan, G. Detection of Impact Damage for Composite Structure by Electrical Impedance Tomography. In ACMSM25; Springer: Berlin/Heidelberg, Germany, 2020; pp. 519–527. [Google Scholar]
- Ghaednia, H.; Owens, C.; Roberts, R.; Tallman, T.N.; Hart, A.J.; Varadarajan, K.M. Interfacial load monitoring and failure detection in total joint replacements via piezoresistive bone cement and electrical impedance tomography. Smart Mater. Struct.
**2020**, 29, 085039. [Google Scholar] [CrossRef][Green Version] - Gao, Z.; Rohani, S.; Gong, J.; Wang, J. Recent developments in the crystallization process: Toward the pharmaceutical industry. Engineering
**2017**, 3, 343–353. [Google Scholar] [CrossRef] - Su, Q.; Nagy, Z.K.; Rielly, C.D. Pharmaceutical crystallisation processes from batch to continuous operation using MSMPR stages: Modelling, design, and control. Chem. Eng. Process. Process Intensif.
**2015**, 89, 41–53. [Google Scholar] [CrossRef][Green Version] - Ricard, F.; Brechtelsbauer, C.; Xu, Y.; Lawrence, C.; Thompson, D. Development of an electrical resistance tomography reactor for pharmaceutical processes. Can. J. Chem. Eng.
**2005**, 83, 11–18. [Google Scholar] [CrossRef] - Ricard, F.; Brechtelsbauer, C.; Xu, X.; Lawrence, C. Monitoring of multiphase pharmaceutical processes using electrical resistance tomography. Chem. Eng. Res. Des.
**2005**, 83, 794–805. [Google Scholar] [CrossRef] - Nagy, Z.; Baker, M.; Pedge, N.; Steele, G. Supersaturation and Direct Nucleation Control of an Industrial Pharmaceutical Crystallisation Process Using a Crystallisation Process Informatics System; Delft Univ. Tech.: Delft, The Netherlands, 2011; pp. 7–9. [Google Scholar]
- Niderla, K.; Rymarczyk, T.; Sikora, J. Manufacturing planning and control system using tomographic sensors. Inform. Control. Econ. Environ. Prot.
**2018**, 8. [Google Scholar] [CrossRef][Green Version] - Dodd, R.; Chiou, A.; Broadfoot, R.; Yu, X. Industrial decision support requirements and expectations for a sugar mill crystallisation stage. In Proceedings of the IECON 2011—37th Annual Conference of the IEEE Industrial Electronics Society, Melbourne, VIC, Australia, 7–10 November 2011; pp. 3054–3059. [Google Scholar]
- Sharifi, M.; Young, B. Towards an online milk concentration sensor using ERT: Correlation of conductivity, temperature and composition. J. Food Eng.
**2013**, 116, 86–96. [Google Scholar] [CrossRef] - Nagy, Z.K.; Fevotte, G.; Kramer, H.; Simon, L.L. Recent advances in the monitoring, modelling and control of crystallization systems. Chem. Eng. Res. Des.
**2013**, 91, 1903–1922. [Google Scholar] [CrossRef] - Lindenberg, C.; Krättli, M.; Cornel, J.; Mazzotti, M.; Brozio, J. Design and optimization of a combined cooling/antisolvent crystallization process. Cryst. Growth Des.
**2009**, 9, 1124–1136. [Google Scholar] [CrossRef] - Kovács, I.; Harmat, P.; Sulyok, A.; Radnóczi, G. Investigation of the kinetics of crystallisation of Al/a-Ge bilayer by electrical conductivity measurement. Thin Solid Films
**1998**, 317, 34–38. [Google Scholar] [CrossRef] - Rao, G.; Jackowska-Strumiłło, L.; Sattar, M.A.; Wajman, R. Application of the 2D-ERT to evaluate phantom circumscribed regions in various sucrose solution concentrations. In Proceedings of the 2019 International Interdisciplinary PhD Workshop (IIPhDW), Wismar, Germany, 15–17 May 2019. [Google Scholar]
- Carletti, C.; Montante, G.; Westerlund, T.; Paglianti, A. Analysis of solid concentration distribution in dense solid-liquid stirred tanks by electrical resistance tomography. Chem. Eng. Sci.
**2014**, 119, 53–64. [Google Scholar] [CrossRef] - Hosseini, S.; Patel, D.; Ein-Mozaffari, F.; Mehrvar, M. Study of solid–liquid mixing in agitated tanks through electrical resistance tomography. Chem. Eng. Sci.
**2010**, 65, 1374–1384. [Google Scholar] [CrossRef] - Sardeshpande, M.V.; Kumar, G.; Aditya, T.; Ranade, V.V. Mixing studies in unbaffled stirred tank reactor using electrical resistance tomography. Flow Meas. Instrum.
**2016**, 47, 110–121. [Google Scholar] [CrossRef] - Stanley, S.; Mann, R.; Primrose, K. Interrogation of a precipitation reaction by electrical resistance tomography (ERT). Aiche J.
**2005**, 51, 607–614. [Google Scholar] [CrossRef] - Boulanger, L. Observations on variations in electrical conductivity of pure demineralized water: Modification (“activation”) of conductivity by low-frequency, low-level alternativing electric fields. Int. J. Biometeorol.
**1998**, 41, 137–140. [Google Scholar] [CrossRef] - Dickin, F.; Wang, M. Electrical resistance tomography for process applications. Meas. Sci. Technol.
**1996**, 7, 247. [Google Scholar] [CrossRef] - Ma, Y.; Wang, H.; Xu, L.-A.; Jiang, C. Simulation study of the electrode array used in an ERT system. Chem. Eng. Sci.
**1997**, 52, 2197–2203. [Google Scholar] [CrossRef] - Yan, P.; Mo, Y. Imaging the complex conductivity distribution in electrical impedance tomography. IFAC Proc. Vol.
**2003**, 36, 73–76. [Google Scholar] [CrossRef] - Mann, R.; Williams, R.A.; Dyakowski, T.; Dickin, F.; Edwards, R. Development of mixing models using electrical resistance tomography. Chem. Eng. Sci.
**1997**, 52, 2073–2085. [Google Scholar] [CrossRef] - Fransolet, E.; Crine, M.; L’Homme, G.; Toye, D.; Marchot, P. Electrical resistance tomography sensor simulations: Comparison with experiments. Meas. Sci. Technol.
**2002**, 13, 1239. [Google Scholar] [CrossRef] - Korteland, S.-A.; Heimovaara, T. Quantitative inverse modelling of a cylindrical object in the laboratory using ERT: An error analysis. J. Appl. Geophys.
**2015**, 114, 101–115. [Google Scholar] [CrossRef] - Xiao, L.; Xue, Q.; Wang, H. Finite element mesh optimisation for improvement of the sensitivity matrix in electrical resistance tomography. IET Sci. Meas. Technol.
**2015**, 9, 792–799. [Google Scholar] [CrossRef] - Wajman, R.; Banasiak, R. Tunnel-based method of sensitivity matrix calculation for 3D-ECT imaging. Sens. Rev.
**2014**, 34, 273–283. [Google Scholar] [CrossRef] - Kim, B.S.; Khambampati, A.K.; Kim, S.; Kim, K.Y. Image reconstruction with an adaptive threshold technique in electrical resistance tomography. Meas. Sci. Technol.
**2011**, 22, 104009. [Google Scholar] [CrossRef] - Vauhkonen, M.; Lionheart, W.R.; Heikkinen, L.M.; Vauhkonen, P.J.; Kaipio, J.P. A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images. Physiol. Meas.
**2001**, 22, 107. [Google Scholar] [CrossRef] [PubMed] - Adler, A.; Lionheart, W.R. Uses and abuses of EIDORS: An extensible software base for EIT. Physiol. Meas.
**2006**, 27, S25. [Google Scholar] [CrossRef] [PubMed][Green Version] - Polydorides, N.; Lionheart, W.R.B. A Matlab toolkit for three-dimensional electrical impedance tomography: A contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project. Meas. Sci. Technol.
**2002**, 13, 1871. [Google Scholar] [CrossRef] - Kim, B.S.; Khambampati, A.K.; Jang, Y.J.; Kim, K.Y.; Kim, S. Image reconstruction using voltage–current system in electrical impedance tomography. Nucl. Eng. Des.
**2014**, 278, 134–140. [Google Scholar] [CrossRef] - Groetsch, C.W.; Groetsch, C. Inverse Problems in the Mathematical Sciences; Springer: Berlin/Heidelberg, Germany, 1993; Volume 52. [Google Scholar]
- Vaukonen, M. Electrical Impedance Tomography and Prior Information. Ph.D. Thesis, University of Kuopio, Kuopio, Finland, 1997. [Google Scholar]
- Kim, B.S.; Kim, S.; Kim, K.Y. Image reconstruction with prior information in electrical resistance tomography. J. Ikee
**2014**, 18, 8–18. [Google Scholar] [CrossRef] - ChuanLei, W.; ShiHong, Y. New selection methods of regularization parameter for electrical resistance tomography image reconstruction. In Proceedings of the 2016 IEEE International Instrumentation and Measurement Technology Conference Proceedings, Taipei, Taiwan, 23–26 May 2016; pp. 1–5. [Google Scholar]
- Borsic, A.; Graham, B.M.; Adler, A.; Lionheart, W.R. Total variation regularization in electrical impedance tomography. Available online: http://eprints.maths.manchester.ac.uk/813/1/TVReglnEITpreprint.pdf (accessed on 1 October 2020).
- Ferrucci, M.; Leach, R.K.; Giusca, C.; Carmignato, S.; Dewulf, W. Towards geometrical calibration of x-ray computed tomography systems—a review. Meas. Sci. Technol.
**2015**, 26, 092003. [Google Scholar] [CrossRef] - Choi, C.T.M.; Sun, S.-H. Method for Improving Imaging Resolution of Electrical Impedance Tomography. U.S. Patent No 9,962,105, 8 May 2018. [Google Scholar]
- Cui, Z.; Wang, Q.; Xue, Q.; Fan, W.; Zhang, L.; Cao, Z.; Sun, B.; Wang, H.; Yang, W. A review on image reconstruction algorithms for electrical capacitance/resistance tomography. Sens. Rev.
**2016**, 36, 429–445. [Google Scholar] [CrossRef] - Tamburrino, A.; Ventre, S.; Rubinacci, G. Reconstruction techniques for electrical resistance tomography. IEEE Trans. Magn.
**2000**, 36, 1132–1135. [Google Scholar] - Yorkey, T.J.; Webster, J.G.; Tompkins, W.J. Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans. Biomed. Eng.
**1987**, BME-34, 843–852. [Google Scholar] [CrossRef] - Wilkinson, A.; Randall, E.; Long, T.; Collins, A. The design of an ERT system for 3D data acquisition and a quantitative evaluation of its performance. Meas. Sci. Technol.
**2006**, 17, 2088. [Google Scholar] [CrossRef] - Majchrowicz, M.; Kapusta, P.; Jackowska-Strumiłło, L.; Banasiak, R.; Sankowski, D. Multi-GPU, Multi-Node Algorithms for Acceleration of Image Reconstruction in 3D Electrical Capacitance Tomography in Heterogeneous Distributed System. Sensors
**2020**, 20, 391. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wang, B.; Huang, Z.; Li, H. Design of high-speed ECT and ERT system. In Proceedings of the Journal of Physics: Conference Series, Naha, Okinawa, Japan, 15–17 December 2008; IOP Publishing: Bristol, UK, 2009; Volume 147, p. 012035. [Google Scholar]
- Feng, D.; Cong, X.; Zhang, Z.; Shangjie, R. Design of parallel electrical resistance tomography system for measuring multiphase flow. Chin. J. Chem. Eng.
**2012**, 20, 368–379. [Google Scholar] - Garbaa, H.; Jackowska-Strumiłło, L.; Grudzień, K.; Romanowski, A. Application of electrical capacitance tomography and artificial neural networks to rapid estimation of cylindrical shape parameters of industrial flow structure. Arch. Electr. Eng.
**2016**, 65, 657–669. [Google Scholar] [CrossRef] - Bera, T.K.; Biswas, S.K.; Rajan, K.; Nagaraju, J. Projection Error Propagation-based regularization (PEPR) method for resistivity reconstruction in electrical impedance tomography (EIT). Measurement
**2014**, 49, 329–350. [Google Scholar] [CrossRef] - Li, S.; Wang, H.; Zhang, L.; Fan, W. Image reconstruction of electrical resistance tomography based on image fusion. In Proceedings of the 2011 IEEE International Instrumentation and Measurement Technology Conference, Binjiang, China, 10–12 May 2011; pp. 1–5. [Google Scholar]
- Giguère, R.; Fradette, L.; Mignon, D.; Tanguy, P.A. ERT algorithms for quantitative concentration measurement of multiphase flows. Chem. Eng. J.
**2008**, 141, 305–317. [Google Scholar] [CrossRef] - Kim, B.S.; Khambampati, A.K.; Kim, S.; Kim, K.Y. Improving spatial resolution of ERT images using adaptive mesh grouping technique. Flow Meas. Instrum.
**2013**, 31, 19–24. [Google Scholar] [CrossRef] - Yue, S.; Wu, T.; Pan, J.; Wang, H. Fuzzy clustering based ET image fusion. Inf. Fusion
**2013**, 14, 487–497. [Google Scholar] [CrossRef] - Yuling, W.; Meng, W.; Yan, Y.; Shulan, G. A method to recognize the contaminated area using K-means in ERT contaminated site surveys. In Proceedings of the 2018 IEEE International Conference on Information and Automation (ICIA), Wuyishan, China, 11–13 August 2018; pp. 1587–1591. [Google Scholar]
- Hampel, U.; Wondrak, T.; Bieberle, M.; Lecrivain, G.; Schubert, M.; Eckert, K.; Reinecke, S. Smart Tomographic Sensors for Advanced Industrial Process Control TOMOCON. Chem. Ing. Tech.
**2018**, 90, 1238–1239. [Google Scholar] [CrossRef][Green Version] - Jackson, R.F.; Silsbee, C.G. Saturation Relations in Mixtures of Sucrose, Dextrose, and Levulose; US Government Printing Office: Washington, DC, USA, 1924.
- Mathlouthi, M.; Reiser, P. Sucrose: Properties and Applications; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1995. [Google Scholar]

**Figure 1.**Schematic of the electrical resistance tomography (ERT) data acquisition and data processing system.

**Figure 3.**Factors affecting quantitative measurements using ERT as an imaging modality for the crystallization process.

**Figure 4.**(

**a**,

**b**) Setup of the laboratory-based batch reactor with sensor and signal conditioning unit mounted on the reactor; (

**c**) signal conditioning unit mounted on the 3D-printed frame.

**Figure 5.**(

**a**) Design of phantoms R1–R5; (

**b**) 3D-printed acrylonitrile butadiene styrene (ABS) phantoms; (

**c**) printing of sensor mounting unit and phantom R6; (

**d**) design and print of phantom R6.

**Figure 6.**Current detection at various electrodes in the reactor for (

**a**) industrial-grade saturated sucrose solution and tap water, and (

**b**) demineralized water.

**Figure 7.**(

**R1**–

**R5**) phantom reference; (

**a1**–

**a5**) Gauss–Newton (GN) reconstructions; (

**b1**–

**b5**) linear back projection (LBP) reconstructions; and (

**c1**–

**c5**) total variation (TV) reconstructions at 10 iterations for tap water.

**Figure 8.**(

**R1**–

**R5**) phantom reference; (

**a1**–

**a5**) Gauss–Newton reconstructions; (

**b1**–

**b5**) LBP reconstructions; and (

**c1**–

**c5**) TV reconstructions at 10 iterations for industrial grade saturated sucrose solution.

**Figure 9.**(

**R1**–

**R5**) phantom reference; (

**a1**–

**a5**) Gauss–Newton reconstructions; (

**b1**–

**b5**) LBP reconstructions; and (

**c1**–

**c5**) TV reconstructions at 10 iterations for demineralized water.

**Figure 10.**(

**a**) Changes in current at various electrodes after phantom placement; (

**b**) detailed view from electrode 2 to 14.

**Figure 11.**(

**a**) Tap water; (

**b**) industrial-grade saturated sucrose solution; (

**c**) demineralized water: (R5, R6-L1, R6-L2) phantom reference; (

**a1**–

**a3**) Gauss–Newton reconstructions; (

**b1**–

**b3**) LBP reconstructions; (

**c1**–

**c3**) TV reconstructions at 10 iterations.

**Figure 12.**(

**a0**–

**a5**) phantom R5 reference and TV iteration 10,8,6,4,2; (

**b1**–

**b5**) surface plot of the reconstructed images for phantom R5; (

**c0**–

**c5**) phantom R6-L1 reference and TV iteration 10,8,6,4,2; (

**d1**–

**d5**) surface plot of the reconstructed images for phantom R6-L1; (

**e0**–

**e5**) phantom R6-L2 reference and TV iteration 10,8,6,4,2; (

**f1**–

**f5**) surface plot of the reconstructed images for phantom R6-L2.

**Figure 13.**Various image segmentation methods for phantom R5. Solution: demineralized water, reconstruction method: total variation, iterations: 2.

**Figure 14.**Comparison of the area percentage for Otsu and G-Channel segmentation using TV, LBP, and GN reconstructions for (a) R1, (b) R2, (c) R3, (d) R4, and (e) R5.

**Figure 15.**Various image segmentation methods for R6-L1. Reconstruction method: total variation, iterations: 2, solution: demineralized water.

**Figure 17.**Contrast profile plot for phantom R6-L2 (2 × 10 mm), reconstruction: TV, iterations: 2–12; channel: green, location: 2.

**Figure 18.**Percentage area covered by phantoms at constant imaging threshold level and the varying number of iterations and erosion factors. Reconstruction: TV, iterations: 2–12; channel: green; for the phantoms (

**a**)R1; (

**b**) R2; (

**c**) R3; (

**d**) R4; (

**e**) R5.

**Figure 19.**Percentage area covered by phantoms at constant imaging thresholds and erosion factor and a varying number of iterations: combined view. Reconstruction: TV, iterations: 2–12; channel: green.

**Figure 20.**Percentage area covered by phantoms at a constant number of iterations and varying imaging thresholds and erosion levels. Reconstruction: TV, iterations: 2; channel: green; for the phantoms (

**a**) R1; (

**b**) R2; (

**c**) R3; (

**d**) R4; (

**e**) R5.

**Figure 21.**Percentage area covered by 2 × 10 mm (

**a**) phantom 1 and (

**b**) phantom 2 at various threshold levels. Reconstruction: TV, iterations: 2, channel: green.

**Figure 23.**Visualization of the sugar crystals in the demineralized solution at various frames representing time points. Reconstruction: TV, segmentation: Otsu and G-Channel at threshold 0.6.

Experimental Variable | Count | |
---|---|---|

1 | Number of solutions with varied conductivities | 3 |

2 | Number of phantoms | 6 |

3 | Number of reconstruction methods compared | 3 |

4 | Number of segmentation methods | 4 |

5 | Number of electrodes | 16 |

6 | Number of planes | 1 |

7 | Minimum accuracy tested | 1.5% of the beaker area |

8 | Location of object | Central and incremental, separability |

Object | Measured Values mm | |
---|---|---|

1 | Batch reactor’s inner diameter | 83 |

2 | Electrode tail diameter | 5 |

3 | Electrode head diameter | 12 |

Phantom | Measured Values mm | Expected Percentage Area of the Phantom Region (A_{P})% | |
---|---|---|---|

1 | Phantom R1 | 50 ± 0.1 | 36.28 |

2 | Phantom R2 | 40 ± 0.1 | 23.22 |

3 | Phantom R3 | 30 ± 0.1 | 13.06 |

4 | Phantom R4 | 20 ± 0.1 | 5.8 |

5 | Phantom R5 | 10 ± 0.1 | 1.45 |

6 | Phantom R6 | 2 × 10 ± 0.1 | 1.45 and 1.45 |

5 | Diameter of the base of phantoms | 50 | |

7 | Distance between centers of phantom R6 | 40 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rao, G.; Sattar, M.A.; Wajman, R.; Jackowska-Strumiłło, L.
Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments. *Sensors* **2021**, *21*, 564.
https://doi.org/10.3390/s21020564

**AMA Style**

Rao G, Sattar MA, Wajman R, Jackowska-Strumiłło L.
Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments. *Sensors*. 2021; 21(2):564.
https://doi.org/10.3390/s21020564

**Chicago/Turabian Style**

Rao, Guruprasad, Muhammad Awais Sattar, Radosław Wajman, and Lidia Jackowska-Strumiłło.
2021. "Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments" *Sensors* 21, no. 2: 564.
https://doi.org/10.3390/s21020564