Article Contents

2024, Volume 2, Issue 2: 93-118. Doi: 10.3934/ammc.2024009

This issue Previous Article Next Article Data-driven approaches for electrical impedance tomography image segmentation from partial boundary data

Kuopio tomography challenge 2023 – electrical impedance tomography competition and open dataset

Department of Technical Physics, University of Eastern Finland, Finland

^*Corresponding author: Mikko Räsänen
^*Corresponding author: Mikko Räsänen

Received: April 2024

Revised: May 2024

Early access: June 2024

Published: June 2024

Abstract / Introduction Full Text(HTML) Figure(13) / Table(4) Related Papers Cited by

Abstract

This paper introduces the Kuopio Tomography Challenge 2023 (KTC 2023), created to inspire and facilitate algorithm development for image reconstruction in electrical impedance tomography (EIT). A laboratory EIT dataset was prepared for the KTC 2023, using conductive and resistive inclusions of various shapes and sizes placed inside a shallow, circular water tank. The task for the competitors of the challenge was to produce segmented images of the inclusions from EIT data in cases of complete coverage of the tank surface with electrodes (lowest level of difficulty) and in cases of decreasing boundary coverage (corresponding to increasing level of challenge difficulty). A total of seven teams, with members from seven countries, participated in KTC 2023, submitting a total of 22 algorithms. The results of the competition show a variety of novel algorithms applied to real EIT data, with high quality image reconstructions from limited boundary data. The EIT data set collected for the challenge is publicly available for future studies on EIT image reconstruction.

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Mathematics Subject Classification: Primary: 35R30, 65K05; Secondary: 90-06.

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Figure 1. Left: Photograph of the water tank before water and inclusions were added. Right: Experimental setup; The KIT4 EIT system is behind the table where the tank is placed. Photographs of the targets were taken from straight above the tank using camera fixed to a frame attached on the ceiling

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Figure 2. Photographs of the four non-homogeneous targets used for the training data set. The significance of colors: Red – metallic, orange – conductive plastic and blue – insulating plastic

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Figure 3. Photographs of the targets used for the evaluation data: Rows 1–4 correspond to difficulty levels 1–4. Photos in columns 1–3 correspond to samples A-C in each of the difficulty levels. The significance of colors: Red – metallic, orange – conductive plastic and blue – insulating plastic

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Figure 4. Photographs of the targets used for the evaluation data: Rows 1–3 correspond to difficulty levels 5–7. Photos in columns 1–3 correspond to samples A-C in each of the difficulty levels. The significance of colors: Red – metallic, orange – conductive plastic and blue – insulating plastic

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Figure 5. Positioning of the circular water chamber in the ground truth pixel images. The red line represents the inner boundary of the water chamber. The pixel size is exaggerated for the sake of illustration

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Figure 6. Left: Photo of the water tank with a single resistive plastic inclusion (blue color) and a single conductive plastic inclusion (orange color). Right: The 256 by 256 ground truth image with the inner boundary of the tank (dashed red line) and the center point of electrode 1 (red, filled circle)

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Figure 7. KTC 2023 results, difficulty level 1, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 8. KTC 2023 results, difficulty level 2, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 9. KTC 2023 results, difficulty level 3, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 10. KTC 2023 results, difficulty level 4, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 11. KTC 2023 results, difficulty level 5, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 12. KTC 2023 results, difficulty level 6, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Figure 13. KTC 2023 results, difficulty level 7, Samples A, B and C. Conductive inclusions are in yellow, and insulating inclusions in light blue

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Table 1. Electrode data removed in each difficulty level. Here, $ N_{ \text{inj}} $ is the number of current injections used in the difficulty level, and $ N_{ \text{meas}} $ is the total number of voltage measurements in the respective difficulty level

Difficulty level	Removed electrodes	$ N_{ \text{inj}} $	$ N_{ \text{meas}} $
1	-	76	76$ \cdot $31 = 2356
2	1, 2	56	56$ \cdot $29 = 1624
3	1, 2, 3, 4	52	52$ \cdot $27 = 1404
4	1, ..., 6	48	48$ \cdot $25 = 1200
5	1, ..., 8	44	44$ \cdot $23 = 1012
6	1, ..., 10	30	30$ \cdot $21 = 630
7	1, ..., 12	27	27$ \cdot $19 = 513

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Table 2. Scores for the evaluation dataset obtained by the example reconstruction algorithm

Level	Sample A	Sample B	Sample C	Total
1	0.74366	0.64263	0.40896	1.79526
2	0.43108	0.22285	0.39186	1.04580
3	0.03469	0.67738	0.04147	0.75355
4	0.39865	0.17563	0.38461	0.95890
5	0.21297	0.27110	0.19635	0.68043
6	0.37339	0.20651	0.18207	0.76198
7	-0.04006	0.17774	0.36839	0.50606

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Table 3. Scores for each sample of the evaluation dataset

Team	Sample	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6	Level 7
$ 01_A $	$ S_n^A $	0.96022	0.89867	0.6643	0.74566	0.18621	0.77558	0.32852
	$ S_n^B $	0.95039	0.69985	0.87397	0.43677	0.60947	0.50172	0.15754
	$ S_n^C $	0.82262	0.89145	0.55774	0.60814	0.30516	0.25955	0.73562
$ 01_B $	$ S_n^A $	0.97251	0.82065	0.35046	0.79256	0.14521	0.72385	0.22862
	$ S_n^B $	0.91261	0.76015	0.84484	0.34345	0.13734	0.45158	0.32337
	$ S_n^C $	0.81064	0.71778	0.54393	0.20099	0.60858	0.32503	0.72188
$ 02_A $	$ S_n^A $	0.92357	0.93093	0.095934	0.65215	0.32268	0.75603	0.21424
	$ S_n^B $	0.90302	0.69122	0.85972	0.3158	0.1298	0.50926	0.53206
	$ S_n^C $	0.81248	0.43986	0.5924	0.55071	0.71876	0.22107	0.30813
$ 02_B $	$ S_n^A $	0.9543	0.9061	0.16182	0.72593	0.34726	0.79047	0.28903
	$ S_n^B $	0.97966	0.76502	0.86991	0.49435	0.10537	0.55468	0.35868
	$ S_n^C $	0.84124	0.92168	0.60296	0.46234	0.23622	0.19323	0.24486
$ 02_C $	$ S_n^A $	0.94759	0.83111	0.097536	0.64512	0.34038	0.67726	0.22933
	$ S_n^B $	0.95374	0.62278	0.89066	0.35399	0.63045	0.50848	0.24818
	$ S_n^C $	0.77218	0.85234	0.55082	0.59148	0.66317	0.19497	0.75289
$ 02_D $	$ S_n^A $	0.9395	0.78964	0.16184	0.53982	0.29484	0.66331	0.20619
	$ S_n^B $	0.88266	0.66224	0.85737	0.35005	0.10124	0.46223	0.38249
	$ S_n^C $	0.78311	0.77796	0.54221	0.45008	0.63658	0.18085	0.74966
$ 02_E $	$ S_n^A $	0.70129	0.69321	0.67504	0.60476	0.16392	0.58817	0.40335
	$ S_n^B $	0.74008	0.6715	0.58318	0.0049623	0.0051137	0.10121	0.0020536
	$ S_n^C $	0.84037	0.63107	0.49829	0.13559	0.3429	0.2353	0.59488
$ 02_F $	$ S_n^A $	0.67071	0.69062	0.00022063	0.70433	0.21532	0.59601	0.40447
	$ S_n^B $	0.75342	0.79923	0.6854	0.0047347	0.0051137	0.24267	0.12096
	$ S_n^C $	0.85153	0.64599	0.4965	0.17775	0.59038	0.22363	0.6039
$ 02_G $	$ S_n^A $	0.96012	0.83245	0.18944	0.67692	0.46376	0.68013	0.29482
	$ S_n^B $	0.928	0.88034	0.90873	0.51759	0.2772	0.49687	0.59512
	$ S_n^C $	0.43078	0.86668	0.7769	0.43049	0.73585	0.29868	0.80019
$ 02_H $	$ S_n^A $	0.95063	0.723	0.20296	0.58708	0.45519	0.60342	0.23514
	$ S_n^B $	0.76766	0.87723	0.88354	0.42999	0.28303	0.45394	0.53747
	$ S_n^C $	0.3791	0.77866	0.67881	0.4439	0.6831	0.38215	0.77077
$ 02_I $	$ S_n^A $	0.74082	0.70654	0.63096	0.67211	0.37867	0.40685	0.46816
	$ S_n^B $	0.78706	0.74854	0.77409	0.40437	0.0051149	0.41118	0.15005
	$ S_n^C $	0.8313	0.70894	0.57827	0.29434	0.45781	0.18463	0.64957
$ 03 $	$ S_n^A $	0.31726	0.71536	0.039398	0.0275	0.04735	0.55186	-0.016521
	$ S_n^B $	0.74241	0.078789	0.74837	0.093607	0.072756	0.063483	0.016966
	$ S_n^C $	0.1979	0.63888	0.50679	0.38619	0.63042	0.15272	0.040005
$ 04 $	$ S_n^A $	0.93263	0.91325	0.42413	0.76044	0.14708	0.65121	0.20317
	$ S_n^B $	0.80267	0.75273	0.82493	0.34089	0.59773	0.053328	0.17242
	$ S_n^C $	0.83335	0.83655	0.52072	0.65756	0.60804	-0.011826	0.75069
$ 05_A $	$ S_n^A $	0.62816	0.54254	0.53309	0.33792	0.056015	0.56261	0.26702
	$ S_n^B $	0.62809	0.53061	0.63073	0.10184	0.53474	0.13624	0.091781
	$ S_n^C $	0.57522	0.56074	0.50374	0.2563	0.03376	0.20809	0.52682
$ 05_B $	$ S_n^A $	0.82986	0.92322	0.034751	0.45707	0.32957	0.23335	0.016423
	$ S_n^B $	0.85027	0.32074	0.80436	0.38807	0.076231	0.039543	0.099949
	$ S_n^C $	0.84768	0.90828	0.62383	0.26928	0.37191	-0.011823	0.68647
$ 05_C $	$ S_n^A $	0.94287	0.26324	0.64302	0.52486	0.27899	0.24078	0.18025
	$ S_n^B $	0.89078	0.62664	0.40502	0.22462	0.57887	0.22329	0.2018
	$ S_n^C $	0.28965	0.75373	0.52108	0.52755	0.16606	0.11553	0.70783
$ 06_A $	$ S_n^A $	0.92474	0.92357	0.55259	0.78262	0.41037	0.76931	0.38347
	$ S_n^B $	0.96431	0.8366	0.86621	0.64495	0.8653	0.64495	0.22513
	$ S_n^C $	0.83624	0.88801	0.85767	0.43116	0.78104	0.56085	0.81422
$ 06_B $	$ S_n^A $	0.98701	0.92507	0.7828	0.70106	0.5266	0.63942	0.49924
	$ S_n^B $	0.96612	0.85026	0.94716	0.66409	0.88019	0.69662	0.33437
	$ S_n^C $	0.89048	0.91984	0.89483	0.57398	0.80711	0.67289	0.86934
$ 06_C $	$ S_n^A $	0.98627	0.92142	0.74469	0.7508	0.43544	0.78684	0.5849
	$ S_n^B $	0.96342	0.79049	0.92438	0.67478	0.81362	0.47867	0.32063
	$ S_n^C $	0.83909	0.9238	0.87488	0.45797	0.83364	0.57153	0.8739
$ 07_A $	$ S_n^A $	0.95804	0.7628	0.12818	0.32632	0.23696	0.090063	0.11749
	$ S_n^B $	0.94151	0.10898	0.37218	0.24965	0.14233	0.25999	0.21642
	$ S_n^C $	0.32321	0.66734	0.51948	0.21429	0.53912	0.14121	0.22274
$ 07_B $	$ S_n^A $	0.96217	0.9236	0.25007	0.5347	0.24355	0.20699	0.34255
	$ S_n^B $	0.98301	0.79505	0.25037	0.43474	0.15299	0.32765	0.26197
	$ S_n^C $	0.83442	0.9243	0.72187	0.2231	0.79925	0.24585	0.25705
$ 07_C $	$ S_n^A $	0.98101	0.83101	0.24815	0.5074	0.17852	0.28831	0.33178
	$ S_n^B $	0.9162	0.76933	0.2601	0.52666	0.16415	0.38689	0.26087
	$ S_n^C $	0.34009	0.84241	0.67362	0.31698	0.40674	0.23883	0.28641

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Table 4. The scores obtained by each solution for each difficulty level, and the leaderboard positions of the teams. We note that the drop-out feature explained in the scoring rules of the challenge affected the leaderboard positions, such that the positions are not completely ordered according to the Total Scores only

Team	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Total score	Position
$ 01_A $	2.7332	2.49	2.096	1.7906	1.1008	1.5369	1.2217	12.9692	2nd
$ 01_B $	2.6958	2.2986	1.7392	1.337	0.89113	1.5005	1.2739	11.7361
$ 02_A $	2.6391	2.062	1.5481	1.5187	1.1712	1.4864	1.0544	11.4798
$ 02_B $	2.7752	2.5928	1.6347	1.6826	0.68885	1.5384	0.89256	11.8051
$ 02_C $	2.6735	2.3062	1.539	1.5906	1.634	1.3807	1.2304	12.3545
$ 02_D $	2.6053	2.2298	1.5614	1.34	1.0327	1.3064	1.3383	11.4139
$ 02_E $	2.2817	1.9958	1.7565	0.74531	0.51193	0.92468	1.0003	9.2162
$ 02_F $	2.2757	2.1358	1.1821	0.88682	0.81082	1.0623	1.1293	9.4829
$ 02_G $	2.3189	2.5795	1.8751	1.625	1.4768	1.4757	1.6901	13.0411	2nd
$ 02_H $	2.0974	2.3789	1.7653	1.461	1.4213	1.4395	1.5434	12.1068
$ 02_I $	2.3592	2.164	1.9833	1.3708	0.8416	1.0027	1.2678	10.9894
$ 03_A $	1.2576	1.433	1.2946	0.5073	0.75052	0.76806	0.04045	6.0515	6th
$ 04 $	2.5686	2.5025	1.7698	1.7589	1.3528	0.69271	1.1263	11.7717	3rd
$ 05_A $	1.8315	1.6339	1.6676	0.69606	0.62452	0.90694	0.88562	8.2461
$ 05_B $	2.5278	2.1522	1.4629	1.1144	0.77772	0.26107	0.80284	9.099
$ 05_C $	2.1233	1.6436	1.5691	1.277	1.0239	0.5796	1.0899	9.3065	4th
$ 06_A $	2.7253	2.6482	2.2765	1.8587	2.0567	1.9751	1.4228	14.9633
$ 06_B $	2.8436	2.6952	2.6248	1.9391	2.2139	2.0089	1.703	16.0285	1st
$ 06_C $	2.7888	2.6357	2.5439	1.8836	2.0827	1.837	1.7794	15.5512
$ 07_A $	2.2228	1.5391	1.0198	0.79026	0.9184	0.49126	0.55665	7.5383
$ 07_B $	2.7796	2.643	1.2223	1.1925	1.1958	0.78049	0.86157	10.6753	5th
$ 07_C $	2.2373	2.4427	1.1819	1.351	0.74942	0.91403	0.87905	9.7555

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