Data-driven approaches for electrical impedance tomography image segmentation from partial boundary data

TL;DR

This work tackles the problem of segmenting electrical impedance tomography (EIT) images from partial boundary data. It introduces three data-driven methods built on a common U‑Net backbone: FC U‑Net (learned reconstruction to a 64×64 grid with upsampling), Post‑Processing (learned post-processing of multiple linearised reconstructions), and Conditional‑Diffusion (conditional diffusion modelling for segmentation). The methods are trained on a large synthetic dataset and evaluated in the Kuopio tomography challenge 2023, with Post‑Processing achieving the best overall score and FC U‑Net showing strong performance on several levels; Conditional‑Diffusion underperformed comparatively but offers a path to uncertainty-aware segmentation. The study highlights the importance of dataset design, level-conditioning, and practical choices (mesh, initial reconstruction) for generalisation to real measurements and suggests future work on uncertainty quantification and robust cross-domain performance.

Abstract

Electrical impedance tomography (EIT) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches were originally submitted to the Kuopio tomography challenge 2023 (KTC2023). First, we introduce a post-processing approach, which achieved first place at KTC2023. Further, we present a fully learned and a conditional diffusion approach. All three methods are based on a similar neural network as a backbone and were trained using a synthetically generated data set, providing with an opportunity for a fair comparison of these different data-driven reconstruction methods.

Figures (10)

• Figure 1: An illustration of the EIT measurement tank ($\Omega$), the electrodes $e_l$, with a sample of the injection patterns. In black we show the adjacent injections; in green all against$e_1$; in pink all against$e_9$; in magenta all against$e_{17}$; in orange all against$e_{25}$. Dashed injection are removed in the $2^{\text{nd}}$ challenge level; dotted ones in the $4^{\text{th}}$; dash dotted in the $6^{\text{th}}$.
• Figure 2: Example initial reconstructions on challenge levels 1 and 6. Level 6 was chosen as it best highlights differences in linearised reconstructions. We evaluate an independent FSM prior, independent SM prior, joint SM+LM prior and two joint priors FSM+SM+LM with different regularisation strengths. The chosen image is a sample of the validation data.
• Figure 3: FC U-Net network. We first use a linear layer to map the measurements to a $64 \times 64$ pixel grid, this is then bilinearly interpolated to the $256 \times 256$ grid. The network is trained to output class probabilities using categorical cross-entropy loss. The class probabilities are converted to segmentation maps by assigning the class with highest probability.
• Figure 4: Post-Processing network. The five linearised reconstructions are interpolated to the pixel grid as described in Section \ref{['sec:initial_reconstruction']}. The network is trained to output class probabilities using categorical cross-entropy loss. The class probabilities are converted to segmentation maps by assigning the class with highest probability.
• Figure 5: Conditional-Diffusion network. The five linearised reconstructions are interpolated to the pixel grid as described in Section \ref{['sec:initial_reconstruction']}. The noisy image and linearised reconstructions are input into the network. Using the $\boldsymbol{\epsilon}$-matching loss function, the network is trained to estimate the noise. Through sampling the network a segmentation map is obtained. Multiple samples are drawn through pixel-wise majority voting the final segmentation map is obtained.