## 3 Materials and Methods
### Input Data
#### 3.1.2 3D ECT Image Dataset  
A dataset of 1042 3D ECT data samples was considered in this study. Each data sample consisted of a phantom and corresponding phantom 3D ECT reconstructions obtained for 4 \(\times\) 4 and 4 \(\times\) 8 electrode sets. The phantoms were generated automatically and represented four equally distributed types of object shapes, namely, balls, rods, and H-shape, and L-shape. The parameters of the shapes, including size, number, position, and orientation, were selected randomly (cf. Table 1). Understanding the interplay between the object parameters for a 3D ECT image dataset and non-uniform electric fields in 3D ECT models is crucial for image quality evaluation. There are also 3D ECT sensor model specific regions within the sensing volume, where changes in object properties have a minimal effect on the measured capacitance. These zones are due to factors such as non-uniform electric fields, electrode geometry, and object properties. The presence of sensitivity dead zones can limit the accuracy of object reconstruction in certain regions and can influence the Quality Assessment. The size of an object significantly affects the magnitude and distribution of the electric field and dead zones as well. Larger objects tend to induce greater capacitance changes, while smaller objects may have limited impact. Multiple objects within the sensing volume can interact and influence each other's electric fields, leading to complex capacitance patterns. The relative positions of the objects within the sensing volume determine the spatial distribution of the electric field. Objects closer to the electrodes will generally have a stronger influence on the measured capacitance. The orientation of objects can affect the direction and magnitude of capacitance changes. For example, a long, thin object oriented parallel to the electric field lines will induce a different capacitance change than one oriented perpendicularly.  
The non-linear reconstruction method (NLECTCM) was applied for both electrode sets, to reconstruct the phantom data. In the phantom data, nodes representing an object  
Figure 5: 3D ECT image cross-sectional view of finite element grid represented as an undirected graph \(\mathcal{G}\) with \(\mathcal{V}\) nodes set (gray dots) and \(\mathcal{E}\) edges set (white lines). Blue indicates lower electrical permittivity (less dense material), while red indicates higher electrical permittivity (denser material) and the location of objects.  
were assigned an electric permittivity of 3, while nodes representing air stored an electric permittivity of 1.  
The FEM-based graphs representing phantom data \(\mathcal{G}_{p}\) and the corresponding 3D ECT reconstructions obtained with different electrode sets (i.e., \(\mathcal{G}^{\prime}{}_{4\times 4}\) and \(\mathcal{G}^{\prime}{}_{4\times 8}\)) exhibited the same structure with \(N\) = 25,350 vertices and \(M\) = 67,974 edges. Thus, each phantom in the dataset had two reconstructions, a High-Quality (HQ) one \(\mathcal{G}^{\prime}{}_{4\times 8}\), and a Low-Quality (LQ) one \(\mathcal{G}^{\prime}{}_{4\times 4}\). This variation was necessary, to assess the relationship between image quality and the similarity calculated by GQA methods between the image and its corresponding phantom. Sample Low-Quality and High-Quality reconstructions of the H-shape phantom are shown in Figure 6.