Stochastic reconstruction using multiple correlation functions with different-phase-neighbor-based pixel selection

A reconstruction methodology based on threshold energy based energy minimization (TA) and different-phase-neighbor (DPN)-based pixel swapping is presented. The TA method uses an energy threshold rather than probabilities as an acceptance criteria for annealing steps. The DPN-based pixel selection method gives priority to pixels which are segregated from clusters instead of random selection. An in-house solver has been developed to obtain two-dimensional reconstructions of heterogeneous two-phase mediums. Compared to conventional simulated annealing with random pixel swapping, the proposed method was found to achieve an optimal structure with up to an order of magnitude reduction in energy. When selecting a threshold tolerance value, the proposed method showed a 50% improvement in convergence time compared to conventional simulated annealing with random pixel swapping. The improved algorithm is used to study the effect of multiple correlation functions during the reconstruction. It was found that a combination of two-point correlation function and lineal path function for both phases results in most accurate reconstructions.

Figure 1

An illustration of chords in a two phase medium.

Figure 2

(a) A normal sampling for chord search. (b) A periodic sampling for chord search.

Figure 3

(a) Illustration of different-phase neighbors of a pixel. (b) Demonstration of biased pixel selection based on DPN. Geometries in decreasing order of priority for pixel of interest.

Figure 4

Reconstruction of a square grid pattern. (a) Reference image. (b) SA based reconstruction. (c) TA based reconstruction.

Figure 5

Comparison of energy convergence for SA based and TA based algorithms for a square grid geometry. Solid line represents average and shaded region represents 95% confidence interval.

Figure 6

(a) A SEM image of PEFC catalyst layer. (b) The binary SEM image after thresholding.

Figure 7

Reconstructions of PEFC catalyst layer. (a) Reconstruction using SA algorithm. (b) Reconstruction using TA algorithm.

Figure 8

Comparison of energy convergence for SA based and TA based algorithms for a PEFC catalyst layer image. Solid line represents average and shaded region represents 95% confidence interval (not visible as the error margin is negligible).

Figure 9

A coarse reconstruction of PEFC catalyst layer using random swapping, used as starting point with $E=4.99\times {10}^{-3}$.

Figure 10

Reconstructed images of PEFC catalyst layer. (a) Reconstruction using DPN base swapping. (b) Reconstruction using interfacial swapping.

Figure 11

Comparison of energy convergence for random, interfacial, and DPN based pixel swapping. Solid line represents average and shaded region represents 95% confidence interval (not visible as the error margin is negligible).

Figure 12

Evolution of reconstructed structures through different stages of reconstruction using DPN based pixel swapping. (a) At iteration number 0, $E=4.99\times {10}^{-3}$. (b) At iteration number 1984, $E=9.97\times {10}^{-4}$. (c) At iteration number $10497$, $E=9.99\times {10}^{-5}$. (d) At iteration number $170502$, $E=9.96\times {10}^{-6}$. (e) At iteration number $386853$, $E=9.93\times {10}^{-7}$.

Figure 13

Comparison of correlation functions for reference and reconstructed PEFC catalyst layer images. Solid line represents average and shaded region represents 95% confidence interval for 15 trials. (a) For reconstruction using $S_2^{\left(v\right)}\left(r\right)$ only. (b) For reconstruction using $S_2^{\left(v\right)}\left(r\right)$, $L^{\left(s\right)}\left(z\right)$, and $L^{\left(v\right)}\left(z\right)$.