Improving stochastic reconstructions by weighting correlation functions in an objective function

Spatial correlation functions (CFs) are prominent descriptors of any structure. In this letter, we show for the first time how proper weighting of CFs in an objective function can lead to significant improvements in reconstruction accuracy and in the likelihood of convergence. We develop a simple weighting scheme and display its effectiveness on two- and three-dimensional structures utilizing up to 27 CFs in one set. Proper weighting of the objective functions led to completely accurate reconstructions not achievable by conventional unweighted approaches. The proposed approach combining numerous CFs can potentially characterize and reconstruct structures of any complexity

Improving pattern reconstruction using directional correlation functions

In this letter we introduce a new method to calculate correlation functions in four principal directions (i.e. two orthogonal and two diagonal) and separately utilize them for image reconstruction. We show that this method is particularly suitable for anisotropic porous media but that it also improves image reconstruction for isotropic structures. Based on the analysis of numerous reconstructions of four binary patterns using different sets of two-point probability and linear (for both phases) correlation functions, we quantify the accuracy of each set. Averaging of correlation functions in all directions almost always results in poorer reconstructions. Addition of separate directions significantly improves the quality of replicas with only a minor increase in computational effort

Mimicking 3D food microstructure using limited statistical information from 2D cross-sectional image

We used statistical correlation functions (CFs) to describe food microstructure and to reconstruct their 3D complexity by using limited information coming from single 2D microtomographic images. Apple fleshy parenchyma tissue and muffin crumb were chosen to test the ability of the reconstructions to mimic structural diversities. Several metrics based on morphological measures and cluster functions were utilized to analyze the fidelity of reconstructions. For the apple, reconstructions are accurate enough proving that lineal, L2, and two-point, S2, functions sufficiently describe the complexity of apple tissue. Muffin structure is isotropic but statistically inhomogeneous showing at least two different porosity domains which reduced the fidelity of reconstructions. Further improvement could be obtained by using more CFs as input data and by implementation of the techniques dealing with statistical non-stationarity. Novel stochastic reconstruction and CF-based characterization methods could improve the fidelity of reconstruction and future advances of this technology will allow estimating macroscopic food properties based on (limited) 2/3D input information

Main concepts of the morphological analysis.

<p>a) morphological parameters calculated for each pore element, and b) examples of pores extracted from original soil images and their shape classifications (all five shape classes are shown in roundness (<i>4πA/P</i>^<i>2</i>)—isometry (<i>D/L</i>) coordinates).</p

Comparison of <i>C</i>_<i>2</i> cluster functions for original and reconstructed soil images for a) soil type I (best case), and b) soil type V (worst case).

<p>The legend is similar to that of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126515#pone.0126515.g004" target="_blank">Fig 4</a> for two-point probability and linear functions.</p

Overall scheme of the reconstruction procedure.

<p>Illustrations are provided for each stage using reconstruction of circles as example.</p

Soil thin-section information.

<p>*according to Russian soil classification [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126515#pone.0126515.ref083" target="_blank">83</a>]</p><p>Soil thin-section information.</p

All original eight soil type images (left column) with their best performing reconstructions based on a cluster function analysis (middle column) or pore morphological analysis (right column) (if reconstruction performance for both analyses is identical, then only one image is shown).

<p>Size of thin section = 2.1×2.1 cm^<i>2</i>. Blue shaded areas highlight pore features that were poorly reconstructed: type II) vertical pore; III) complex elongated pores; V) one connected pore dominating entire image; VI) one connected fissure-like pore; VII) numerous horizontal cracks; VIII) horizontal features in the upper-right marked region.</p

Correlation functions for pores (solid and dashed lines) and solid phase (dash dot line).

<p><b><i>S</i></b>_{<b><i>2</i></b>}^{<b><i>(w)</i></b>}<b>and <i>L</i></b>_{<b><i>2</i></b>}^{<b><i>(w)</i></b>}<b>are, respectively, two-point probability and linear functions for pore phase; <i>L</i></b>_{<b><i>2</i></b>}^{<b><i>(b)</i></b>}<b>is a linear function for solid phase.</b> All correlation functions are evaluated in four principal directions according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126515#pone.0126515.g001" target="_blank">Fig 1</a>. Example is for soil type I exhibiting the largest spatial correlation length of <i>L</i>_{<b><i>2</i></b>}^<i>(b)</i> across all soil types.</p