This paper deals with the simulation of microbial degradation of organic matter in soil within the pore space at a microscopic scale. Pore space was analysed with micro-computed tomography and ...described using a sphere network coming from a geometrical modelling algorithm. The biological model was improved regarding previous work in order to include the transformation of dissolved organic compounds and diffusion processes. We tested our model using experimental results of a simple substrate decomposition experiment (fructose) within a simple medium (sand) in the presence of different bacterial strains. Separate incubations were carried out in microcosms using five different bacterial communities at two different water potentials of -10 and -100 cm of water. We calibrated the biological parameters by means of experimental data obtained at high water content, and we tested the model without changing any parameters at low water content. Same as for the experimental data, our simulation results showed that the decrease in water content caused a decrease of mineralization rate. The model was able to simulate the decrease of connectivity between substrate and microorganism due the decrease of water content.
•New experimental data set of 3D images of air–water interfaces in a soil.•Remarkably accurate prediction of air–water interfaces by the two-phase LBM.•Acceptable prediction of air–water interfaces ...by the morphological MOSAIC model.
Recent progress in the understanding of soil microbial processes at micrometric scales has created a need for models that accurately predict the microscale distribution of water, and the location of air–water interfaces in pores. Various models have been developed and used for these purposes, but how well they fare against real data has yet largely to be determined. In this context, for the first time, this article compares the prediction of two of these models to experimental data obtained on soil material. The distribution of water and air in soil samples constituted of repacked aggregates, equilibrated at three matric potentials (−0.5 kPa, −1 kPa and −2 kPa), was measured via synchrotron X-ray computed tomography at a resolution of 4.6 µm. Water distribution was simulated by a two-phase lattice Boltzmann model (LBM) and a morphological model (MOSAIC). Results indicate that, when one lifts the assumption, motivated by capillary theory, that a pore can drain only if a connecting pore is already full of air, MOSAIC gives an acceptable approximation of the observed air–water interfaces. However, discretization of pores as geometrical primitives causes interfaces predicted by MOSAIC to have nonphysical shapes. By contrast, LBM is able to predict remarkably well the location of air–water interfaces. Nevertheless, given the huge difference in computing time (minutes versus tens of hours) required to run these two models, it is recommended that further research be carried out on the development of both, in parallel.
The pore size distribution (PSD) of the void space is widely used to predict a range of processes in soils. Recent advances in X-ray computed tomography (CT) now afford novel ways to obtain exact ...data on pore geometry, which has stimulated the development of algorithms to estimate the pore size distribution from 3D data sets. To date there is however no clear consensus on how PSDs should be estimated, and in what form PSDs are best presented. In this article, we first review the theoretical principles shared by the various methods for PSD estimation. Then we select methods that are widely adopted in soil science and geoscience, and we use a robust statistical method to compare their application to synthetic image samples, for which analytical solutions of PSDs are available, and X-ray CT images of soil samples selected from different treatments to obtain wide ranging PSDs. Results indicate that, when applied to the synthetic images, all methods presenting PSDs as pore volume per class size (i.e., Avizo, CTAnalyser, BoneJ, Quantim4, and DTM), perform well. Among them, the methods based on Maximum Inscribed Balls (Bone J, CTAnalyser, Quantim4) also produce similar PSDs for the soil samples, whereas the Delaunay Triangulation Method (DTM) produces larger estimates of the pore volume occupied by small pores, and Avizo yields larger estimates of the pore volume occupied by large pores. By contrast, the methods that calculate PSDs as object population fraction per volume class (Avizo, 3DMA, DFS-FIJI) perform inconsistently on the synthetic images and do not appear well suited to handle the more complex geometries of soils. It is anticipated that the extensive evaluation of method performance carried out in this study, together with the recommendations reached, will be useful to the porous media community to make more informed choices relative to suitable PSD estimation methods, and will help improve current practice, which is often ad hoc and heuristic.
•The need to evaluate existing methods for pore size distribution estimation is explained.•A review of the theoretical principles of pore size distribution estimation is presented.•A selection of commercially and freely available software for pore size distribution estimation are tested.•Performance of methods on synthetic 3D images and X-ray CT images of soils is analysed.•Recommendations on the use of methods for pore size distribution estimation are made.
Conventional stereo algorithms often fail in accurately reconstructing a 3D object because the image data do not provide enough information about the geometry of the object. We propose a way to ...incorporate a priori information in a reconstruction process from a sequence of calibrated face images. A 3D mesh modeling the face is iteratively deformed in order to minimize an energy function. Differential information extracted from the object shape is used to generate an adaptive mesh. We also propose to explicitly incorporate a priori constraints related to the differential properties of the surface where the image information cannot yield an accurate shape recovery.
During the past 10 years, soil scientists have started to use 3D Computed Tomography in order to gain a clearer understanding of the geometry of soil structure and its relationships with soil ...properties. We propose a geometric model for the 3D representation of pore space and a practical method for its computation. Our basic idea consists in representing pore space using a minimal set of maximal balls (Delaunay spheres) recovering the shape skeleton. In this representation, each ball could be considered as a maximal local cavity corresponding to the “intuitive” notion of a pore as described in the literature. The space segmentation induced by the network of balls (pores) was then used to spatialize biological dynamics. Organic matter and microbial decomposers were distributed within the balls (pores). A valuated graph representing the pore network, organic matter and distribution of micro-organisms was then defined. Microbial soil organic matter decomposition was simulated by updating this valuated graph. The method was implemented and tested using real CT images. The model produced realistic simulated results when compared with data in the literature in terms of the water retention curve and carbon mineralization. A decrease in water pressure decreased carbon mineralization, which is also in accordance with findings in the literature. From our results we showed that the influence of water pressure on decomposition is a function of organic matter distribution in the pore space. As far as we know, this is the approach to have linked pore space geometry and biological dynamics in a formal way. Our next goal will be to compare the model with experimental data of decomposition using different soil structures, and to define geometric typologies of pore space shape that can be attached to specific biological and dynamic properties.
Thin nets are the lines where the grey level function is locally extremum in a given direction. Recently, we have shown that it is possible to characterize the thin nets using differential properties ...of the image surface. However, the method failed when these structures present different widths. In this paper we show that the extraction process of the thin nets, having different width, requires a multi-scale analysis of the image. To design the fusion process of the multi-scale information, we will study the behavior of the differential properties of the image surface, in particular the curvatures, in scale space. We illustrate the efficiency of the proposed multi-scale approach by extracting roads and blood vessels of different widths in satellite and medical images.
This study is the follow-up to a previous one devoted to soil pore space modelling. In the previous study, we proposed algorithms to represent soil pore space by means of optimal piecewise ...approximation using simple 3D geometrical primitives: balls, cylinders, cones, etc. In the present study, we use the ball-based piecewise approximation to simulate biological activity. The basic idea for modelling pore space consists in representing pore space using a minimal set of maximal balls (Delaunay spheres) recovering the shape skeleton. In this representation, each ball is considered as a maximal local cavity corresponding to the “intuitive” notion of a pore as described in the literature. The space segmentation induced by the network of balls (pores) is then used to spatialise biological dynamics. Organic matter and microbial decomposers are distributed within the balls (pores). A valuated graph representing the pore network, organic matter and microorganism distribution is then defined. Microbial soil organic matter decomposition is simulated by updating this valuated graph. The method has been implemented and tested on real data. As far as we know, this approach is the first one to formally link pore space geometry and biological dynamics. The long-term goal is to define geometrical typologies of pore space shape that can be attached to specific biological dynamic properties. This paper is a first attempt to achieve this goal.
This paper presents a geometrical model of soil pore space based on the quantitative analysis of synchrotron X-ray microtomography data. Our model calculated the minimal set of balls that recovered ...the skeleton of the pore space using Delaunay tessellation, and the simply connected sets of balls that could be considered as potential pore channels. This model (DTM software) was then applied to three-dimensional tomography reconstructions of soil aggregates (~
5
mm diameter) from two management systems (conventionally tilled soil, namely CTT and grassland soil, namely GL) with a voxel edge length of 3.2
μm and 5.4
μm, respectively. Geometric characteristics such as the frequency distribution of pore radius, length, and tortuosity as well as the retention curve were calculated using our model. The organic matter decomposition was also simulated using DTM approach. The results were compared with pore space statistics obtained during a previously published study on the same data using algorithms based on the medial axis and throat computation (
3dma software). The same tendency on the geometrical statistic was obtained using both methods, with more pores of smaller length and diameter calculated for the aggregate from the conventionally tilled site compared to the grassland aggregate. However, the
3dma method generated a larger quantity of voxels (385,673 and 189,250 for CTT and GL, respectively) compared to the amount of balls in DTM (170,250 and 64,273 for CTT and GL, respectively) and shorter channels because of the presence of throats.
► A sophisticated model based on Delaunay triangulation method was presented. ► It extracts soil pores with maximal balls or connected ball chains. ► The model was applied to two 3D contrasting soil images. ► Pore space characteristics of the two soils were very different. ► The results of the model were close to those obtained with a more standard approach.
Three-dimensional edge detection in voxel images is used to locate points corresponding to surfaces of 3D structures. The next stage is to characterize the local geometry of these surfaces in order ...to extract points or lines which may be used by registration and tracking procedures. Typically one must calculate second-order differential characteristics of the surfaces such as the maximum, mean, and Gaussian curvature. The classical approach is to use local surface fitting, thereby confronting the problem of establishing links between 3D edge detection and local surface approximation. To avoid this problem, we propose to compute the curvatures at locations designated as edge points using directly the partial derivatives of the image. By assuming that the surface is defined locally by a isointensity contour (i.e., the 3D gradient at an edge point corresponds to the normal to the surface), one can calculate directly the curvatures and characterize the local curvature extrema (ridge points) from the first, second, and third derivatives of the gray level function. These partial derivatives can be computed using the operators of the edge detection. In the more general case where the contours are not isocontours (i.e., the gradient at an edge point only appoximates the normal to the surface), the only differential invariants of the image are in
R
4. This leads us to treat the 3D image as a hypersurface (a three-dimensional manifold) in
R
4. We give the relationships between the curvatures of the hypersurface and the curvatures of the surface defined by edge points. The maximum curvature at a point on the hypersurface depends on the second partial derivatives of the 3D image. We note that it may be more efficient to smooth the data in
R
4. Moreover, this approach could also be used to detect corners of vertices. We present experimental results obtained using real data (X ray scanner data) and applying these two methods. As an example of the stability, we extract ridge lines in two 3D X ray scanner data of a skull taken in different positions.
This paper focuses on the modeling of soil microstructures using generalized cylinders, with a specific application to pore space. The geometric modeling of these microstructures is a recent area of ...study, made possible by the improved performance of computed tomography techniques. X-scanners provide very-high-resolution 3D volume images (
3
–
5
μ
m
) of soil samples in which pore spaces can be extracted by thresholding. However, in most cases, the pore space defines a complex volume shape that cannot be approximated using simple analytical functions. We propose representing this shape using a compact, stable, and robust piecewise approximation by means of generalized cylinders. This intrinsic shape representation conserves its topological and geometric properties. Our algorithm includes three main processing stages. The first stage consists in describing the volume shape using a minimum number of balls included within the shape, such that their union recovers the shape skeleton. The second stage involves the optimum extraction of simply connected chains of balls. The final stage copes with the approximation of each simply optimal chain using generalized cylinders: circular generalized cylinders, tori, cylinders, and truncated cones. This technique was applied to several data sets formed by real volume computed tomography soil samples. It was possible to demonstrate that our geometric representation supplied a good approximation of the pore space. We also stress the compactness and robustness of this method with respect to any changes affecting the initial data, as well as its coherence with the intuitive notion of pores. During future studies, this geometric pore space representation will be used to simulate biological dynamics.
► 3D computer vision techniques to compute a hierarchical geometrical representation of pore space microstructures. ► Initial data: high resolution 3D volume computed tomography images of soil samples. ► Composite representation of pore space using a set of volume primitives including generalized cylinders. ► Basic geometrical representation: minimum set of balls included within the shape and recovering shape skeleton. ► Implementation and experimental validation on several real data sets.
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