Revisiting Sphere Unfolding Relationships for the Stereological Analysis of Segmented Digital Microstructure Images

Payton, E.J.

doi:10.4236/jmmce.2012.113018

Cited by 7 publications

(7 citation statements)

References 21 publications

(30 reference statements)

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“…This phenomenon occurs when the measured number of profiles in a class is lower than its expected value and occurs most frequently with the smallest spheres in a sample [26]. In general, the problem can be solved by using an expectation-maximization algorithm [6][10], error bars [12], and/or histogram smoothing. In our image analysis, we avoided negative binning by The % difference estimates the volume of entrained air The difference estimates the volume of entrained air.…”

Section: Reconstruction Of the Air Void Size Distributionmentioning

confidence: 99%

An image analysis procedure to quantify the air void system of mortar and concrete

Fonseca

Scherer

2014

Mater Struct

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The entrained air void system in cement paste and concrete directly affects both the fresh-state workability and the freeze-thaw durability of concrete pavements and structures. In order to effectively study the air void system, the volume, spacing, and size distribution of the air bubbles must be quantified. This manuscript describes an inexpensive and effective procedure to quantify the air void system using automatic image analysis. We compare various materials used for sample preparation and recommend a procedure to create more accurate images. We further implement a stereological analysis method in the form of a user-friendly and customizable Matlab script. The script was verified by comparing bulk density measurements between air-entrained and control samples with the air content computed by image analysis. As a result, the user can quantify the air void system in a variety of samples by computing the air content, specific surface, spacing, and size distribution of the bubbles.

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Section: Reconstruction Of the Air Void Size Distributionmentioning

confidence: 99%

An image analysis procedure to quantify the air void system of mortar and concrete

Fonseca

Scherer

2014

Mater Struct

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“…The 1% variability in the simulation results came predominantly from three sources: the number of bins and their allowed relative size shift in lineal intercept measurements from step 1 of our methodology; the number of bins used to describe P D and P LI in steps 2 and 3; and the percentile chosen to determine the value of D max . While error propagation in the Saltikov method is a well‐known problem, it did not significantly affect the results of the present work (viz. Equation , Figure ) because the large number of simulated measurements and high binning resolution produced a good approximation of the distribution of intercepts of a dispersion of tetrakaidecahedra, which was well‐behaved in the inverse Saltikov calculation.…”

Section: Resultsmentioning

confidence: 62%

On the grain size proportionality constants calculated in M.I. Mendelson's “Average Grain Size in Polycrystalline Ceramics”

et al. 2018

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In 1969, M.I. Mendelson published a paper in the Journal of the American Ceramic Society that introduced a proportionality constant of 1.558 for estimating the average 3D grain size from the mean 2D lineal intercept under the assumption of lognormally distributed grains. Recent simulations by the authors revealed that the lognormal parameterization in the original work actually calculates the median grain size instead of the mean. The relationship between the mean caliper diameter and mean lineal intercept was found to be 1.60 when using common parameterizations. In addition, it is demonstrated through simulations that the correct proportionality constant can range from 1.776 to below unity depending on a material's grain size dispersion, such that 1.60 should only be used as a crude approximation. K E Y W O R D Scharacterization, grain size distribution microstructure, particle size distribution, simulations, stereology

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“…Meanwhile, this unfolding analysis is known to be sensitive to the different void systems (e.g. regarding the sphere size and choice of size bins) [25]. Therefore, investigating the idealized void systems avoids the unnecessary complexity involved with real concrete.…”

Section: Unfolding Accuracy For Idealized Void Distributionsmentioning

confidence: 99%

“…In this regard, a possible solution lies in altering the binning strategy. Specifically, the logarithmic binning provides a better representation of the lognormal distribution of concrete air voids [25]. This is because logarithmic binning, as compared to linear binning, enlarges the bin spacing for the large voids and reduces that for the small voids.…”

Section: Experimental Workmentioning

confidence: 99%

“…But such a task can be accomplished using 2D imaging techniques such as the flatbed scanner method [14,19]. Nonetheless, the accuracy of the unfolding analysis can be strongly affected by several parameters, such as void population, void size, as well as image resolution [25,26]. As a result, improper unfolding can bias the air void analysis.…”

Section: Introductionmentioning

confidence: 99%

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Image-based restoration of the concrete void system using 2D-to-3D unfolding technique

Shen

Damiani

et al. 2021

Construction and Building Materials

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Hardened air void analysis provides essential information of concrete freeze-thaw durability based on the size and spacing of air voids in the material. As the physical freeze-thaw experiment is timeconsuming and costly, the characteristics of concrete air voids are often deemed as a proxy of the freeze-thaw performance. This analysis is typically done by measuring the 2D air void intersections on polished samples, but the current interpretation of the 2D void characters does not accurately represent the actual void structure in 3D. To solve this problem, a 2D-to-3D unfolding technique has been proposed in the field of stereology. However, the unfolding analysis is known to be sensitive to several factors, such as void population and size along with a binning scheme, where improper unfolding can considerably bias the prediction of the actual concrete void system. This study investigates the optimal strategy of conducting the unfolding analysis for concrete. The investigation is carried out on both idealized void systems to interrogate the influence of the critical factors individually, and real concrete samples with varying levels of air entrainment to assess the concrete-specific impacts. The concrete void system is studied based on a stereological model emulating the intersected 3D air voids on the surface of polished concrete. The results highlight that, for unfolding concrete voids, logarithmic binning scheme is far more accurate to linear binning. The low unfolding error of the concrete samples indicates that the proposed methodology enables an accurate restoration of 3D void size distribution.

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Revisiting Sphere Unfolding Relationships for the Stereological Analysis of Segmented Digital Microstructure Images

Cited by 7 publications

References 21 publications

An image analysis procedure to quantify the air void system of mortar and concrete

An image analysis procedure to quantify the air void system of mortar and concrete

On the grain size proportionality constants calculated in M.I. Mendelson's “Average Grain Size in Polycrystalline Ceramics”

Image-based restoration of the concrete void system using 2D-to-3D unfolding technique

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