Intersection Counting Research Articles

A novel framework for crash frequency prediction: Geographic support vector regression based on agent-based activity models in Greater Melbourne

The field of spatial analysis in traffic crash studies can often enhance predictive performance by addressing the inherent spatial dependence and heterogeneity in crash data. This research introduces the Geographical Support Vector Regression (GSVR) framework, which incorporates generated distance matrices, to assess spatial variations and evaluate the influence of a wide range of factors, including traffic, infrastructure, socio-demographic, travel demand, and land use, on the incidence of total and fatal-or-serious injury (FSI) crashes across Greater Melbourne’s zones. Utilizing data from the Melbourne Activity-Based Model (MABM), the study examines 50 indicators related to peak hour traffic and various commuting modes, offering a detailed analysis of the multifaceted factors affecting road safety. The study shows that active transportation modes such as walking and cycling emerge as significant indicators, reflecting a disparity in safety that heightens the vulnerability of these road users. In contrast, car commuting, while a consistent factor in crash risks, has a comparatively lower impact, pointing to an inherent imbalance in the road environment. This could be interpreted as an unequal distribution of risk and safety measures among different types of road users, where the infrastructure and policies may not adequately address the needs and vulnerabilities of pedestrians and cyclists compared to those of car drivers. Public transportation generally offers safer travel, yet associated risks near train stations and tram stops in city center areas cannot be overlooked. Tram stops profoundly affect total crashes in these areas, while intersection counts more significantly impact FSI crashes in the broader metropolitan area. The study also uncovers the contrasting roles of land use mix in influencing FSI versus total crashes. The proposed framework presents an approach for dynamically extracting distance matrices of varying sizes tailored to the specific dataset, providing a fresh method to incorporate spatial impacts into the development of machine learning models. Additionally, the framework extends a feature selection technique to enhance machine learning models that typically lack comprehensive feature selection capabilities.

Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision Trees

We revisit Hopcroft’s problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O ( n 4/3 ) time, which matches the conjectured lower bound and improves the best previous time bound of \(n^{4/3}2^{O(\log ^*n)}\) obtained almost 30 years ago by Matoušek [ 58 ]. We describe two interesting and different ways to achieve the result: The first is randomized and uses a new two-dimensional version of fractional cascading for arrangements of lines; the second is deterministic and uses decision trees in a manner inspired by the sorting technique of Fredman [42]. The second approach extends to any constant dimension. Many consequences follow from these new ideas: For example, we obtain an O ( n 4/3 )-time algorithm for line segment intersection counting in the plane, O ( n 4/3 )-time randomized algorithms for distance selection in the plane and bichromatic closest pair and Euclidean minimum spanning tree in three or four dimensions, and a randomized data structure for halfplane range counting in the plane with O ( n 4/3 ) preprocessing time and space and \(O(n^{1/3})\) query time.

Parallel intersection counting on shared-memory multiprocessors and GPUs

Computing intersections among sets of one-dimensional intervals is an ubiquitous problem in computational geometry with important applications in bioinformatics, where the size of typical inputs is large and it is therefore important to use efficient algorithms. In this paper we propose a parallel algorithm for the 1D intersection-counting problem, that is, the problem of counting the number of intersections between each interval in a given set A and every interval in a set B. Our algorithm is suitable for shared-memory architectures (e.g., multicore CPUs) and GPUs. The algorithm is work-efficient because it performs the same amount of work as the best serial algorithm for this kind of problem. Our algorithm has been implemented in C++ using the Thrust parallel algorithms library, enabling the generation of optimized programs for multicore CPUs and GPUs from the same source code. The performance of our algorithm is evaluated on synthetic and real datasets, showing good scalability on different generations of hardware.

Histomorphology of Chorionic Villi of Term Placentae of Mothers Exposed to Retroviral and Hepatitis B Viruses

Retroviral and hepatitis B infections can be potential threats to foetomaternal health through inducing distortions of the architecture and structure of the placenta. Improved insights into the effects of these infections on placental morphology would be integral to our understanding of maternal and neonatal health. Aim: To histomorphologically and stereologically investigate selected placental structures in virus-infected (HIV [human immunodeficiency virus] and hepatitis B virus [HBV]) and uninfected women at term. Method: This cross-sectional study involved the screening of 237 placentae collected at term (38 ± 2 weeks) from the maternity delivery units and surgical theatres of the LEKMA and Weija/Gbawe Municipal Hospitals in Accra. Venous blood samples from the umbilical vein and placenta basal plate blood were screened for HIV, HBV, and hepatitis C virus (HCV) using serological test kits (RDT). A total of 34 placentae were selected, comprising 20 cases and 14 controls that were gestational age-matched. Using stereology and a systematic random sampling technique with test point and intersection counting of photomicrographs, the mean volume densities of syncytial knots, syncytial denudations, foetal capillaries, and intervillous spaces of the placentae were estimated on a total of 2720 photomicrographs. Results: On stereological assessment, there was a statistically significant difference in the mean volume densities of syncytial knots (HIV-infected = 0.562 ± 0.115, HBV-infected = 0.516 ± 0.090, control group = 0.171 ± 0.018, p = 0.001), syncytial denudations (HIV-infected = 0.121 ± 0.022, HBV-infected = 0.111 ± 0.016, control group = 0.051 ± 0.00, p = 0.004), and foetal capillaries (HIV-infected = 0.725 ± 0.152, HBV-infected = 0.902 ± 0.078, control group = 0.451 ± 0.064, p = 0.006) among the different groups of placentae (control) at term. A statistically significant decrease in intervillous space (p = 0.022) was recorded in HBV-infected placentae compared to the control (from 15.450 ± 1.075 to 11.32 ± 0.952). Conclusion: Placental viral infections might lead to significant increases in syncytial knots, foetal capillaries, and syncytial denuded areas of the chorionic villi and a significant decrease in intervillous spaces. This finding could signify evidence of advanced gestation, placental malperfusion, hypermaturity of the placenta, and a possible vertical transmission of the viral antigen to the foetus, which may be crucial in understanding perinatal outcomes.

Microvascular maturation of the septal capillary layers takes place in parallel to alveolarization in human lungs.

Primary and secondary septa formed during lung development contain a double-layered capillary network. To improve gas exchange, the capillary network is remodeled into a single-layered one, a process that is called microvascular maturation (MVM). It takes place during classical and continued alveolarization. Classical alveolarization is defined as a formation of new septa from immature septa and continued alveolarization as a formation from mature septa. Until now, MVM was never quantitatively evaluated in human lungs. To correlate alveolarization and MVM, and to determine the transition point from classical to continued alveolarization, the degree of MVM was stereologically estimated. In 12 human lungs (0.1-15 yr), the alveolar surface area of immature and mature septa was estimated stereologically by intersection counting. An MVM-quotient (RMVM) was defined as the mature alveolar surface area over total alveolar surface area. The MVM-quotient increased logarithmically over age and showed a biphasic increase similar to alveolarization. It did not reach 100% maturity in these samples. A linear correlation between the MVM-quotient and the logarithm of the number of alveoli was observed. We conclude that MVM increased logarithmically and biphasically in parallel to alveolarization until alveolarization ceased. However, at 2-3 yr of age three-quarters of the alveolar microvasculature are mature. This result may explain a previous postulate that MVM is finished at this age. We hypothesize that as long as alveolarization takes place, MVM will take place in parallel. We propose that the transition from classical to continued alveolarization takes place between the ages of 1-3 yr in humans.NEW & NOTEWORTHY Newly formed alveolar septa contain a double-layered capillary network. To optimize gas exchange, the two layers fuse to a single-layered capillary network during microvascular maturation. Because its timing is unknow in humans, microvascular maturation was stereologically estimated throughout postnatal human lung development. It is shown that maturation of the microvascular and alveolar septa takes place in parallel to alveolarization. At an age of 2-3 yr three-quarters of the septa are mature.

Associations between neighborhood walkability and walking following residential relocation: Findings from Alberta's Tomorrow Project.

Cross-sectional studies consistently find that the neighborhood built environment (e.g., walkability) is associated with walking. However, findings from the few existing longitudinal residential relocation studies that have estimated associations between changes in neighborhood built characteristics and walking are equivocal. The study objective was to estimate whether changes in neighborhood walkability resulting from residential relocation were associated with leisure, transportation, and total walking levels among adults. This study included longitudinal data from the "Alberta's Tomorrow Project"-a province-wide cohort study (Alberta, Canada). The analysis included data collected at two time points (i.e., baseline and follow-up) from 5,977 urban adults. The International Physical Activity Questionnaire (IPAQ) captured self-reported walking. We estimated neighborhood walkability, an index capturing intersection, destination, and population counts for the 400 m Euclidean buffer around participants' homes. Using household postal codes reported at baseline and follow-up, we categorized participants into three groups reflecting residential relocation ("non-movers:" n = 5,679; "movers to less walkability:" n = 164, and; "movers to more walkability:" n = 134). We used Inverse-Probability-Weighted Regression Adjustment to estimate differences [i.e., average treatment effects in the treated (ATET)] in weekly minutes of leisure, transportation, and total walking at follow-up between residential relocation groups, adjusting for baseline walking, sociodemographic characteristics, and walkability. The median time between baseline and follow-up was 2-years. The three residential relocation groups mainly included women (61.6-67.2%) and had a mean age of between 52.2 and 55.7 years. Compared to "non-movers" (reference group), weekly minutes of transportation walking at follow-up was significantly lower among adults who moved to less walkable neighborhoods (ATET: -41.34, 95 CI: -68.30, -14.39; p < 0.01). We found no other statistically significant differences in walking between the groups. Our findings suggest that relocating to less walkable neighborhoods could have detrimental effects on transportation walking to the extent of adversely affecting health. Public health strategies that counteract the negative impacts of low walkable neighborhoods and leverage the supportiveness of high walkable neighborhoods might promote more walking.

Absolutely Complex Balanced Kinetic Systems

A complex balanced kinetic system is absolutely complex balanced (ACB) if every positive equilibrium is complex balanced. Two results on absolute complex balancing were foundational for modern chemical reaction network theory (CRNT): in 1972, M. Feinberg proved that any deficiency zero complex balanced system is absolutely complex balanced. In the same year, F. Horn and R. Jackson showed that the (full) converse of the result is not true: any complex balanced mass action system, regardless of its deficiency, is absolutely complex balanced. In this paper, we present initial results on the extension of the Horn and Jackson ACB Theorem. In particular, we focus on other kinetic systems with positive deficiency where complex balancing implies absolute complex balancing. While doing so, we found out that complex balanced power law reactant determined kinetic systems (PL-RDK) systems are not ACB. In our search for necessary and sufficient conditions for complex balanced systems to be absolutely complex balanced, we came across the so-called CLP systems (complex balanced systems with a desired "log parametrization" property). It is shown that complex balanced systems with bi-LP property are absolutely complex balanced. For non-CLP systems, we discuss novel methods for finding sufficient conditions for ACB in kinetic systems containing non-CLP systems: decompositions, the Positive Function Factor (PFF) and the Coset Intersection Count (CIC) and their application to poly-PL and Hill-type systems.

Counting intersections of normal curves

A fast algorithm for counting intersections of two normal curves on a triangulated surface is proposed. It yields a convenient way for treating mapping class groups of punctured surfaces by presenting mapping classes by matrices, and the composition by an exotic matrix multiplication. An efficient solution of the word problem for mapping class groups of punctured surfaces is proposed, with efficiency understood in a more restrictive way than the most common one.

Differential associations of the built environment on weight gain by sex and race/ethnicity but not age.

Objective:To explore the built environment (BE) and weight change relationship by age, sex, and racial/ethnic subgroups in adults.Methods:Weight trajectories were estimated using electronic health records for 115,260 insured Kaiser Permanente Washington members age 18–64 years. Member home addresses were geocoded using ArcGIS. Population, residential, and road intersection densities and counts of area supermarkets and fast food restaurants were measured with SmartMaps (800 and 5,000-meter buffers) and categorized into tertiles. Linear mixed-effect models tested whether associations between BE features and weight gain at 1, 3, and 5 years differed by age, sex, and race/ethnicity, adjusting for demographics, baseline weight and residential property values.Results:Denser urban form and greater availability of supermarkets and fast food restaurants were associated with differential weight change across sex and race/ethnicity. At 5 years, the mean difference in weight change comparing the 3rd versus 1st tertile of residential density was significantly different between males (−0.49 kg, 95% CI: −0.68, −0.30) and females (−0.17 kg, 95% CI: −0.33, −0.01) (P-value for interaction = 0.011). Across race/ethnicity, the mean difference in weight change at 5 years for residential density was significantly different among non-Hispanic (NH) Whites (−0.47 kg, 95% CI: −0.61, −0.32), NH Blacks (−0.86 kg, 95% CI: −1.37, −0.36), Hispanics (0.10 kg, 95% CI: −0.46, 0.65), and NH Asians (0.44 kg, 95% CI: 0.10, 0.78) (P-value for interaction < 0.001). These findings were consistent for other BE measures.Conclusion:The relationship between the built environment and weight change differs across demographic groups. Careful consideration of demographic differences in associations of BE and weight trajectories is warranted for investigating etiological mechanisms and guiding intervention development.

Partial 3D object retrieval using local binary QUICCI descriptors and dissimilarity tree indexing

A complete pipeline is presented for accurate and efficient partial 3D object retrieval based on Quick Intersection Count Change Image (QUICCI) binary local descriptors and a novel indexing tree. It is shown how a modification to the QUICCI query descriptor makes it ideal for partial retrieval. An indexing structure called Dissimilarity Tree is proposed which can significantly accelerate searching the large space of local descriptors; this is applicable to QUICCI and other binary descriptors. The index exploits the distribution of bits within descriptors for efficient retrieval. The retrieval pipeline is tested on the artificial part of SHREC’16 dataset with near-ideal retrieval results.

Evaluation of three methods for manually counting fish in dam turbines using DIDSON

Mortality of fish entering the turbine draft tube (DT) from the tailrace is common during turbine startup or dewatering in Brazilian hydropower dams. Mortality can be reduced if such operations occur when few fish are present in the DT, but estimating abundance therein using traditional gears (e.g., cast net, gillnet, hook-and-line) is constrained by flow and access. We deployed a Dual frequency IDentification SONar (DIDSON) to record and count fish in the DT for the first time using an innovative approach. Methods used elsewhere for manual counting fish in DIDSON images generated dissimilar results. Therefore, we compared three methods of counting fish manually in the frames of DIDSON software from two Brazilian dams: numerical counting (number of fish in the frame), qualitative counting (percent of the frame occupied by fish), and intersection counting (number of intersections of the grid frame with fish). We assumed that the numerical counting provided the best estimates of the true value but could not be used in 32.2% of the frames from one of the dams due to the presence of uncountable aggregation of fish, bubble curtain, or poor contrast between fish and the DT floor. Qualitative counting was the most congruent, whereas intersection counting was the least, based on comparisons with numerical counting.

SU(3)-skein algebras and webs on surfaces

The \(SU_3\)-skein algebra of a surface F is spanned by isotopy classes of certain framed graphs in \(F\times I\) called 3-webs subject to the skein relations encapsulating relations between \(U_q(sl(3))\)-representations. It is expected that their theory parallels that of the Kauffman bracket skein algebras. We make the first step towards developing that theory by proving that the reduced \(SU_3\)-skein algebra of any surface of finite type is finitely generated. We achieve that result by developing a theory of canonical forms of webs in surfaces. Specifically, we show that for any ideal triangulation of F every reduced 3-web can be uniquely decomposed into unions of pyramid formations of hexagons and disjoint arcs in the faces of the triangulation with possible additional “crossbars” connecting their edges along the ideal triangulation. We show that such canonical position is unique up to “crossbar moves”. That leads us to an associated system of coordinates for webs in triangulated surfaces (counting intersections of the web with the edges of the triangulation and their rotation numbers inside of the faces of the triangulation) which determine a reduced web uniquely. Finally, we relate our skein algebras to \({\mathcal {A}}\)-varieties of Fock–Goncharov and to \(\text {Loc}_{SL(3)}\)-varieties of Goncharov–Shen. We believe that our coordinate system for webs is a manifestation of a (quantum) mirror symmetry conjectured by Goncharov–Shen.

The measurement of the dislocation density using TEM

The line intercept method is well developed for estimating the dislocation density in metals, but its application is limited by the intersection counting, which is deeply depending on the TEM image quality. Manual interscetion counting is quite time and labor consuming. If most of the dislocations has good contrast and homogenous background in an image, it is possible to perform automatic counting by the computer program. In this work a series of imaging conditions were investigated on a slightly deformed IF steel thin foil. Though the invisibility criterion remains applicable for both the conventional transmission electron microscopy (CTEM) and the scanning transmission electron microscopy (STEM), the STEM images revealed more dislocations and had more homogenous background than the CTEM images. The STEM bright field (BF), annular dark field (ADF) and annular bright field (ABF) images at a low index zone axis contained the most dislocations visible and were suitable for automatic intersection counting of dislocations.

Development and Validation of a Seven-County Regional Pedestrian Volume Model

This study describes the development and validation of pedestrian intersection crossing volume models for the seven-county Milwaukee metropolitan region. The set of three models, among the first developed at a multi-county scale, can be used to estimate the total number of pedestrian crossings per year at four-leg intersections along state highways and other major thoroughfares. Outputs are appropriate for annual volumes ranging from 1,000 to 650,000. We used negative binomial regression to relate annual pedestrian volumes at 260 intersections to roadway and surrounding neighborhood socioeconomic and land-use variables. The three models include seven variables that have significant positive associations with annual pedestrian volume: population density within 400 m of the intersection; employment density within 400 m; number of bus stops within 100 m; number of retail businesses within 100 m; number of restaurant and bar businesses within 100 m; presence of a school within 400 m; and proportion of households without a motor vehicle within 400 m. Results suggest that square root or cube root transformations of continuous explanatory variables could potentially improve model fit. The models have fair accuracy, with each of the three model formulations predicting 60% or more of validation intersection counts to within half or double the observed value. Future research could address overprediction by creating new variables to better represent the number of lanes on each intersection leg and low socioeconomic status of adjacent neighborhoods.

Anti-angiogenic effects of beta-eudesmol and atractylodin in developing zebrafish embryos

Angiogenesis is the process of formation of new blood vessels which plays an essential role in the normal physiological development of the organs and systems. Several factors contribute to and regulate this process. Unregulated angiogenesis, however, is harmful and is usually found in tumors and cancerous cells. β-Eudesmol and atractylodin are sesquiterpenoid contents extracted from the rhizome of Atractylodes lancea (AL). Reports suggest potential anti-angiogenic activities of both compounds. In this study, the anti-angiogenic activities of both compounds were investigated using the well-established zebrafish in vivo model. Zebrafish embryos were treated with a series of concentrations (6.3, 12.5, 25, and 50 μM) of β-eudesmol and (6.3, 12.5, and 25 μM) of atractylodin up to 72 h post-fertilization. Assessment of the effects on phenotypic blood vessel development (sub-intestinal vessel intersection count) revealed that both the compounds inhibited vessel development, particularly at higher concentrations. At the genetic levels, only β-eudesmol significantly downregulated the expression of the Vegfaa gene and also its receptor Vegfr2. β-Eudesmol also affected the expression of Vegfaa protein in a concentration-dependent manner. Results indicate that β-eudesmol exerts anti-angiogenic property through inhibition of Vegfaa at both the gene and protein levels. However, atractylodin does not possess this property.

An indexing scheme and descriptor for 3D object retrieval based on local shape querying

A binary descriptor indexing scheme based on Hamming distance called the Hamming tree for local shape queries is presented. A new binary clutter resistant descriptor named Quick Intersection Count Change Image (QUICCI) is also introduced. This local shape descriptor is extremely small and fast to compare. Additionally, a novel distance function called Weighted Hamming applicable to QUICCI images is proposed for retrieval applications. The effectiveness of the indexing scheme and QUICCI is demonstrated on 828 million QUICCI images derived from the SHREC2017 dataset, while the clutter resistance of QUICCI is shown using the clutterbox experiment.

Radial intersection count image: A clutter resistant 3D shape descriptor

A novel shape descriptor for cluttered scenes is presented, the Radial Intersection Count Image (RICI), and is shown to significantly outperform the classic Spin Image (SI) and 3D Shape Context (3DSC) in both uncluttered and, more significantly, cluttered scenes. It is also faster to compute and compare. The clutter resistance of the RICI is mainly due to the design of a novel distance function, capable of disregarding clutter to a great extent. As opposed to the SI and 3DSC, which both count point samples, the RICI uses intersection counts with the mesh surface, and is therefore noise-free. For efficient RICI construction, novel algorithms of general interest were developed. These include an efficient circle-triangle intersection algorithm and an algorithm for projecting a point into SI-like (α, β) coordinates. The ’clutterbox experiment’ is also introduced as a better way of evaluating descriptors’ response to clutter. The SI, 3DSC, and RICI are evaluated in this framework and the advantage of the RICI is clearly demonstrated.

P136 EPSTEIN-BARR VIRUS TRANSCRIPTION CO-FACTORS BIND TO MANY INFLAMMATORY BOWEL DISEASE RISK LOCI

Abstract Objective IBD is a chronic inflammatory disorder of the GI tract with complex etiology that involves both genetic variants and environmental factors. Several viruses and bacteria have been suggested as potential causes of the disease. The clinical course of IBD appears to be influenced by EBV tissue infection. With a prevalence of &amp;gt;90% in the adult human population, EBV infection is nearly ubiquitous. We reported that the EBV transcription co-factor EBNA2 was concentrated in the risk loci of IBD relative to the remainder of the genome (Pc=1.24E-13, (RR) = 3.33, Nature Genetics 50:699, 2018). The objective of this study was to determine whether new data and studies made available since the data used for our 2018 study further supported the possibility that EBV was related to some IBD as a potential etiologic agent. Methods Genomic approaches offer previously unavailable perspectives for understanding disease mechanisms. The previous analysis was based upon the 9 viral transcription factor and co-factor (TF) datasets available in human cells in 2015.Of the 52 now available there are 29 from EBV. The number of established IBD loci qualifying for analysis has expanded from 112 in 2015 to 324 available now. We applied simulation analysis to assess statistical significance of TF associations with IBD risk loci using RELI (Regulatory Element Locus Intersection) (Nat Genet 50:699, 2018). RELI tests the probability of the observed association by the count of intersections of the same variant from two sources. We extracted 700 SNPs in European ancestry from 93 published GWAS and 350 additional candidate gene studies for IBD. All variants with linkage disequilibrium r2&amp;gt;0.8 of the best variant were included, while loci with r2&amp;gt;0.2 with a more highly significant locus were excluded. Results Among the 52 viral TF datasets, 139 of the 324 IBD loci were occupied by EBNALP (RR=2.08793, Pc=3.7321E-23), 113 by EBNA3C (RR=2.35113, Pc=2.84678E-22), 88 loci by EBNA2 (RR=3.2, Pc=7.8E-32) and 28 loci by EBNA3ABC, which used an antibody that did not distinguish between EBNA3 subtypes. Analysis of 11,535 human TF ChIP-seq datasets produced 1578 with strong associations (p&amp;lt;E-6) with IBD risk loci. The locus intersections of the three EBV gene products optimally clustered at 150 IBD loci (46%) with a set of 26 human TFs (p&amp;lt;2E-308), thereby nominating these loci as potentially having EBV-dependent mechanisms that alter genetic risk for IBD. The human TFs were enriched for (ChIP-seq) data obtained from EBV-infected B lymphocyte cell line (OR = 10.12425329, Chi-squared = 241.2925605) Moreover, the human TFs that participate in the super-enhancers that form in the latency III EBV infected and transformed B cell are also concentrated among the statistically significant associations (p&amp;lt;E-6) with the IBD risk loci (OR) = 2.9448, P = 10E-7). Conclusion These preliminary findings nominate EBV for a role in the pathogenesis and etiology of IBD by mechanisms operating in transformed B cells through the latency III EBV program of viral gene expression.

Level curves of rational functions and unimodular points on rational curves

We obtain an improvement and broad generalisation of a result of N. Ailon and Z. Rudnick (2004) on common zeros of shifted powers of polynomials. Our approach is based on reducing this question to a more general question of counting intersections of level curves of complex functions. We treat this question via classical tools of complex analysis and algebraic geometry.

Evaluation of Uncertainty in Determining Average Grain Size by ASTM E112 Standard

In this paper, the ASTM grain size number of aluminium alloy specimen was determined respectively by Abrams Three-Circle Procedure and Planimetric Procedure of ASTM E112-13 Standard, and the uncertainty of the result was evaluated. The results are as follows: 1) Using the Abrams Three-Circle Procedure determines G, G=4.13, U=0.26, k=2; Using the Planimetric Procedure determines G, G=3.94, U=0.15, k=2. 2) It is suggested that the ASTM E112 standard should provide that the errors of counting grain boundary intersection count or number of grains should be less than or equal to 2, and the ruler that determines the diameter of test circle or scale length should be with the scale that is less than or equal to 0.10 mm. On this condition, the uncertainties caused by them in determining G can be negligible. 3) The main sources of uncertainty for the determination of G by Abrams Three-Circle Procedure and Planimetric Procedure are repetitive measurement, which depends on the uniformity of grain size of specimen. 4) The %RA limit of ASTM E112 for determining G should be redefined according to the measurement uncertainty in order to be up to the precision requirement (±0.25).