APPLICATIONS OF 3D PCA METHOD FOR EXTRACTION OF MEAN SHAPE AND GEOMETRICAL FEATURES OF BIOLOGICAL OBJECTS SET

2008 ◽  
Vol 13 (3) ◽  
pp. 413-420 ◽  
Author(s):  
Michal Rychlik ◽  
Witold Stankiewicz ◽  
Marek Morzyński
Keyword(s):  
Three Dimensional ◽  
Principal Component ◽  
Mean Value ◽  
Analysis Method ◽  
3D Objects ◽  
Biological Objects ◽  
Geometrical Features ◽  
Mean Shape ◽  
Pca Method ◽  
The Mean

This article presents application of the Principal Component Analysis method for analysis of geometry of biological objects and computation of three dimensional anthropometric database. In this work as the biological objects the fifteen human femur bones were used. The geometry of each bone was obtained by using 3D structural light scanner. For PCA analysis all objects have to be described with the same FEM mesh. To achieve this, the modified fluid registration was used. PCA decomposes the set of 3D objects into mean geometry and individual features (empirical modes) describing deviations from mean value. In this paper the mean shape and features of real bones were presented and discussed.

scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

scholarly journals On the fuzziness of circulation types derived from the application of obliquely rotated principal component analysis to a T-mode climatic field

2021 ◽  
Author(s):  
Chibuike Chiedozie Ibebuchi
Keyword(s):  
Principal Component Analysis ◽  
Frequency Distribution ◽  
Principal Component ◽  
Component Analysis ◽  
Threshold Values ◽  
Study Region ◽  
Probability Of Occurrence ◽  
Circulation Types ◽  
Mean Shape ◽  
The Mean

Abstract This study examined the separability of circulation types (CTs) classified from the application of principal component analysis (PCA) to the T-mode matrix (variable is time series and observation is grid points) of a climatic field that explains atmospheric circulation; in addition to the uncertainty introduced on (i) the probability of occurrence, (ii) the mean shape of the CTs, (iii) the trend in the annual frequency of occurrence, (iv) the frequency distribution of the CTs, by using varying threshold values within the range of 0.2–0.35 to assign days to a given CT. The study region is Africa, south of the equator. Some large clusters were classified with most days in the analysis period assigned to them; these classes are interpreted as the dominant states of the atmosphere and generally, their existence results in the poor separability of the CTs since their features overlap with other CTs. Qualitatively, the choice of the threshold values within the defined range has little or no influence on the overall structure of the probability of occurrence of the CTs, the mean shape of the CTs, and the year-to-year variations in the annual occurrence of the CTs. However, it significantly impacts the frequency distribution of the CTs and the statistical significance of the trend in the annual occurrence of the CTs. Stringent threshold values within the defined range might benefit studies that aim to isolate days when specific CTs are most expressed and analyze their mechanism using composite maps, without focus on the frequency distribution and annual occurrence of the CTs. Overall, for the study region, lower threshold values within the defined range might be recommended since relatively, they do not tend to further constrain the probability of group membership, and equally seem to reveal the mechanisms that might be consistent when a given CT occurred regardless of the strength of its signal at a given time.

scholarly journals Wits Appraisal of a Qatari Male Population: A Comparative Study. Part II

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
Hayder A. Hashim ◽  
Najat Al-Sayed ◽  
Ayah AL-Qaisi
Keyword(s):  
Three Dimensional ◽  
Mean Value ◽  
Cone Beam ◽  
Facial Appearance ◽  
Male Population ◽  
Significant Difference ◽  
The Mean ◽  
Age Range ◽  
Relationship Of ◽  
Gender Specific

Introduction: Cephalometric analysis aims to determine skeletal and dental relationships. The ANB angle, initially suggested by Rediel and applied by Steiner. is the most used angle in establishing the anteroposterior relationship of the mandible to the maxilla. However, limitations to the accuracy of the ANB angle for this purpose have been reported. To avoid these potential sources of inaccuracy a diagnostic tool was introduced by Jenkins and later modified by Jacobson and became known as the “Wits appraisal”. Aims: The aim of this study was to establish the Wits appraisal value in a sample of Qatari males, a group which had not previously been studied in this context, and to compare the findings with those from racially and ethnically differing groups as reported in the literature. Materials and Methods: The sample consisted of 28 lateral cephalometric radiographs of Qatari males with an age range of 15 to 32 years, presenting with a well-balanced facial appearance and an acceptable profile. Results: The mean value of the Wits appraisal for Qatari males in the present study was 0.50 ± 2.96. This differed at a statistically significant level from the mean value in the Jacobson study with no gender significant difference noted. On the other hand, significant differences were found when compared with previous reports on different races. Conclusion: The Wits appraisal value for the Qatari male population studied was 0.5±2.96, a result which is significantly higher than that reported in Jacobson’s study. This study revealed that the Wits appraisal is not ethnicity or gender-specific, and therefore cannot be used to differentiate between different ethnic groups. However, it can find application as an alternative to the ANB angle in the treatment of borderline cases. The application of cone beam computed tomography (CBCT) will enhance the diagnosis and treatment of cases by yielding three-dimensional views.

scholarly journals Three-Dimensional Stochastic Seepage Field Analysis of Multimedia Embankment

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaoming Zhao ◽  
Shiyu Shang ◽  
Yuanlin Yang ◽  
Mingming Hu
Keyword(s):  
Hydraulic Conductivity ◽  
Random Field ◽  
Three Dimensional ◽  
Mean Value ◽  
Field Analysis ◽  
Anisotropy Ratio ◽  
Seepage Field ◽  
The Monte Carlo Method ◽  
Total Head ◽  
The Mean

The soil hydraulic conductivity of an embankment has strong spatial variability due to the spatiotemporal variation, both natural and artificial. The strong randomness of the hydraulic conductivity can be expressed by the coefficient of variation (COV) and the fluctuation scale θ. Moreover, different coefficients of variation and fluctuation scales correspond to different random field structures. To study the characteristics of the three-dimensional stochastic seepage field in an embankment under different COVs and fluctuation scales, we generate a three-dimensional random field of the hydraulic conductivity of multimedia embankment based on the local average subdivision technique. In particular, a calculation method for a three-dimensional random seepage field based on the Monte Carlo method combined with a three-dimensional multimedia random field and a deterministic analysis is proposed. The results showed that after three thousand realizations and considering the randomness of the hydraulic conductivity, the position of the free surface of each section in the embankment differed. The mean value of the total head decreased when the COV increased. Furthermore, when the COV was small, the change in the total head with anisotropy ratio was not evident, while the COV was large. The mean value of the total head increased with the anisotropy ratio. When the anisotropy ratio increased, the mean value of the standard deviation of the total head increased first and then decreased.

scholarly journals Monitoring and Analysis of Auto Body Precision Based on Big Data

2021 ◽  
Vol 25 (1) ◽  
pp. 90-100
Author(s):  
Yixin Yang ◽  
Jianjun Gao ◽  
Konghui Guo ◽  
◽  
Keyword(s):  
Big Data ◽  
Failure Modes ◽  
Principal Component ◽  
Analysis Method ◽  
Traditional Management ◽  
Complex Dimension ◽  
Data Platform ◽  
Correlation Analysis Method ◽  
Pca Method ◽  
Auto Body

In this paper, a Hadoop-based big data system for auto body precision is established. The system unifies the elements that affect auto body precision into a big data platform, which is more efficient than traditional management methods. Using big data analysis, we devised algorithms to improve the efficiency and accuracy of body precision monitoring. Furthermore, we developed techniques to analyze complex dimension deviation problems using a correlation analysis method, principal component analysis (PCA), and improved PCA method. We further established failure modes and devised monitoring and diagnosis models based on time series analysis.

scholarly journals Comparison of Valgus Correction Angle between Patients with Developmental Dysplasia Hip and Normal Volunteers Measured by Three-Dimensional Reconstruction and X-Ray

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Aobo Zhang ◽  
Qing Han ◽  
Bingpeng Chen ◽  
Chenyu Wang ◽  
Xue Zhao ◽  
...  
Keyword(s):  
3D Reconstruction ◽  
Three Dimensional ◽  
Mean Value ◽  
Normal Group ◽  
Correction Angle ◽  
X Ray ◽  
Normal Volunteers ◽  
Significant Difference ◽  
The Mean ◽  
Valgus Correction Angle

Background and purpose. A new method of three-dimensional (3D) reconstruction technology was used to take place of X-ray in measuring valgus correction angle (VCA) of both DDH patients and normal volunteers to improve precision. Two different ways to define VCA according to the various conditions of patients were compared and analyzed. Methods. Bilateral VCA of 50 DDH patients and 56 normal volunteers were measured by Mimics software in the 3D method and X-ray in 2D. Two VCA (the upper VCA and the lower VCA) were measured in both two methods. Every VCA was measured by observer A and observer B for twice separately. The statistical analyses of the differences were calculated among the measurements of the VCA. Results. The mean value of the upper VCA measured in 3D was 4.95°±0.76° in DDH group and 5.56°±0.62° in the normal group with significant difference (t=−6.457, p<0.01). The VCA of DDH group and normal group measured by 3D was larger than 2D, both the upper VCA and the lower VCA. The differences indicated statistically significant. The mean value of lower VCA was 0.60° smaller than the mean value of upper VCA in normal volunteers. The mean value of the lower VCA was 0.58° larger than the mean value of the upper VCA in DDH patients. Conclusions. Compared to X-ray, 3D reconstruction technology is more accurate without conventional limitations. The lower VCA of DDH patients should be regarded as the femoral intramedullary guide angle in TKA, especially for patients with femoral deformities.

scholarly journals Intra-line and inter-line genetic diversity in sire lines of the Old Kladruber horse based on microsatellite analysis of DNA

2011 ◽  
Vol 56 (No. 4) ◽  
pp. 163-175 ◽  
Author(s):  
L. Vostrý ◽  
O. Kracíková ◽  
B. Hofmanová ◽  
V. Czerneková ◽  
T. Kott ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Dna Analysis ◽  
Genetic Difference ◽  
Principal Component ◽  
Genetic Distances ◽  
Mean Value ◽  
Pedigree Information ◽  
Mean Values ◽  
The Mean ◽  
Coefficient Of Relationship

The Old Kladruber horse is the oldest original Czech horse breed &ndash; gene resource, with pedigree records spanning three centuries. Because the population is closed, there is a concern about the loss of genetic variation. The genetic diversity within and amongst sire lines was evaluated using microsatellite markers and based on pedigree information. The DNA analysis, covering 16 microsatellite loci, revealed that the genetic diversity (observed heterozygosity = 0.637, genetic diversity = 0.678 and the mean number of alleles = 8.25) for the Old Kladruber horse is consistent with other populations of horses. Inter-line genetic difference in sire lines reached the mean value (the F<sub>ST</sub> values ranged from 0.020 to 0.017). Differences amongst the sire lines were identified using genetic distances and principal component analysis. One gene cluster comprised black variation sire lines, while the second cluster included the sire lines of the grey variation. In the subjects monitored, the average inbreeding coefficient of 0.076 was estimated on the basis of pedigree information. The highest mean values of the coefficient of relationship were estimated within the colour variations. When comparing the genetic distance and the average coefficient of relationship, differences were found out. These results are useful for the development of breeding strategies which consider classical horse breeding as well as recent achievements of population and conservation genetics.

A Taylor Expansion Approach for Computing Structural Performance Variation Over a Shape Population

2016 ◽  
Author(s):  
Xilu Wang ◽  
Xiaoping Qian
Keyword(s):  
Numerical Study ◽  
Principal Component ◽  
Taylor Series Expansion ◽  
Structural Performance ◽  
Shape Variation ◽  
Element Analysis ◽  
Plate Deformation ◽  
Performance Variation ◽  
Mean Shape ◽  
The Mean

In this paper, we present a formal and efficient method for computing structural performance variation over its shape population. Each shape in the population is represented as discrete points. These shapes are then aligned together and principal component analysis is conducted to obtain the shape variation, which is represented as a sum of variations in multiple principal modes. Finite element analysis is conducted on the mean shape. For each shape specified by the shape parameters, we then invoke a thin-plate deformation based scheme to automatically deform the mesh nodes. The performance of the shapes is approximated via Taylor series expansion of the FE solution of the mean shape. Numerical study illustrates the accuracy and efficiency of this method.

A comparison between the dynamic stability of three types of nonlinear orthotropic functionally graded plates under random lateral loads

2015 ◽  
Vol 23 (15) ◽  
pp. 2520-2537 ◽  
Author(s):  
A Asnafi ◽  
M Abedi
Keyword(s):  
Dynamic Stability ◽  
Three Dimensional ◽  
Mean Value ◽  
Functionally Graded ◽  
Kolmogorov Equation ◽  
Lateral Loads ◽  
Functionally Graded Plates ◽  
The Mean ◽  
Stochastic Loads ◽  
Stable Zone

In this manuscript, the dynamic stability and bifurcation occurrence for three famous types of plates including orthotropic sigmoid, power-law and exponential functionally graded plates under lateral stochastic loads are studied. Due to randomness, the behavior and analysis are not conventional deterministic investigation. So, the dynamic stability zone and border curves of bifurcation are evaluated using probability density function of the response. The latter is computed from a completely exact solution of the Fokker Planck Kolmogorov equation. The three dimensional dynamic stable zone and the border surfaces of bifurcation are obtained as a function of material parameter, in-plane forces and the mean value of lateral load. To generalize the results, all the parameters are transformed to some proper non-dimensional variables and then the effects of all prescribed parameters on the dynamic stability are completely discussed and compared. The comparison is done between the plates with themselves and also the corresponding homogenous plate. Finally the results are validated by the bifurcation diagrams of non dimensional deflection of plates that are obtained directly and numerically from the governing equations of plates.

Pcbs in Soils around an Old Electric Transformer Factory in North China

2014 ◽  
Vol 587-589 ◽  
pp. 550-553
Author(s):  
Zhi Yong Li ◽  
Lan Chen ◽  
Yu Heng Quan ◽  
Yan Song
Keyword(s):  
North China ◽  
Surface Soil ◽  
Principal Component ◽  
Mean Value ◽  
Transformer Oil ◽  
Total Pcbs ◽  
Pcb Congeners ◽  
Transformer Oils ◽  
The Mean ◽  
Compositional Patterns

The 28 surface soil samples (0-10 cm) were collected from the urban area of Baoding city nearby an old electric transformer factory for analysis of 84 PCB congeners. Total PCBs concentrations ranged from 0.69 to 11.15 ng/g (mean: 3.62 ng/g). The PCBs concentration (5.72 ng/g) for sampling sites in the vicinity (0-2.5 km) of the transformer factory was higher than that (2.96 ng/g) for other sampling sites. Compositional patterns of individual congener and homologs were similar to those of Chinese transformer oils. The top five congeners were PCB-6, 18, 22, 33 and 31/28 among the identified PCBs. Low chlorinated PCBs (di-to tetra-CBs) accounted for 69.58% of total PCBs concentrations and the predominant PCB homologs were tri-CBs (46.38%), penta-CBs (13.73%) and di-CBs (9.47%), respectively. Principal component analysis showed that technical formulations such as Chinese transformer oil, Aroclor1242, 1016, KC-300 and A-30 were the main sources of soils PCBs from Baoding city. The TEQ concentrations based on ten dioxin-like PCBs ranged from 0 to 26.0986 ng/kg with the mean value as 7.3336 ng/kg.

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