• Journal of Applied Reliability
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• v.1 no.1
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• pp.17-33
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• 2001

The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.317-323
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• 2010

Measures are very useful tools for comparing the shape variability in statistical shape analysis. For examples, the Procrustes statistic(PS) is isolated measure, and the mean Procrustes statistic(MPS) and the root mean square measure(RMS) are overall measures. But these measures are very subjective, complicated and moreover these measures are not statistical for comparing the shape variability. Therefore we need to study some tests. It is well known that the Hotelling's $T^2$ test is used for testing shape variability of two independent samples. And for testing shape variabilities of several independent samples, instead of the Hotelling's $T^2$ test, one way analysis of variance(ANOVA) can be applied. In fact, this one way ANOVA is based on the balanced samples of equal size which is called as BANOVA. However, If we have unbalanced samples with unequal size, we can not use BANOVA. Therefore we propose the unbalanced analysis of variance(UNBANOVA) for testing shape variabilities of several independent samples of unequal size.

• The Korean Journal of Applied Statistics
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• v.32 no.1
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• pp.15-27
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• 2019

The reliability of the data means the overall consistency of the measurement results. Methods for evaluating reliability have been continuously studied because it affects the results of the statistical analysis. Cronbach's ${\alpha}$ coefficient or intraclass correlation coefficient is used for reliability evaluation; however, these measures cannot be applied to data consisting of three-dimensional coordinates to represent an object. In this study, we propose a measure to evaluate the reliability of three dimensional shapes based on statistical shape analysis that is made possible by extracting the shape information from the measured three dimensional coordinates and decomposing the shape variation.

• Journal of Biosystems Engineering
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• v.30 no.5 s.112
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• pp.268-273
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• 2005

This study was conducted to investigate the specificities of four fulcrum types for geo-statistical analysis of elevation within rice paddy field. In Korea, the spaces between inter-rows and between hills for rice transplanting are 30cm and 11cm to 14cm, respectively. So, the size and shape of fulcrum for field elevation measurement should be considered according to the inter-row and the hill spaces. Four kinds of fulcrum were chosen such as round-shape with 2.5cm diameter, circular-shape with 10cm diameter, 10cm (one third of inter-row space) by 24cm (double of hill space) rectangular-shape, and 20cm (two-thirds of inter-row space) by 24cm rectangular-shape. The resulting descriptive statistics couldn't determine the best fulcrum type to measure the rice paddy field elevation. But the results of geo-statistical analysis could determine the best fulcrum type. In the case of 10cm by 24cm rectangular-shape fulcrum, Nugget and range, meaning measurement error and/or noise, and limit of spatial connection, respectively, were minimum; Q value meaning weight of spatial structure and $r^2$ value were minimum, and residual sum of squares was minimum. It means that 10cm by 24 cm rectangular-shape fulcrum could best describe the rice paddy field elevation.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.37-48
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• 2023

Shape analysis is a method for measuring, describing and comparing the shape of objects in geometric space. An important aspect is to obtain Procrustes distance based on least square method. We note that the shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object. However, and unfortunately, when we cannot measure some landmarks which are some biologically or geometrically meaningful points of any object, it is not possible to measure the variation of all shapes of an object, including that of the incomplete object. Hence, we need to replace the missing landmarks. In particular, Albers and Gower (2010) studied the missing rows of configurations in Procrustes analysis. They noted that the convergence of their approach can be quite slow. In this study, alternatively, we derive an algorithm for estimating the missing landmarks based on the pre-shapes. The pre-shape is invariant under the location and scaling of the original configuration with the centroid size of the pre-shape being one. Therefore we expect that we can reduce the amount of total computing time for obtaining the estimate of the missing landmarks.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.673-685
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• 2018

Procrustes analysis is a useful technique useful to measure, compare shape differences and estimate a mean shape for objects; however it is based on a least squares criterion and is affected by some outliers. Therefore, we propose two generalized Procrustes analysis methods based on M-estimation and least median of squares estimation that are resistant to object outliers. In addition, two algorithms are given for practical implementation. A simulation study and some examples are used to examine and compared the performances of the algorithms with the least square method. Moreover since these resistant GPA methods are available for higher dimensions, we need some methods to visualize the objects and mean shape effectively. Also since we have concentrated on resistant fitting methods without considering shape distributions, we wish to shape analysis not be sensitive to particular model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.10
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• pp.1139-1145
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• 2014

Creation of a human skeleton model and characterization of the variation in the bone shape are fundamentally important in many applications of biomechanics. In this paper, we present a parametric shape modeling method for femurs that is based on extracting the main parameter of variations of the femur shape from a 3D model database by using statistical shape analysis. For this shape analysis, principal component analysis (PCA) is used. Application of the PCA to 3D data requires bringing all the models in correspondence to each other. For this reason, anatomical landmarks are used for guiding the deformation of the template model to fit the 3D model data. After subsequent application of PCA to a set of femur models, we calculate the correlation between the dominant components of shape variability for a target population and the anatomical parameters of the femur shape. Finally, we provide tools for visualizing and creating the femur shape using the main parameter of femur shape variation.

• Transactions of Materials Processing
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• v.20 no.2
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• pp.124-131
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• 2011

A flexible stretch forming process is useful for small quantity batch production because various shape changes of the flexible die can be achieved conveniently. In this study, the design variables, namely, the punch size, curvature radius and elastic pad thickness, were quantitatively evaluated to understand their influence on sheet formability using statistical methods such as the correlation and regression analyses. Forming simulations were designed and conducted by a three-way factorial design to obtain numerical values of a shape error. Linear relationships between the design variables and the shape error resulted from the Pearson correlation analysis. Subsequently, a regression analysis was also conducted between the design variables and the shape error. A regression equation was derived and used in the flexible die design stage to estimate the shape error.

• Imaging Science in Dentistry
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• v.51 no.2
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• pp.167-174
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• 2021

Purpose: Sex determination can be done by morphological analysis of different parts of the body. The mastoid region, with its anatomical location at the skull base, is ideal for sex identification. Statistical shape analysis provides a simultaneous comparison of geometric information on different shapes in terms of size and shape features. This study aimed to investigate the geometric morphometry of the inter-mastoid triangle as a tool for sex determination in the Iranian population. Materials and Methods: The coordinates of 5 landmarks on the mastoid process on the 80 cone-beam computed tomographic images(from individuals aged 17-70 years, 52.5% female) were registered and digitalized. The Cartesian x-y coordinates were acquired for all landmarks, and the shape information was extracted from the principal component scores of generalized Procrustes fit. The t-test was used to compare centroid size. Cross-validated discriminant analysis was used for sex determination. The significance level for all tests was set at 0.05. Results: There was a significant difference in the mastoid size and shape between males and females(P<0.05). The first 2 components of the Procrustes shape coordinates explained 91.3% of the shape variation between the sexes. The accuracy of the discriminant model for sex determination was 88.8%. Conclusion: The application of morphometric geometric techniques will significantly impact forensic studies by providing a comprehensive analysis of differences in biological forms. The results demonstrated that statistical shape analysis can be used as a powerful tool for sex determination based on a morphometric analysis of the inter-mastoid triangle.

• Journal of the Korean Ceramic Society
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• v.36 no.10
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• pp.1069-1074
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• 1999