• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.863-879
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• 2019

In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.

• 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.

• 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.

• Women's Health Nursing
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• v.7 no.4
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• pp.622-630
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• 2001

This study aims at examining relationships between body mass index and perceived body shape and image. Using a purposive sampling method, 404 female college students were recruited from three universities located in Busan from April 2000 to June 2000. To classify the levels of obesity, Broca's method was used. Secord & Jourard's Body Cathexis Scale(1953) modified by Kim mi ok(1997) was also used to measure body image. The collected data were analyzed with the percentages, Mean, Standard deviation, T-test, and Pearson correlation Coefficient. The results of this study were as follows. 1. 56.4 % of subjects were under weight, and 42.1% were normal for BMI. 2. 55.9% of subjects were very satisfied with their body shape and 15.1% were satisfied. 3. The mean values of perceived body shape according to the BMI were 3.0 for the overweight group, 2.65 for the normal weight group, and 2.21 for the low weight group, the mean differences among three groups were significantly satisfied (F= 21.42, P= .000). 4. The mean scores of body image according to the BMI was 160.21 for low weight group, 155.57 for the normal weight group, and 140.0 for overweight group. The mean differences among the three groups were not significantly satisfied. 5. The mean scores of body image according to perceived body shape were 17819 for the satisfaction group, 161.08 for the moderate group and 150.82 for dissatisfied group. The mean differences among the three groups were significantly satisfied (F= 35.72, P=. 000). 6. There were high positive correlations between BMI and perceived body shape(r= .317) and between perceived body shape and body image (r=- .415).

• Korean Journal of Applied Biomechanics
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• v.26 no.2
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• pp.161-166
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• 2016

Objective: The purpose of this study was to determine the knee and ankle joint kinematics and kinetics by comparing downhill walking with valley-shape combined slope walking. Method: Eighteen healthy men participated in this study. A three-dimensional motion capture system equipped with eight infrared cameras and a synchronized force plate, which was embedded in the sloped walkway, was used. Obtained kinematic and kinetic parameters were compared using paired two-tailed Student's t-tests at a significance level of 0.05. Results: The knee flexion angle after the mid-stance phase, the mean peak knee flexion angle in the early swing phase, and the ankle mean peak dorsiflexion angle were greater during downhill walking compared with valley-shape combined slope walking (p < 0.001). Both the mean peak vertical ground reaction force (GRF) in the early stance phase and late stance phase during downhill walking were smaller than those values during valley-shape combined slope walking. (p = 0.007 and p < 0.001, respectively). The mean peak anterior GRF, appearing right after toe-off during downhill walking, was also smaller than that of valley-shape combined slope walking (p = 0.002). The mean peak knee extension moment and ankle plantar flexion moment in late stance phase during downhill walking were significantly smaller than those of valley-shape combined slope walking (p = 0.002 and p = 0.015, respectively). Conclusion: These results suggest that gait strategy was modified during valley-shape combined slope walking when compared with continuous downhill walking in order to gain the propulsion for lifting the body up the incline for foot clearance.

• Journal of the Korean Institute of Landscape Architecture
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• v.23 no.4
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• pp.12-19
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• 1996

Urban parks, as remnant patches, of two older cities and two new towns can be analyzed by a landscape ecological approach. The index of patch shape, the dispersion of patches, the mean edge length, and the mean patch size of parks of each city are ocmpared. The findings of this study are as follows : 1) The mean edge length of urban parks of older cities is longer than that of new towns : Seoul>Suwon>Bundang>Ansan. 2) The mean patch size of urban parks in Seoul is much greater than those of other cities : Seoul> Ansan>Suwon>Bundang. 3) The index of patch shape of urban parks of older cities is greater than that of new towns : Seoul>Suwon>BundangAnsan. 4) The dispersion of patches is in the order of Bundang >Ansan>Seoul>Suwon. The new towns have relatively even distributions of urban parks than older cities. Further research is required to find out the relationship between the index of patch shape and patch interior dynamics.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.134-143
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• 2007

A new approach based on mean value coordinate combined with Laplacian coordinate is proposed for shape deformation of a large polygon model composed of triangular net. In the method, the spherical mean value coordinates for closed control meshes is introduced to describe a vertex in the triangle meshes to be deformed. Furthermore, the well known quardratic least square method for the Laplacian coordinates is employed in order to deform the control meshes. Because the mean value coordinates are continuous and smooth on the interior of control meshes, deforming operation of control meshes change the shape of polygon model while preserving the intrinsic surface detail. The effectiveness and validity of this novel approach was demonstrated by using it to deform large and complex polygon models with arbitrary topologies.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.136-141
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• 2009

This paper proposed a framework for handover method in continuously tracking a person of interest across cooperative pan-tilt-zoom (PTZ) cameras. The algorithm here is based on a robust non-parametric technique for climbing density gradients to find the peak of probability distributions called the mean shift algorithm. Most tracking algorithms use only one cue (such as color). The color features are not always discriminative enough for target localization because illumination or viewpoints tend to change. Moreover the background may be of a color similar to that of the target. In our proposed system, the continuous person tracking across cooperative PTZ cameras by mean shift tracking that using color and shape histogram to be feature distributions. Color and shape distributions of interested person are used to register the target person across cameras. For the first camera, we select interested person for tracking using skin color, cloth color and boundary of body. To handover tracking process between two cameras, the second camera receives color and shape cues of a target person from the first camera and using linear color calibration to help with handover process. Our experimental results demonstrate color and shape feature in mean shift algorithm is capable for continuously and accurately track the target person across cameras.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.1
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• pp.160-170
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• 2008

Shape morphing is the process of transforming a source shape, through intermediate shapes, into a target shape. Two main problems to be considered in three dimensional shape morphing are vertex correspondence and path interpolation. In this paper, an approach which uses the linear interpolation of the Laplacian coordinates of the source and target meshes is introduced for the determination of more plausible path when two topologically identical shapes are morphed. When two shapes to be morphed are different in shape and topology, a new method which combines shape deformation theory based on Laplacian coordinate and mean value coordinate with distance field theory is proposed for the efficient treatment of vertex correspondence and path interpolation problems. The validity and effectiveness of the suggested method was demonstrated by using it to morph large and complex polygon models including male and female whole body models.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.