• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• 대한수학회보
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• 제57권6호
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• pp.1367-1382
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• 2020

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.689-694
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• 2004

We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권2호
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• pp.49-57
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• 2007

In fingerprints, singular regions including core or delta points have different directional characteristics from non-singular regions. Generally, the ridges of singular regions change more abruptly than those of nonsingular areas, thus in order to effectively enhance fingerprint images regardless of region, local ridge curvature information needs to be used. In this paper, we present an improved Directional Filter Bank (DFB)-based fingerprint image enhancement method that effectively takes advantage of such ridge curvature information. The proposed method first decomposes a fingerprint image into 8 directional subbands using the DFB and then classifies the image into background, low curvature, and high curvature regions using the directional energy estimates calculated from the subbands. Thereafter, the weight values for directional subband processing are determined using classification information and directional energy estimates. Finally, the enhanced image is obtained by synthesizing the processed subbands. The experimental results show that the proposed approach is effective in enhancing both singular and non-singular regions.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.482-486
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• 2009

Scale-invariant feature is an effective method for retrieving and classifying images. In this study, we analyze a scale-invariant planar curve features for developing 2D shapes. Scale-space filtering is used to determine contour structures on different scales. However, it is difficult to track significant points on different scales. In mathematics, curvature is considered to be fundamental feature of a planar curve. However, the curvature of a digitized planar curve depends on a scale. Therefore, automatic scale detection for curvature analysis is required for practical use. We propose a technique for achieving automatic scale detection based on difference of curvature. Once the curvature values are normalized with regard to the scale, we can calculate difference in the curvature values for different scales. Further, an appropriate scale and its position are detected simultaneously, thereby avoiding tracking problem. Appropriate scales and their positions can be detected with high accuracy. An advantage of the proposed method is that the detected significant points do not need to be located in the same contour. The validity of the proposed method is confirmed by experimental results.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 추계종합학술대회 논문집(4)
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• pp.211-214
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• 2000

In this paper, we propose a regular-texture image retrieval approach relating In curvature. Maximum curvature and minimum curvature are computed from the query and each regular-texture image in the database. Seven features are computed from curvature characterizing statistical properties of the corresponding image. Each regular-texture image in the database is then represented as the seven CM (curvature measurement)-features. Query comparison and matching can be done using the corresponding CM-features. Experimental results on Brodatz texture show that the proposed approach is effective.

• Journal of the Korean Data and Information Science Society
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• 제24권1호
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• pp.179-187
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• 2013

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervals for fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.

• 한국통신학회논문지
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• 제17권2호
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• pp.187-195
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• 1992

본 논문에서는 입력으로 들어온 레이지 데이터에서 표면곡률을 계산하여 물체의 형상정보를 추출하는데 있어서 형상을 분류하기 위해 필요한 임계값을 선정하는 방법을 제안하고자 한다. 이는 우선 입력으로 들어온 레인지 데이타에서 평균곡률과 가우스곡률 등과 같은 표면곡률을 계산한다. 그 후 계산된 표면곡률값의 범위에 따라 물체의 형상특징을 분류하게 되는데 이때 임계값을 잘못 선정하게 되면 물체의 형상을 잘못 분류하게 되어 물체를 오인식하게 되는 문제점을 야기하게 된다. 따라서 본 논문에서는 통계적인 관점에서 표면이 평면인 경우 평균곡률과 가우스곡률이 동시에 0으로 간주될 수 있는 신뢰영역을 도출할 수 있는 방법을 제안하고자 하며, 경험적으로 정한 임계값과 본 논문에서 제안한 임계값으로 선정한 결과를 비교함으로써 본 논문의 유용성을 입증하고자 한다.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2002년도 Proceedings of International Symposium on Remote Sensing
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• pp.54-58
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• 2002

Mean curvature diffusion (MCD) is a selective smoothing technique that promotes smoothing within a region instead of smoothing across boundaries. By using mean curvature diffusion, noise is eliminated and edges are preserved. In this paper, we propose methods of automatic parameter selection and implementation for the MCD model coupled to min/max flow. The algorithm has been applied to high resolution aerial images and the results show that noise is eliminated and edges are preserved after removal of noise.