• Advances in Computational Design
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• v.7 no.1
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• pp.37-56
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• 2022

Phase-type distributions are the distributions of the time to absorption in finite and absorbing Markov chains. They generalize, while at the same time, retain the tractability of the exponential distributions and their family. They are widely used as stochastic models from queuing theory, reliability, dependability, and forecasting, to computer networks, security, and computational design. The ability to fit phase-type distributions to intractable or empirical distributions is, therefore, highly desirable for many practical purposes. Many methods and tools currently exist for this fitting problem. In this paper, we present the results of our investigation on using orthogonal-distance fitting as a method for fitting phase-type distributions, together with a comparison to the currently existing fitting methods and tools.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.121-142
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• 2002

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Korean Journal of Computational Design and Engineering
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• v.14 no.1
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• pp.10-17
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• 2009

Surface detection and parameter estimation in point cloud is a relevant subject in CAD/CAM, reverse engineering, computer vision, coordinate metrology and digital factory. In this paper we present a software for a fully automatic surface detection and parameter estimation in unordered, incomplete and error-contaminated point cloud with a large number of data points. The software consists of three algorithmic modules each for object identification, point segmentation, and model fitting, which work interactively. Our newly developed algorithms for orthogonal distance fitting(ODF) play a fundamental role in each of the three modules. The ODF algorithms estimate the model parameters by minimizing the square sum of the shortest distances between the model feature and the measurement points. We demonstrate the performance of the software on a variety of point clouds generated by laser radar, computer tomography, and stripe-projection method.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2010-2014
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• 2005

Object detection and parameter estimation in point cloud data is a relevant subject to robotics, reverse engineering, computer vision, and sport mechanics. In this paper a software is presented for fully-automatic object detection and parameter estimation in unordered, incomplete and error-contaminated point cloud with a large number of data points. The software consists of three algorithmic modules each for object identification, point segmentation, and model fitting. The newly developed algorithms for orthogonal distance fitting (ODF) play a fundamental role in each of the three modules. The ODF algorithms estimate the model parameters by minimizing the square sum of the shortest distances between the model feature and the measurement points. Curvature analysis of the local quadric surfaces fitted to small patches of point cloud provides the necessary seed information for automatic model selection, point segmentation, and model fitting. The performance of the software on a variety of point cloud data will be demonstrated live.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.33 no.4
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• pp.231-244
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• 2015

The accuracy of reference point of VLBI antenna is mandatory to perform collocation of different space geodetic techniques. In this study, we evaluated the optimal methods for the 3D circle fitting to enhance the accuracy of the reference point of VLBI antenna. Two kinds of methodologies for the orthonormal coordinate system with translation of planar observation point and the unitary coordinate transforamation were suggested and their fitting accuracies were evaluated where the orthogonal distance was calculated by residual between observation point and fitting model and the recursive calculation was performed to improve the accuracy of 3D circle fitting. Finally, we found that the methodology for the unitary coordinate transformation is highly appropriate to determine the optimal equation for azimuth-axis and elevation-axis of VLBI antenna. Therefore, the reference point of VLBI antenna with high accuracy can be determined by the intersection of the above two axises (azimuth-axis and elevation-axis). This result is expected to be utilized for a variety of researches for connection between VLBI observation results and the national control point.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.83-86
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• 2005

This paper presents a method for point-based 3D building reconstruction using LiDAR data and digital map. The proposed method consists of three processes: extraction of building roof points, identification of roof types, and 3D building reconstruction. After extracting points inside the polygon of building, the ground surface, wall and tree points among the extracted points are removed through the filtering process. The filtered points are then fitted into the flat plane using ODR(Orthogonal Distance Regression). If the fitting error is within the predefined threshold, the surface is classified as a flat roof. Otherwise, the surface is fitted and classified into a gable or arch roof through RMSE analysis. Based on the roof types identified in automated fashion, the 3D building reconstruction is performed. Experimental results showed that the proposed method classified successfully three different types of roof and that the fusion of LiDAR data and digital map could be a feasible method of modelling 3D building reconstruction.

• Journal of Korean Society for Geospatial Information Science
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• v.13 no.3 s.33
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• pp.25-32
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• 2005

This paper presents a method for point-based 3D building reconstruction using Lidar data and digital map. The proposed method consists of three processes: extraction of building roof points, identification of roof types, and 3D building reconstruction. After extracting points inside the polygon of building, the ground surface, wall and tree points among the extracted points are removed through the filtering process. The filtered points are then fitted into the flat plane using ODR(Orthogonal Distance Regression) in the first place. If the fitting error is within the predefined threshold, the surface is classified as a flat roof. Otherwise, the surface is fitted and classified into a gable or arch roof through RMSE analysis. Experimental results showed that the proposed method classified successfully three different types of roof and that the fusion of LIDAR data and digital map could be a feasible method of modeling 3D building reconstruction.

• The KIPS Transactions:PartB
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• v.16B no.1
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• pp.47-54
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• 2009

Automatic object recognition in 3D measuring data is of great interest in many application fields e.g. computer vision, reverse engineering and digital factory. In this paper we present a software tool for a fully automatic object detection and parameter estimation in unordered and noisy point clouds with a large number of data points. The software consists of three interactive modules each for model selection, point segmentation and model fitting, in which the orthogonal distance fitting (ODF) plays an important role. The ODF algorithms estimate model parameters by minimizing the square sum of the shortest distances between model feature and measurement points. The local quadric surface fitted through ODF to a randomly touched small initial patch of the point cloud provides the necessary initial information for the overall procedures of model selection, point segmentation and model fitting. The performance of the presented software tool will be demonstrated by applying to point clouds.