• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.7
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• pp.453-457
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• 2005

With the expansion of Internet, a variety of image databases are widely used and it is needed to select the part of an image what he wants. In contents-based image retrieval system, Zernikie moment and ART Descriptors are used fur shape descriptors in MPEC-7. This paper presents a fast computation method to determine the radius of a bounding circle that encloses an object in a binary image. With conventional methods, the whole area of the image should be scanned first and the distance from every pixel to the center point be computed. The proposed 4-directional scan method and fast circle-drawing algorithm is utilized to minimize the scanning area and reduce the number of operations fur computing the distance. Experimental results show that proposed method saves the computation time to determine the radius of a bounding circle efficiently.

• International Journal of Contents
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• v.2 no.3
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• pp.22-26
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• 2006

In this paper we introduce a new circle detection algorithm for occluded on/off pupil and iris boundary extraction. The proposed algorithm employs 7-step processing to detect a center and radius of occluded on/off eye images using the property of the chords. The algorithm deals with two types of occluded pupil and iris boundary information; one is composed of circle-shaped, incomplete objects, which is called occluded on iris images and the other type consists of arc objects in which circular information has partially disappeared, called occluded off iris images. This method shows that the center and radius of iris boundary can be detected from as little as one-third of the occluded on/off iris information image. It is also shown that the proposed algorithm computed the center and radius of the incomplete iris boundary information which has partially occluded and disappeared. Experimental results on RGB images and IR images show that the proposed method has encouraging performance of boundary detection for pupil and iris segmentation. The experimental results show satisfactorily the detection of circle from incomplete circle shape information which is occluded as well as the detection of pupil/iris boundary circle of the occluded on/off image.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.9
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• pp.142-150
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• 2002

This study describes a method of finding an optimal path of a soccer robot by using a concentric circle method with different radii of rotation. Comparing with conventional algorithms which try to find the shortest path length, the variable concentric circle method find the shortest moving time. The radius fur the shortest moving time for a given ball location depends on the relative location between a shooting robot and a ball. Practically it is difficult to find an analytical solution due to many unknowns. Assuming a radius of rotation within a possible range, total path moving time can be calculated by adding the times needed for straight path and circular path. Among these times the shortest time is obtained. In this paper, a graphical solution is presented such that the game ground is divided into 3 regions with a minimum, medium, and maximum radius of rotation.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.87-94
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• 2002

Trot(1999) considered how to calculate the expected area of a random triangle in the unit square $[0,1]{\times}[0,1]$. He used the Mathematica software package for the computational part. In this article, we study various aspects of the probability distribution of a triangle randomly chosen inside the circle of radius r. A simulation activity that can be conducted in statistics and probability classrooms is also considered.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• Journal of the Korea Society of Computer and Information
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• v.23 no.2
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• pp.27-34
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• 2018

In this paper, we propose a new method to read the hand of analog gauges to prepare for the smart factory. In addition, we suggest a new and improved method that can apply, in general, diverse analog gauges even if their scale types and ranges are various. Many companies are making great efforts to build smart factories that increase energy efficiency and automation. Managers use a variety of equipment and tools to manage the production process at the factory. In this kind of factory, analog gauges have been often used with many equipment and tools. Analog gauges are mostly circular in shape, and most papers use circular hough transform to find the center and radius of a circle. However, when the object to be found is not of the correct circle type, it takes a long time to recognize the circle using the circular hough transform, and the center and radius of the circle can not be calculated accurately. The proposed method was tested on various circular analog gauges. As a result, we confirmed that our method is outstanding.

• Journal of Digital Convergence
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• v.11 no.2
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• pp.215-220
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• 2013

They are well-known geometric properties of a circle that the perpendicular bisector of a chord passes through the center of a circle, and the intersection of the perpendicular bisectors of any two chords is its center. This paper is related to a fast pupil detection method capable of detecting the center and the radius of a pupil using these geometric properties at high speed when detecting the pupil region for iris segmentation. The proposed method is characterized as rapidly detecting the center and the radius of the pupil, extracting the candidate points of the circle in human eye images using morphological operations, and finding two chords using four points on the circular edge, and taking the intersection of the perpendicular bisectors of these two chords for its center. The proposed method can not only detect the center and the radius of a pupil rapidly but also find partially occluded pupils in human eye images.

• Journal of Korea Multimedia Society
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• v.10 no.12
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• pp.1601-1611
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• 2007

In this paper, we presented geometric CAD watermarking scheme for Architectural design drawings using line, arc, and circle components to prevent infringement of copyright from unlawfulness reproductions and distribution. The conventional CAD watermarking scheme can be applied to both line and arc components. But the proposed scheme consists of line, arc and circle watermarking schemes for three basic components of CAD design. After extracting line, arc and circle components from designed drawing, the watermark is embedded into the length of Line component, the angle of arc component, and the radius of circle component considering the robustness against various geometric transformations. The embedding strengths in each component are determined to be preserving the transparency of the watermark. By experimental result, we confirmed the robustness and the invisibility of embedded watermarks in several conversions of architectural design drawing.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.3
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• pp.52-60
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• 2019

This paper presents a numerically robust algorithm to construct a Voronoi diagram of circles in the plane. The circles are allowed to have intersections among them, but one circle cannot fully contain another circle. The Voronoi diagram is a tessellation of the plane into Voronoi regions of given circles. Each circle has its Voronoi region which is defined by a set of points in the plane closer to the circle than any other circles. The distance from a point p to a circle $c_i$ of center $p_i$ and radius $r_i$ is ${\parallel}p-p_i{\parallel}-r_i$, which is the closest Euclidean distance from p to the circle boundary. The proposed algorithm first constructs the point Voronoi diagram of centers of given circles, then it enlarges each point to the circle and expands its Voronoi region accordingly. This region-expansion process is done by local modifications and after completing this process for the whole circles the desired circle Voronoi diagram can be obtained. The proposed algorithm is numerically robust and we provide with a few examples to show its robustness. The algorithm runs in $O(n^2)$ time in the worst case and O(n) time on average where n is the number of the circles. The experiment shows that the region-expansion algorithm is robust and runs fast with strong linear time behavior.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.4
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• pp.365-370
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• 2012

Most path planning algorithms for a marine robot in the ocean environment have been developed without considering the robot's heading angle. As a result, the robot has a difficulty in following the path correctly. In this paper, we propose a limit-cycle circle set that applies to the $Theta^*$ algorithm. The minimum turning radius of a marine robot is calculated using a limit-cycle circle set, and circles of this radius is used to generate a configuration space of an occupancy grid map. After applying $Theta^*$ to this configuration space, the limit-cycle circle set is also applied to the start and end nodes to find the appropriate path with specified heading angles. The benefit of this algorithm is its fast computation time compared to other 3-D ($x,y,{\theta}$) path planning algorithms, along with the fact that it can be applied to the 3-D kinematic state of the robot. We simulate the proposed algorithm and compare it with 3-D $A^*$ and 3-D $A^*$ with post smoothing algorithms.