• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.1
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• pp.188-198
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• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.2
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• pp.380-389
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• 2005

The Goldschmidt iterative algorithm for a floating point divide calculates it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's divide algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To calculate a floating point divide '$\frac{N}{F}$', multifly '$T=\frac{1}{F}+e_t$' to the denominator and the nominator, then it becomes ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'. And the algorithm repeats the following operations: ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than ‘$e_r=2^{-p}$'. The value of p is 29 for the single precision floating point, and 59 for the double precision floating point. Let ’$F_i=1+e_i$', there is $F_{i+1}=1-e_{i+1},\;e_{i+1}',\;where\;e_{i+1}, If '$[F_i-1]<2^{\frac{-p+3}{2}}$ is true, ’$e_{i+1}<16e_r$' is less than the smallest number which is representable by floating point number. So, ‘$N_{i+1}$ is approximate to ‘$\frac{N}{F}$'. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables ($T=\frac{1}{F}+e_t$) with varying sizes. 1'he superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a divider. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• The KIPS Transactions:PartA
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• v.12A no.2 s.92
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• pp.95-102
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal which is widely used for a floating point division, calculates the reciprocal by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the reciprocal of a floating point number F, the algorithm repeats the following operations: '$'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$ with the initial value $'X_0=\frac{1}{F}{\pm}e_0'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 27 for the single precision floating point, and 57 for the double precision floating point. Let $'X_i=\frac{1}{F}+e_i{'}$, these is $'X_{i+1}=\frac{1}{F}-e_{i+1},\;where\;{'}e_{i+1}, is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to $'\frac{1}{F}{'}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables $(X_0=\frac{1}{F}{\pm}e_0)$ with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal unit. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia scientific computing, etc.

• Journal of the Daesoon Academy of Sciences
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• v.32
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• pp.137-173
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• 2019

Modern scientists are trying to find the basic unit of order, fractal geometry, in the complex systems of the universe. Fractal is a term often used in mathematics or physics, it is appropriate as a principle to explain why some models of ultimate reality are represented as multifaceted. Fractals are already widely used in the field of computer graphics and as a commercial principle in the world of science. In this paper, using observations from fractal geometry, I present the embodiment of ultimate reality as understood in Daesoon Thought. There are various models of ultimate reality such as Dao (道, the way), Sangje (上帝, supreme god), Sinmyeong (神明, Gods), Mugeuk (無極, limitlessness), Taegeuk (太極, the Great Ultimate), and Cheonji (天地, heaven and earth) all of which exist in Daesoon Thought, and these concepts are mutually interrelated. In other words, by revealing the fact that ultimate reality is embodied within fractal geometry, it can be shown that concordance and transformation of various models of ultimate reality are supported by modern science. But when the major religions of the world were divided along lines of personality (personal gods) and non-personality (impersonal deities), most religions came to assume that ultimate reality was either transcendental or personal, and they could not postulate a relationship between God and humanity as Yin Yang (陰陽) fractals (Holon). In addition, religions, which assume ultimate reality as an intrinsic and impersonal being, are somewhat different in terms of their degree of Holon realization - all parts and whole restitution. Daesoon Thought most directly states that gods (deities) and human beings are in a relationship of Yin Yang fractals. In essence, "deities are Yin, and humanity is Yang" and furthermore, "human beings are divine beings." Additionally, in the Daesoon Thought, these models of ultimate reality are presented through various concepts from various viewpoints, and they are revealed as mutually interrelated concepts. As such, point of view regarding the universe wherein Holarchy becomes a models in a key idea within perennial philosophy. According to a universalized view of religious phenomena, perennial philosophy was adopted by the world's great spiritual teachers, thinkers, philosophers, and scientists. From this viewpoint, when ultimate reality coincides, human beings and God are no longer different. In other words, the veracity of the theory of ultimate reality that has appeared in Daesoon Thought can find support in both modern science and perennial philosophy.

• Korean Journal of Heritage: History & Science
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• v.39
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• pp.351-378
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• 2006

With the development of media, the methods for the documentation of intangible cultural heritage have been also developed and diversified. As well as the previous analogue ways of documentation, the have been recently applying new multi-media technologies focusing on digital pictures, sound sources, movies, etc. Among the new technologies, the documentation of intangible cultural heritage using the method of 'Motion Capture' has proved itself prominent especially in the fields that require three-dimensional documentation such as dances and performances. Motion Capture refers to the documentation technology which records the signals of the time varing positions derived from the sensors equipped on the surface of an object. It converts the signals from the sensors into digital data which can be plotted as points on the virtual coordinates of the computer and records the movement of the points during a certain period of time, as the object moves. It produces scientific data for the preservation of intangible cultural heritage, by displaying digital data which represents the virtual motion of a holder of an intangible cultural heritage. National Research Institute of Cultural Properties (NRICP) has been working on for the development of new documentation method for the Important Intangible Cultural Heritage designated by Korean government. This is to be done using 'motion capture' equipments which are also widely used for the computer graphics in movie or game industries. This project is designed to apply the motion capture technology for 3 years- from 2005 to 2007 - for 11 performances from 7 traditional dances of which body gestures have considerable values among the Important Intangible Cultural Heritage performances. This is to be supported by lottery funds. In 2005, the first year of the project, accumulated were data of single dances, such as Seungmu (monk's dance), Salpuri(a solo dance for spiritual cleansing dance), Taepyeongmu (dance of peace), which are relatively easy in terms of performing skills. In 2006, group dances, such as Jinju Geommu (Jinju sword dance), Seungjeonmu (dance for victory), Cheoyongmu (dance of Lord Cheoyong), etc., will be documented. In the last year of the project, 2007, education programme for comparative studies, analysis and transmission of intangible cultural heritage and three-dimensional contents for public service will be devised, based on the accumulated data, as well as the documentation of Hakyeonhwadae Habseolmu (crane dance combined with the lotus blossom dance). By describing the processes and results of motion capture documentation of Salpuri dance (Lee Mae-bang), Taepyeongmu (Kang seon-young) and Seungmu (Lee Mae-bang, Lee Ae-ju and Jung Jae-man) conducted in 2005, this report introduces a new approach for the documentation of intangible cultural heritage. During the first year of the project, two questions have been raised. First, how can we capture motions of a holder (dancer) without cutoffs during quite a long performance? After many times of tests, the motion capture system proved itself stable with continuous results. Second, how can we reproduce the accurate motion without the re-targeting process? The project re-created the most accurate motion of the dancer's gestures, applying the new technology to drew out the shape of the dancers's body digital data before the motion capture process for the first time in Korea. The accurate three-dimensional body models for four holders obtained by the body scanning enhanced the accuracy of the motion capture of the dance.

• Journal of Intelligence and Information Systems
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• v.18 no.1
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• pp.1-21
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• 2012

In recent years, mobile phone has experienced an extremely fast evolution. It is equipped with high-quality color displays, high resolution cameras, and real-time accelerated 3D graphics. In addition, some other features are includes GPS sensor and Digital Compass, etc. This evolution advent significantly helps the application developers to use the power of smart-phones, to create a rich environment that offers a wide range of services and exciting possibilities. To date mobile AR in outdoor research there are many popular location-based AR services, such Layar and Wikitude. These systems have big limitation the AR contents hardly overlaid on the real target. Another research is context-based AR services using image recognition and tracking. The AR contents are precisely overlaid on the real target. But the real-time performance is restricted by the retrieval time and hardly implement in large scale area. In our work, we exploit to combine advantages of location-based AR with context-based AR. The system can easily find out surrounding landmarks first and then do the recognition and tracking with them. The proposed system mainly consists of two major parts-landmark browsing module and annotation module. In landmark browsing module, user can view an augmented virtual information (information media), such as text, picture and video on their smart-phone viewfinder, when they pointing out their smart-phone to a certain building or landmark. For this, landmark recognition technique is applied in this work. SURF point-based features are used in the matching process due to their robustness. To ensure the image retrieval and matching processes is fast enough for real time tracking, we exploit the contextual device (GPS and digital compass) information. This is necessary to select the nearest and pointed orientation landmarks from the database. The queried image is only matched with this selected data. Therefore, the speed for matching will be significantly increased. Secondly is the annotation module. Instead of viewing only the augmented information media, user can create virtual annotation based on linked data. Having to know a full knowledge about the landmark, are not necessary required. They can simply look for the appropriate topic by searching it with a keyword in linked data. With this, it helps the system to find out target URI in order to generate correct AR contents. On the other hand, in order to recognize target landmarks, images of selected building or landmark are captured from different angle and distance. This procedure looks like a similar processing of building a connection between the real building and the virtual information existed in the Linked Open Data. In our experiments, search range in the database is reduced by clustering images into groups according to their coordinates. A Grid-base clustering method and user location information are used to restrict the retrieval range. Comparing the existed research using cluster and GPS information the retrieval time is around 70~80ms. Experiment results show our approach the retrieval time reduces to around 18~20ms in average. Therefore the totally processing time is reduced from 490~540ms to 438~480ms. The performance improvement will be more obvious when the database growing. It demonstrates the proposed system is efficient and robust in many cases.