• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.47 no.1
• /
• pp.1-14
• /
• 2010

With the rapid growth of 3D content industry fields, 3D content-based hashing (or hash function) has been required to apply to authentication, trust and retrieval of 3D content. A content hash can be a random variable for compact representation of content. But 3D content-based hashing has been not researched yet, compared with 2D content-based hashing such as image and video. This paper develops a robust 3D content-based hashing based on key-dependent 3D surface feature. The proposed hashing uses the block surface coefficient using shape coordinate of 3D SSD and curvedness for 3D surface feature and generates a binary hash by a permutation key and a random key. Experimental results verified that the proposed hashing has the robustness against geometry and topology attacks and has the uniqueness of hash in each model and key.

• Education of Primary School Mathematics
• /
• v.14 no.2
• /
• pp.103-116
• /
• 2011

'The nine chapters on the mathematical art' has dominated the history of Chinese mathematics. It contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. But it has been greatly by improved by the commentary given Liu Hui and it was transformed from arithmetic text to mathematics. The improved book served as important textbook in China but also the East Asian countries for the past 2000 years. Also It is comparable in significance to Euclid's Elements in the West. In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early on 'The nine chapters' and 'ShuLiJingYun(數理精蘊)'. Their studies gave rise to a momentum for a prominent development of Choson mathematics in the century. Nam Byung Gil is also commentator on 'The Nine Chapters'. His commentary is 'GuJangSulHae(九章術解)'. This book provides figures and explanations of how the algorithms work. These are very helpful for prospective elementary teachers. We try to plan programs of elementary teacher education on the basis of 'The Nine Chapters' and 'GuJangSulHae'.

• Journal of KIISE:Computing Practices and Letters
• /
• v.7 no.6
• /
• pp.696-702
• /
• 2001

In this paper, we design IDEA cipher algorithm which is cryptographically superior to DES. To improve the encryption throughput, we propose an efficient design methodology for high-speed implementation of multiplicative inverse modulo $2^{15}$+1 which requires the most computing powers in IDEA. The efficient hardware architecture for the multiplicative inverse in derived from applying of Fermat's Theorem. The computing powers for multiplicative inverse in our proposal is a decrease 50% compared with the existing method based on Extended Euclid Algorithm. We implement IDEA by applying a single iterative round method and our proposal for multiplicative inverse. With a system clock frequency 20MGz, the designed hardware permits a data conversion rate of more than 116 Mbit/s. This result show that the designed device operates about 2 times than the result of the paper by H. Bonnenberg et al. From a speed point of view, out proposal for multiplicative inverse is proved to be efficient.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.28 no.2A
• /
• pp.80-85
• /
• 2003

This paper proposes Galois Field Arithmetic Unit(GFAU) whose structure does addition, multiplication and division in GF(2m). GFAU can execute maximum two additions, or two multiplications, or one addition and one multiplication. The base architecture of this GFAU is a divider based on modified Euclid's algorithm. The divider was modified to enable multiplication and addition, and the modified divider with the control logic became GFAU. The GFAU for GF(2193) was implemented with Verilog HDL with top-down methodology, and it was improved and verified by a cycle-based simulator written in C-language. The verified model was synthesized with Samsung 0.35um, 3.3V CMOS standard cell library, and it operates at 104.7MHz in the worst case of 3.0V, 85$^{\circ}C$, and it has about 25,889 gates.

• Publications of The Korean Astronomical Society
• /
• v.30 no.2
• /
• pp.397-399
• /
• 2015

Recently, cosmic voids have been recognized as a powerful cosmological probe. A number of studies have focused on the effects of the gravitational lensing by voids on the temperature (and in some cases polarization) anisotropy of the Cosmic Microwave Background (CMB) background at relatively large to medium scales, l ~ 1000. Many of these studies attempt to explain the unusually large cold spot in CMB temperature maps and dynamical evidence of dark energy via detections of late-time integrated Sachs Wolfe (ISW) effect. Here, the effects of lensing by voids on the CMB temperature anisotropy at small scales, up to l = 3000, will be investigated. This work is carried out in the light of the benefits of adding large catalogues of cosmic voids, to be identified by future large galaxy surveys such as EUCLID and LSST, to the analysis of CMB data such as those from Planck mission. Our numerical simulation utilizes two methods, namely, the small-de ectionangle approximation and full ray-tracing analysis. Using the fitted void density profiles and radius (RV ) distribution available in the literature from N-body simulations, we simulated the secondary temperature anisotropy (lensing) of CMB photons induced by voids along a line of sight from redshift 0 to 2. Each line of sight contains approximately 1000 voids of effective radius $RV_{,eff}=35h^{-1}Mpc$ with randomly distributed radial and projected positions. Both methods are used to generate temperature maps. The two methods will be compared for their accuracy and effciency in the implementation of theoretical modeling.

• The Mathematical Education
• /
• v.58 no.2
• /
• pp.319-335
• /
• 2019

In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.

• Journal of Biomedical Engineering Research
• /
• v.44 no.5
• /
• pp.346-353
• /
• 2023

In this paper, we propose an innovative approach that leverages deep learning to find optimal reference points for achieving precise tooth segmentation in three-dimensional tooth point cloud data. A dataset consisting of 350 aligned maxillary and mandibular cloud data was used as input, and both end coordinates of individual teeth were used as correct answers. A two-dimensional image was created by projecting the rendered point cloud data along the Z-axis, where an image of individual teeth was created using an object detection algorithm. The proposed algorithm is designed by adding various modules to the Unet model that allow effective learning of a narrow range, and detects both end points of the tooth using the generated tooth image. In the evaluation using DSC, Euclid distance, and MAE as indicators, we achieved superior performance compared to other Unet-based models. In future research, we will develop an algorithm to find the reference point of the point cloud by back-projecting the reference point detected in the image in three dimensions, and based on this, we will develop an algorithm to divide the teeth individually in the point cloud through image processing techniques.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.11 no.2
• /
• pp.107-112
• /
• 2011

It is very difficult to factorize composite number, $n=pq$ to integer factorization, p and q that is almost similar length of digits. Integer factorization algorithms, for the most part, find ($a,b$) that is congruence of squares ($a^2{\equiv}b^2$ (mod $n$)) with using factoring(factor base, B) and get the result, $p=GCD(a-b,n)$, $q=GCD(a+b,n)$ with taking the greatest common divisor of Euclid based on the formula $a^2-b^2=(a-b)(a+b)$. The efficiency of these algorithms hangs on finding ($a,b$) and deciding factor base, B. This paper proposes a efficient algorithm. The proposed algorithm extracts B from integer factorization with 3 digits prime numbers of $n+1$ and decides f, the combination of B. And then it obtains $x$(this is, $a=fxy$, $\sqrt{n}$ < $a$ < $\sqrt{2n}$) from integer factorization of $n-2$ and gets $y=\frac{a}{fx}$, $y_1$={1,3,7,9}. Our algorithm is much more effective in comparison with the conventional Fermat algorithm that sequentially finds $\sqrt{n}$ < $a$.

• The KIPS Transactions:PartB
• /
• v.19B no.1
• /
• pp.1-8
• /
• 2012

Mosaic is to make a big image by gathering lots of small materials having various colors. With advance of digital imaging techniques, photomosaic techniques using photos are widely used. In this paper, we presents an automatic photomosaic algorithm based on adaptive tiling and block matching. The proposed algorithm is composed of two processes: photo database generation and photomosaic generation. Photo database is a set of photos (or tiles) used for mosaic, where a tile is divided into $4{\times}4$ regions and the average RGB value of each region is the feature of the tile. Photomosaic generation is composed of 4 steps: feature extraction, adaptive tiling, block matching, and intensity adjustment. In feature extraction, the feature of each block is calculated after the image is splitted into the preset size of blocks. In adaptive tiling, the blocks having similar similarities are merged. Then, the blocks are compared with tiles in photo database by comparing euclidean distance as a similarity measure in block matching. Finally, in intensity adjustment, the intensity of the matched tile is replaced as that of the block to increase the similarity between the tile and the block. Also, a tile redundancy minimization scheme of adjacent blocks is applied to enhance the quality of mosaic photos. In comparison with Andrea mosaic software, the proposed algorithm outperforms in quantitative and qualitative analysis.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.11 no.4
• /
• pp.157-164
• /
• 2011

It is very difficult problem to factorize composite number. Integer factorization algorithms, for the most part, find ($a,b$) that is congruence of squares ($a^2{\equiv}b^2$(mode $n$)) with using factoring(factor base, B) and get the result, $p=GCD(a-b,n)$, $q=GCD(a+b,n)$ with taking the greatest common divisor of Euclid based on the formula $a^2-b^2=(a-b)(a+b)$. The efficiency of these algorithms hangs on finding ($a,b$). Fermat's algorithm that is base of congruence of squares finds $a^2-b^2=n$. This paper proposes the method to find $a^2-b^2=kn$, ($k=1,2,{\cdots}$). It is supposed $b_1$=0 or 5 to be surely, and b is a double number. First, the proposed method decides $k$ by getting kn that satisfies $b_1=0$ and $b_1=5$ about $n_2n_1$. Second, it decides $a_2a_1$ that satisfies $a^2-b^2=kn$. Third, it figures out ($a,b$) from $a^2-b^2=kn$ about $a_2a_1$ as deciding $\sqrt{kn}$ < $a$ < $\sqrt{(k+1)n}$ that is in $kn$ < $a^2$ < $(k+1)n$. The proposed algorithm is much more effective in comparison with the conventional Fermat algorithm.