• 한국컴퓨터그래픽스학회논문지
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• 제7권1호
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• pp.19-25
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• 2001

본 논문에서는 평면 다항식 피타고리안 호도그라프 곡선을 그 근들의 관점에서 특별한 기하학적 재 매개화하는 것에 관하여 연구한다. 피타고라스 호도그라프 곡선들은 그 호도그라프의 근들에 의하여 완전히 결정된다. 피타고라스 호도그라프 곡선들의 근들의 자취는 아주 흥미로운 기하학적 성질들을 만족함을 보인다.

• 대한수학회지
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• 제55권3호
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.

• 대한수학회보
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• 제60권1호
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• pp.47-73
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• 2023

This paper is devoted to establishing certain L^p bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by h ∈ ∆_γ(ℝ₊) and Ω ∈ Wℱ_β(S^n-1) for some γ, β ∈ (1, ∞]. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley g^*_λ functions and area integrals are also presented.

• 정보처리학회논문지B
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• 제19B권3호
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• pp.201-208
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• 2012

혈관 내 초음파 영상(IVUS: Intravascular ultrasoundimages)에서 내강(Lumen) 경계 영역을 검출하는 것은 환자의 심혈관 상태를 파악하는데 중요한 정보를 제공하며, 이를 통해 심혈관계 질환을 예측하고 진단할 수 있다. 따라서 정확하게 내강 경계를 분할하는 것은 매우 중요한 단계이다. 본 논문에서는 비모수적 확률 밀도 함수와 스무딩 함수를 사용하여 자동으로 내강 영역을 분할하는 기법을 제안한다. 각각의 혈관내 초음파 영상들을 극좌표 이미지로 변환 후 웨이블릿 변환을 적용하여 초기 관심 점들을 검출한다. 초기 관심점들 중에서 잡음과 칼슘에 의해 발생된 튀는 점들을 제거하기 위해 비모수적 밀도 함수와 스무딩 함수를 이용하여 튀는 점들을 제거하고 경계면에 해당하는 중요 관심 점만을 남긴다. 마지막으로, 다항곡선 접합(Polynomial curve fitting) 함수를 정의하고 다항식과 실제 내강 경계선에 접합된 관심 점을 이용하여 자연스러운 내강 경계면을 추정한다. 본 논문에서 제안한 방법을 다양한 초음파 영상에 대해 실험한 결과, 기존에 제안된 방법 보다 정확하게 경계면을 검출함을 알 수 있었다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2008년도 추계종합학술대회 B
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• pp.544-547
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• 2008

3차원 가상환경에서 탐색항해는 현실세계에 비해 부족한 정보를 활용하기 때문에 많은 어려움이 있다. 3차원 가상환경에서의 탐색항해 보조도구 개발은 3차원 가상현실에서 중요한 연구주제 이다. 본 연구는 스플라인 곡선을 활용한 탐색항해 패스 설정에 대해연구 하였다. 스플라인 곡선은 다항식 함수이기 때문에 미분가능하다. 특히, 2차 3차 스플라인 곡선은 2번이상 미분가능하기 때문에 컴퓨터그래픽스에서 요구하는 충분히 부드러운 곡선이다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.2576-2578
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• 2001

Elliptic curve cryptosystems based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm in an elliptic curve group appears to be more difficult than discrete logarithm problem in other groups while using the relatively small key size. An implementation of elliptic curve cryptosystems needs finite field arithmetic computation. Hence finite field arithmetic modules must require less hardware resources to archive high performance computation. In this paper, a new architecture of finite field multiplier using conversion scheme of normal basis representation into polynomial basis representation is discussed. Proposed architecture provides less resources and lower complexity than conventional bit serial multiplier using normal basis representation. This architecture has synthesized using synopsys FPGA express successfully.

• 한국공작기계학회논문집
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• 제13권5호
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• pp.103-109
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• 2004

This paper presents a fairing method for reverse engineering of a free-formed surface. Utilizing measured data points, reverse engineering is a useful method to construct a CAD model from physical model. Measured data points should be faired since raw data may have outliers. A fairing algorithm of polynomial regression model generates smooth curves of approximation in this paper. The faired curves are utilized to construct a free-formed surface. For a verifying example, an impeller blade is digitized with a CMM to collect raw data on the surfacce and a CAD model is constructed. This research produces impeller blades with 5-axis machining center through the CAD model and compares them with a physical model. As a result the produced surface modeled with the fairing method gives less error than that without the fairing.

• Current Optics and Photonics
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• 제4권5호
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• pp.411-420
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• 2020

Non-contact three-dimensional (3D) measuring technology is used to identify defects in miniature products, such as optics, polymers, and semiconductors. Hence, this technology has garnered significant attention in computer vision research. In this paper, we focus on shape from focus (SFF), which is an optical passive method for 3D shape recovery. In existing SFF techniques using interpolation, all datasets of the focus volume are approximated using one model. However, these methods cannot demonstrate how a predefined model fits all image points of an object. Moreover, it is not reasonable to explain various shapes of datasets using one model. Furthermore, if noise is present in the dataset, an error will be generated. Therefore, we propose an algorithm based on polynomial regression analysis to address these disadvantages. Our experimental results indicate that the proposed method is more accurate than existing methods.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 II
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• pp.935-938
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• 2003

The performance of elliptic curve based on public key cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. This work describes a finite field multiplier and divider which is implemented using SystemC. Also this present an efficient hardware for performing the elliptic curve point multiplication using the polynomial basis representation. In order to improve the speed of the multiplier with as a little extra hardware as possible, adopted hybrid finite field multiplication and finite field divider.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 하계종합학술대회 논문집(2)
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• pp.305-308
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• 2001

This paper describes the design of elliptic curve cryptographic (ECC) coprocessor over binary fields for the If card. This coprocessor is implemented by the shift-and-add algorithm for the field multiplication algorithm. And the modified almost inverse algorithm(MAIA) is selected for the inverse multiplication algorithm. These two algorithms is merged to minimize the hardware size. Scalar multiplication is performed by the binary Non Adjacent Format(NAF) method. The ECC we have implemented is defined over the field GF(2$^{163}$), which is a SEC-2 recommendation［7］..