• 대한전자공학회논문지SD
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• 제42권1호
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• pp.57-67
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• 2005

고속 스칼라곱 연산은 타원곡선 암호 응용을 위해서 매우 중요하다. 보안 상황에 따라 유한체의 크기를 변경하려면 타원곡선 암호 보조프로세서가 크기 가변 유한체 연산 장치를 제공하여야 한다. 크기 가변 유한체 연산기의 효율적인 연산 구조를 연구하기 위하여 전형적인 두 종류의 스칼라곱 연산 알고리즘을 FPGA로 구현하였다. Affine 좌표계 알고리즘은 나눗셈 연산기를 필요로 하며, projective 좌표계 알고리즘은 곱셈 연산기만 사용하나 중간 결과 저장을 위한 메모리가 더 많이 소요된다. 크기 가변 나눗셈 연산기는 각 비트마다 궤환 신호선을 추가하여야 하는 문제점이 있다. 본 논문에서는 이로 인한 클록 속도저하를 방지하는 간단한 방법을 제안하였다. Projective 좌표계 구현에서는 곱셈 연산으로 널리 사용되는 디지트 serial 곱셈구조를 사용하였다. 디지트 serial 곱셈기의 크기 가변 구현은 나눗셈의 경우보다 간단하다. 최대 256 비트 크기의 연산이 가능한 크기 가변 유한체 연산기를 이용한 암호 프로세서로 실험한 결과, affine 좌표계 알고리즘으로 스칼라곱 연산을 수행한 시간이 6.0 msec, projective 좌표계 알고리즘의 경우는 1.15 msec로 나타났다. 제안한 타원곡선 암호 프로세서를 구현함으로써, 하드웨어 구현의 경우에도 나눗셈 연산을 사용하지 않는 projective 좌표계 알고리즘이 속도 면에서 우수함을 보였다. 또한, 메모리의 논리회로에 대한 상대적인 면적 효율성이 두 알고리즘의 하드웨어 구현 면적 요구에 큰 영향을 미친다.

• 대한수학회논문집
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• 제37권2호
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• 한국CDE학회논문집
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• 제9권4호
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• pp.397-405
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• 2004

Texture mapping is the process of covering 3D models with texture images in order to increase the visual realism of the models. For proper mapping the coordinates of texture images need to coincide with those of the 3D models. When projective images from the camera are used as texture images, the texture image coordinates are defined by a camera calibration method. The texture image coordinates are determined by the relation between the coordinate systems of the camera image and the 3D object. With the projective camera images, the distortion effect caused by the camera lenses should be compensated in order to get accurate texture coordinates. The distortion effect problem has been dealt with iterative methods, where the camera calibration coefficients are computed first without considering the distortion effect and then modified properly. The methods not only cause to change the position of the camera perspective line in the image plane, but also require more control points. In this paper, a new iterative method is suggested for reducing the error by fixing the principal points in the image plane. The method considers the image distortion effect independently and fixes the values of correction coefficients, with which the distortion coefficients can be computed with fewer control points. It is shown that the camera distortion effects are compensated with fewer numbers of control points than the previous methods and the projective texture mapping results in more realistic image.

• ETRI Journal
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• 제30권3호
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• pp.365-376
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• 2008

This paper presents the design and implementation of a hyperelliptic curve cryptography (HECC) coprocessor over affine and projective coordinates, along with measurements of its performance, hardware complexity, and power consumption. We applied several design techniques, including parallelism, pipelining, and loop unrolling, in designing field arithmetic units, group operation units, and scalar multiplication units to improve the performance and power consumption. Our affine and projective coordinate-based HECC processors execute in 0.436 ms and 0.531 ms, respectively, based on the underlying field GF($2^{89}$). These results are about five times faster than those for previous hardware implementations and at least 13 times better in terms of area-time products. Further results suggest that neither case is superior to the other when considering the hardware complexity and performance. The characteristics of our proposed HECC coprocessor show that it is applicable to high-speed network applications as well as resource-constrained environments, such as PDAs, smart cards, and so on.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2002년도 추계종합학술대회
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• pp.226-230
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• 2002

본 논문은 영상 모자이킹을 위한 사영 변환 행렬의 정밀도를 개선하는 방법을 제안한다. Shift Theorem을 이용하여 영상간의 전역 이동 성분을 추출하고 구해진 이동 성분을 이용하여 영상간의 일치점을 찾음으로서 기존의 일치점 검출의 문제점을 해결하였다. 일치점 집합을 RANSAC 알고리즘을 적용하여 신뢰도가 높은 일치점을 추출함으로서 잡음의 영향에 강인하도록 하였으며 일치점의 좌표를 정규화 하여 사영변환 행렬의 정밀도를 개선하였다.

• Smart Structures and Systems
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• 제25권2호
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• pp.135-153
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• 2020

There has been a sustained interest towards the non-contact structural displacement measurement by means of videogrammetric technique. On the way forward, one of the major concerns is the spurious image drift induced by temperature variation. This study therefore carries out an investigation into the temperature effect of videogrammetric technique, focusing on the exploration of the mechanism behind the temperature effect and the elimination of the temperature-caused measurement error. 2D videogrammetric measurement tests under monotonic or cyclic temperature variation are first performed. Features of measurement error and the casual relationship between temperature variation and measurement error are then studied. The variation of the temperature of digital camera is identified as the main cause of measurement error. An excellent linear relationship between them is revealed. After that, camera parameters are extracted from the mapping between world coordinates and pixels coordinates of the calibration targets. The coordinates of principle point and focal lengths show variations well correlated with temperature variation. The measurement error is thought to be an outcome mainly attributed to the variation of the coordinates of principle point. An approach for eliminating temperature-caused measurement error is finally proposed. Correlation models between camera parameters and temperature are formulated. Thereby, camera parameters under different temperature conditions can be predicted and the camera projective matrix can be updated accordingly. By reconstructing the world coordinates with the updated camera projective matrix, the temperature-caused measurement error is eliminated. A satisfactory performance has been achieved by the proposed approach in eliminating the temperature-caused measurement error.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권9호
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• pp.3177-3195
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• 2014

In many moving object detection problems of an aerial video, accurate and robust stabilization is of critical importance. In this paper, a novel accurate image alignment algorithm for aerial electronic image stabilization (EIS) is described. The feature points are first selected using optimal derivative filters based Harris detector, which can improve differentiation accuracy and obtain the precise coordinates of feature points. Then we choose the Delaunay Triangulation edges to find the matching pairs between feature points in overlapping images. The most "useful" matching points that belong to the background are used to find the global transformation parameters using the projective invariant. Finally, intentional motion of the camera is accumulated for correction by Sage-Husa adaptive filtering. Experiment results illustrate that the proposed algorithm is applied to the aerial captured video sequences with various dynamic scenes for performance demonstrations.

• 한국멀티미디어학회논문지
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• 제15권6호
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• pp.770-783
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• 2012

본 논문에서는 다중 영상에서 추출된 특징점을 사용해서 투영 공간에서의 카메라 행렬과 3차원 정점좌표를 계산하는 방법을 제안한다. 수치적인 안정성을 위해서 특징점을 정규화한 후 복원하며 얻어지는 카메라 행렬과 3차원 정점에 대해서 비정규화한다. 카메라 행렬과 3차원 정점의 초기값을 얻기 위해서 특이값 분해기법을 사용해서 투영 깊이가 적용된 측정 행렬을 분해한다. 행렬 분해 제약을 사용하여 카메라 행렬과 3차원 정점을 투영 복원한다. 투영 복원 과정에서는 비선형 반복적 최적화 방법이 사용된다. 실험 결과 제안방법은 대체로 적절한 정확성을 얻었고 오차의 편차가 크지 않았다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2022년도 춘계학술대회
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• pp.246-248
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• 2022

Bernstein이 제안한 새로운 타원곡선 형태인 이진 에드워즈 곡선 (binary Edwards curves; BEdC)는 예외점이 없어 완전한 덧셈 법칙이 만족한다. 본 논문에서는 투영 좌표계를 적용한 BEdC 상의 점 스칼라 곱셈의 효율적인 하드웨어 구현에 대해 기술한다. 점 스칼라 곱셈을 위해 modified Montgomery ladder 알고리듬을 적용하였으며, 257-비트 이진 덧셈기와 이진 제곱기, 32-비트 이진 곱셈기를 사용하여 하위 이진체 연산을 구현했다. Zynq UltraScale+ MPSoC 디바이스에 구현하여 설계된 BEdC 크립토 코어를 검증하였으며, 점 스칼라 곱셈 연산에 521,535 클록 사이클이 소요된다.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2009년도 9th International Meeting on Information Display
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• pp.1014-1017
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• 2009

The analytical expression for quality function is found including the dependence on disparity. The problem is considered in the projective coordinates for which the forward and backward transformation matrices are found. The formation of side observer regions is considered. The probability of the pseudo stereo effect is also estimated. Testing patterns are improved in order to provide higher accuracy of measurements. This is confirmed in experiments.