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Simplified projective transform for reconstruction of cylindrical panorama (실린더 파노라마 영상의 재구성을 위한 단순화된 사영 변환)

Lee Kang-Ho
- Journal of the Korea Society of Computer and Information
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- v.11 no.2 s.40
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- pp.169-175
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- 2006
In this paper we propose a method of reconstruction of cylindrical panorama using simplified projective transform from the panning image on the fixed camera. For the practical construction of cylindrical panorama we consider the rotation of the camera on the Y-axis only, even though considering the rotation components on all of the X,Y,Z axis on three-dimensional space for projective transform between general panoramas. The restriction mentioned above simplifies projective transform with existing 8 degrees of freedom into the one with 4 degrees of freedom. In the results, overall computation for projective transform can be decreased to the great extents in quantify, because the number of corresponding points required for inducing the transforming formula is gone down by half. Proposed algorithm from the simulation carried out in this paper shows similar performance and decreased computational quantity compared with existing algorithm. Also, it shows the construction of cylindrical panorama using simplified projective transform.
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Elliptic Curve Cryptography Coprocessors Using Variable Length Finite Field Arithmetic Unit (크기 가변 유한체 연산기를 이용한 타원곡선 암호 프로세서)

Lee Dong-Ho
- Journal of the Institute of Electronics Engineers of Korea SD
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- v.42 no.1
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- pp.57-67
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- 2005
Fast scalar multiplication of points on elliptic curve is important for elliptic curve cryptography applications. In order to vary field sizes depending on security situations, the cryptography coprocessors should support variable length finite field arithmetic units. To determine the effective variable length finite field arithmetic architecture, two well-known curve scalar multiplication algorithms were implemented on FPGA. The affine coordinates algorithm must use a hardware division unit, but the projective coordinates algorithm only uses a fast multiplication unit. The former algorithm needs the division hardware. The latter only requires a multiplication hardware, but it need more space to store intermediate results. To make the division unit versatile, we need to add a feedback signal line at every bit position. We proposed a method to mitigate this problem. For multiplication in projective coordinates implementation, we use a widely used digit serial multiplication hardware, which is simpler to be made versatile. We experimented with our implemented ECC coprocessors using variable length finite field arithmetic unit which has the maximum field size 256. On the clock speed 40 MHz, the scalar multiplication time is 6.0 msec for affine implementation while it is 1.15 msec for projective implementation. As a result of the study, we found that the projective coordinates algorithm which does not use the division hardware was faster than the affine coordinate algorithm. In addition, the memory implementation effectiveness relative to logic implementation will have a large influence on the implementation space requirements of the two algorithms.
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DEFORMATION SPACES OF CONVEX REAL-PROJECTIVE STRUCTURES AND HYPERBOLIC AFFINE STRUCTURES

Darvishzadeh, Mehdi-Reza;William M.Goldman
- Journal of the Korean Mathematical Society
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- v.33 no.3
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- pp.625-639
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- 1996
A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.
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HOLOMORPHIC EMBEDDINGS OF STEIN SPACES IN INFINITE-DIMENSIONAL PROJECTIVE SPACES

BALLICO E.
- Journal of the Korean Mathematical Society
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- v.42 no.1
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- pp.129-134
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- 2005
Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.
https://doi.org/10.4134/JKMS.2005.42.1.129 인용 PDF KSCI

On the projectively flat finsler space with a special $(alpha,beta)$-metric

Kim, Byung-Doo
- Communications of the Korean Mathematical Society
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- v.11 no.2
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- pp.407-413
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- 1996
The $(\alpha, \beta)$-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\Beta$; it has been sometimes treat in theoretical physics. In particular, the projective flatness of Finsler space with a metric $L^2 = 2\alpha\beta$ is considered in detail.
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