• Honam Mathematical Journal
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• v.42 no.1
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• pp.75-91
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• 2020

In this study, we have generalized pseudo-Finsler map by introducing the concept of semi-Riemannian map and have found pseudo-Finsler eikonal equations using pseudo-Finsler map. After that, we have obtained some sufficient theorems on pseudo-Finsler manifolds for the existence of solutions to the eikonal equation. At the same time, we have introduced a natural definition for the affine maps between pseudo-Finsler manifolds and have reached the affine solutions of them.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1149-1165
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• 2016

In this paper, we show that there exists no left invariant Riemannian metric h on the Heisenberg group H such that (H, h) is a symmetric Riemannian manifold, and there does not exist any H-invariant metric $\bar{h}$ on the Heisenberg manifold $H/{\Gamma}$ such that the Riemannian connection on ($H/{\Gamma},\bar{h}$) is a Yang-Mills connection. Moreover, we get necessary and sufficient conditions for a group homomorphism of (SU(2), g) with an arbitrarily given left invariant metric g into (H, h) with an arbitrarily given left invariant metric h to be a harmonic and an affine map, and get the totality of harmonic maps of (SU(2), g) into H with a left invariant metric, and then show the fact that any affine map of (SU(2), g) into H, equipped with a properly given left invariant metric on H, does not exist.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.877-880
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• 2000

In this paper, we develop an algorithm of soccer image sequences mosaicing using reverse affine transform. The continuous mosaic images of soccer ground field allows the user/viewer to view a “wide picture” of the player’s actions The first step of our algorithm is to automatic detection and tracking player, ball and some lines such as center circle, sideline, penalty line and so on. For this purpose, we use the ground field extraction algorithm using color information and player and line detection algorithm using four P-rules and two L-rules. The second step is Affine transform to map the points from image to model coordinate using predefined and pre-detected four points. General Affine transformation has many holes in target image. In order to delete these holes, we use reverse Affine transform. We tested our method in real image sequence and the experimental results are given.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.237-257
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• 1998

By introducing the notion of a generalized normal state space, we give a necessary and sufficient condition for that there exists a unital normal completely map from a von Neumann algebra into another, in terms of their generalized normal state spaces.

• Journal of Korean Society for Geospatial Information Science
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• v.22 no.4
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• pp.3-11
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• 2014

Recently, rapid urbanization has necessitated continuous updates in digital map to provide the latest and accurate information for users. However, conventional aerial photogrammetry has some restrictions on periodic updates of small areas due to high cost, and as-built drawing also brings some problems with maintaining quality. Alternatively, this paper proposes a scheme for efficient and accurate update of digital map using point cloud data acquired by Terrestrial Laser Scanner (TLS). Initially, from the whole point cloud data, the building sides are extracted and projected onto a 2D image to trace out the 2D building footprints. In order to register the footprint extractions on the digital map, 2D Affine model is used. For Affine parameter estimation, the centroids of each footprint groups are randomly chosen and matched by means of a modified RANSAC algorithm. Based on proposed algorithm, the experimental results showed that it is possible to renew digital map using building footprint extracted from TLS data.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.10a
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• pp.309-315
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• 2003

This study is aimed to research the precise and efficient method for coordinate transformation. In Korea, it is necessary to convert existing digital maps in TM coordinates to that in KTRF from 2007. In this study, coordinate transformation methods and conversion area are tested and analyzed. In the results of experiment, it shows that Affine method is preciser than Helmert method. But Affine method is have more distortion than Helmert method.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.105-112
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• 2022

Let g : X ⟶ Y and f : Y ⟶ Z be two maps between real normed linear spaces. Then f is called generalized isometry or g-isometry if for each x, y ∈ X, ║f(g(x)) - f(g(y))║ = ║g(x) - g(y)║. In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.509-518
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• 1997

In this paper, we study the developing maps of the Lie groups with left-invariant affinely flat structures. We make some bacis observations on the nature of the developing images and show that the developing map for an incomplete affine structure splits as a product of a covering map of codimension 1 and a diffeomorphism of dimension 1.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.265-277
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• 1997

Let E be a real, non-degenerate, indefinite inner product space with dim $E \geq 3$. It is shown that any bijection of E which preserves the light cones is an affine map.