• 호남수학학술지
• /
• 제42권1호
• /
• pp.75-91
• /
• 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.

• 대한수학회지
• /
• 제53권5호
• /
• pp.1149-1165
• /
• 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.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2000년도 ITC-CSCC -2
• /
• pp.877-880
• /
• 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.

• 대한수학회지
• /
• 제35권1호
• /
• pp.237-257
• /
• 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.

• 대한공간정보학회지
• /
• 제22권4호
• /
• pp.3-11
• /
• 2014

최근 도시는 신규건축, 재건축 및 부분적인 리모델링 등 다양한 형태로 변화하고 있으며, 이에 따라 수치지도 또한 최신성 및 정확도를 유지할 수 있도록 지속적인 수정 및 갱신을 통해 사용자들에게 최적의 서비스를 제공할 수 있어야 한다. 일반적으로 수치지도 수정 및 갱신 방법으로는 항공사진 혹은 준공도면을 이용하고 있으나, 항공사진은 촬영주기제한 및 경제성 측면에서 국소 지역에 대한 수시 갱신이 어렵고 준공도면의 경우 품질 확보의 어려움이 존재한다. 본 연구에서는 빠르게 변하는 도심지의 건물 개발 현황을 수치지도상의 건물 정보에 신속하게 반영하기 위해 지상라이다로부터 추출한 건물 footprint 자료를 이용하는 방법론을 제안하였다. 우선 지상라이다로부터 취득된 전체 건물의 포인트 클라우드 자료로부터 대표 옆면을 추출하고, 2차원 영상으로 투영한다. 투영된 포인트 클라우드 자료로부터 footprint를 추출하고, 추출된 footprint와 수치지도 상의 건물 footprint 간의 정합을 위해 2D Affine 모델을 사용하였다. 2D Affine 파라미터의 추정에는 두 footprint 자료로부터 취득된 무게중심을 사용하였으며, 무작위로 추출된 무게중심 간의 매칭을 위해 수정된 RANSAC (RANdom SAmple Consensus) 알고리즘을 제시하였다. 다양한 조건하에서 수행된 실험결과 제안된 알고리즘을 적용할 경우, 지상라이다로부터 추출된 건물데이터를 활용하여 효율적인 수치지형도의 갱신이 가능함을 확인할 수 있었다.

• 한국측량학회:학술대회논문집
• /
• 한국측량학회 2003년도 추계학술발표회 논문집
• /
• pp.309-315
• /
• 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.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.105-112
• /
• 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.

• 충청수학회지
• /
• 제22권4호
• /
• pp.771-776
• /
• 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).

• 대한수학회보
• /
• 제34권4호
• /
• pp.509-518
• /
• 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.

• 대한수학회지
• /
• 제34권2호
• /
• pp.265-277
• /
• 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.