• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.652-655
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• 2004

The geometry of satellite image captured by linear pushbroom scanner is different from that of frame camera image. Since the exterior orientation parameters for satellite image will vary scan line by scan line, the epipolar geometry of satellite image differs from that of frame camera image. As we know, 2D affine orientation for the epipolar image of linear pushbroom scanners system are well-established by using the collinearity equation (Testsu Ono, 1999). Also, another epipolar geometry of linear pushbroom scanner system is recently established by Habib(2002). He reported that the epipolar geometry of linear push broom satellite image is realized by parallel projection based on 2D affine models. Here, in this paper, we compared the Ono's method with Habib's method. In addition, we proposed a method that generates epipolar resampled images. For the experiment, IKONOS stereo images were used in generating epipolar images.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.5
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• pp.477-486
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• 2020

Drone has been widely used for many applications ranging from amateur and leisure to professionals to get fast and accurate 3-D information of the surface of the interest. Most of commercial softwares developed for this purpose are performing automatic matching based on SIFT (Scale Invariant Feature Transform) or SURF (Speeded-Up Robust Features) using nadir-looking stereo image sets. Since, there are some situations where not only nadir and nadir-looking matching, but also nadir and oblique-looking matching is needed, the existing software for the latter case could not get good results. In this study, a matching experiment was performed to utilize images with differences in geometry. Nadir and oblique-looking images were acquired through drone for a total of 2 times. SIFT, SURF, which are feature point-based, and IMAS (Image Matching by Affine Simulation) matching techniques based on affine transformation were applied. The experiment was classified according to the identity of the geometry, and the presence or absence of a building was considered. Images with the same geometry could be matched through three matching techniques. However, for image sets with different geometry, only the IMAS method was successful with and without building areas. It was found that when performing matching for use of images with different geometry, the affine transformation-based matching technique should be applied.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.9
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• pp.3856-3863
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• 2012

A 3D reconstruction technique from stereo images that requires minimal intervention from the user has been developed. The reconstruction problem consists of three steps of estimating specific geometry groups. The first step is estimating the epipolar geometry that exists between the stereo image pairs which includes feature matching in both images. The second is estimating the affine geometry, a process to find a special plane in the projective space by means of vanishing points. The third step, which includes camera self-calibration, is obtaining a metric geometry from which a 3D model of the scene could be obtained. The major advantage of this method is that the stereo images do not need to be calibrated for reconstruction. The results of camera calibration and reconstruction have shown the possibility of obtaining a 3D model directly from features in the images.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1047-1067
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• 1996

In this paper, we are interested in left invariant flat affine structures on Lie groups. These structures has been studied by many authors in different contexts. One of the fundamental questions is the existence of complete affine structures for solvable Lie groups G, raised by Minor [15]. But recently Benoist answered negatively even for the nilpotent case [1]. Also moduli space of such structures for lower dimensional cases has been studied by several authors, sometimes with compatible metrics [5,10,4,12].

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.297-305
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• 2006

We classify centroaffine minimal surfaces with constant curvature metric under some natural conditions on the cubic differentials.

• Journal of Digital Convergence
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• v.14 no.8
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• pp.555-564
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• 2016

Space perception is generally treated as a problem relevant to the ability to recognize objects. Alternatively, the data from shape perception studies contributes to discussions about the geometry of visual space. This geometry is generally acknowledged not to be Euclidian, but instead, elliptical, hyperbolic or affine, which is to say, something that admits the distortions found in so many shape perception studies. The purpose of this review article is to understand perceived shape and the geometry of visual space in the context of visually guided action. Thus, two prominent approaches that explain the relation between perception and action were compared. It is important to understand the fundamental information of how human perceive visual space and perform visually guided action for the convergence on embodied cognition, and further on artificial intelligence researches.

• Journal of Korean Society for Geospatial Information Science
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• v.15 no.4
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• pp.81-88
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• 2007

The geometry of satellite image captured by linear CCD sensor is different from that of frame camera image. The fact that the exterior orientation parameters for satellite image with linear CCD sensor varies from scan line by scan line, causes the difference of image geometry between frame and linear CCD sensor. Therefore, we need the epipolar geometry for linear CCD image which differs from that of frame camera image. In this paper, we proposed a method of resampling linear CCD satellite image in epipolar geometry under the assumption that image is not formed in perspective projection but in parallel projection, and the sensor model is a 2D affine sensor model based on parallel projection. For the experiment, IKONOS stereo images, which are high resolution linear CCD images, were used and tested. As results, the spatial accuracy of 2D affine sensor model is investigated and the accuracy of epipolar resampled image with RFM was presented.

• East Asian mathematical journal
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• v.15 no.2
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• pp.277-290
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• 1999

In this paper, we investigate the existence of a two dimensional surface in a four dimensional equiaffine space and characterize that surface.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.31-37
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• 1987

I want to focus on developments in the areas of general relativity and gauge theory. The topics to be considered are the singularity theorms of Hawking and Penrose, the positivity of mass, instantons on the four-dimensional sphere, and the string picture of quantum gravity. I should mention that I will not have time do discuss either classical mechanics or symplectic structures. This is especially unfortunate, because one of the roots of differential geometry is planted firmly in mechanics, Cf. [GS]. The French geometer Elie Cartan first formulated his invariant approach to geometry in a series of papers on affine connections and general relativity, Cf. [C]. Cartan was trying to recast the Newtonian theory of gravity in the same framework as Einstein's theory. From the historical perspective it is significant that Cartan found relativity a convenient framework for his ideas. As about the same time Hermann Weyl in troduced the idea of gauge theory into geometry for purposes much different than those for which it would ultimately prove successful, Cf. [W]. Weyl wanted to unify gravity with electromagnetism and though that a conformal structure would fulfill thel task but Einstein rebutted this approach.