• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.8 no.1
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• pp.127-135
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• 2009

This paper presents a new technique for corner shape based object retrieval from a database. The proposed feature matrix consists of values obtained through a neighborhood operation of detected corners. This results in a significant small size feature matrix compared to the algorithms using color features and thus is computationally very efficient. The corners have been extracted by finding the intersections of the detected lines found using Hough transform. As the affine transformations preserve the co-linearity of points on a line and their intersection properties, the resulting corner features for image retrieval are robust to affine transformations. Furthermore, the corner features are invariant to noise. It is considered that the proposed algorithm will produce good results in combination with other algorithms in a way of incremental verification for similarity.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.2
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• pp.55-65
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• 2011

In this paper, a novel method of marker detection robust against marker occlusion in augmented reality is proposed. the proposed method consists of four steps. In the first step, in order to effectively detect an occluded marker, we first utilize the Affine-SIFT (ASIFT, Affine-Scale Invariant Features Transform) for detecting matching points between an enrolled marker and an input images with an occluded marker. In the second step, we apply the Principal Component Analysis (PCA) for eliminating outlier of the matching points in the enrolled marker. And then matching points are projected to the first and second axis for longest value and the shortest value of an ellipse are determined by average distance between the projected points and a center of the points. In the third step, Convex-hull vertices including matching points are considered as polygon vertices for estimating a geometric affine transformation. In the final step, by estimating the geometric affine transformation of the points, a marker robust against a marker occlusion is detected. Experimental results have shown that the proposed method effectively detects occlude markers.

• The Journal of Korea Robotics Society
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• v.4 no.3
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• pp.185-191
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• 2009

This paper presents a new shape-based algorithm using affine category shape model for object category recognition and model learning. Affine category shape model is a graph of interconnected nodes whose geometric interactions are modeled using pairwise potentials. In its learning phase, it can efficiently handle large pose variations of objects in training images by estimating 2-D homography transformation between the model and the training images. Since the pairwise potentials are defined on only relative geometric relationship betweenfeatures, the proposed matching algorithm is translation and in-plane rotation invariant and robust to affine transformation. We apply spectral matching algorithm to find feature correspondences, which are then used as initial correspondences for RANSAC algorithm. The 2-D homography transformation and the inlier correspondences which are consistent with this estimate can be efficiently estimated through RANSAC, and new correspondences also can be detected by using the estimated 2-D homography transformation. Experimental results on object category database show that the proposed algorithm is robust to pose variation of objects and provides good recognition performance.

• 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].

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.523-537
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• 2020

In this work we consider the Sol₃ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.

• 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.61 no.4
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• pp.743-760
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• 2024

In this paper, we are devoted to study a forth order curve flow for a smooth closed curve in centro-affine geometry. Firstly, a new evolutionary equation about this curve flow is proposed. Then the related geometric quantities and some meaningful conclusions are obtained through the equation. Next, we obtain finite order differential inequalities for energy by applying interpolation inequalities, Cauchy-Schwartz inequalities, etc. After using a completely new symbolic expression, the n-order differential inequality for energy is considered. Finally, by the means of energy estimation, we prove that the forth order curve flow has a smooth solution all the time for any closed smooth initial curve.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.28 no.3
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• pp.353-359
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• 2010

In this paper, we propose the automatic image-to-image registration of high resolution satellite images using local properties of tie points to improve the registration accuracy. A spatial distance between interest points of reference and sensed images extracted by Scale Invariant Feature Transform(SIFT) is additionally used to extract tie points. Coefficients of affine transform between images are extracted by invariant descriptor based matching, and interest points of sensed image are transformed to the reference coordinate system using these coefficients. The spatial distance between interest points of sensed image which have been transformed to the reference coordinates and interest points of reference image is calculated for secondary matching. The piecewise linear function is applied to the matched tie points for automatic registration of high resolution images. The proposed method can extract spatially well-distributed tie points compared with SIFT based method.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.9
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• pp.3782-3796
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• 2020

A three-dimensional (3D) reconstruction is an important research area in computer vision. The ability to detect and match features across multiple views of a scene is a critical initial step. The tracking matrix W obtained from a 3D reconstruction can be applied to structure from motion (SFM) algorithms for 3D modeling. We often fail to generate an acceptable number of features when processing face or medical images because such images typically contain large homogeneous regions with minimal variation in intensity. In this study, we seek to locate sufficient matching points not only in general images but also in face and medical images, where it is difficult to determine the feature points. The algorithm is implemented on an adaptive threshold value, a scale invariant feature transform (SIFT), affine SIFT, speeded up robust features (SURF), and affine SURF. By applying the algorithm to face and general images and studying the geometric errors, we can achieve quasi-dense matching points that satisfy well-functioning geometric constraints. We also demonstrate a 3D reconstruction with a respectable performance by applying a column space fitting algorithm, which is an SFM algorithm.