• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.5
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• pp.972-978
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• 2009

In order to achieve color constancy, this paper proposes a method that can detect an invariant direction that affects formation of an intrinsic image significantly, using eigenvector in the $\chi$-chromaticity space. Firstly, image is converted into datum in the $\chi$-chromaticity space which was suggested by Finlayson et al. Secondly, it removes datum, like noises, with low probabilities that may affect an invariant direction. Thirdly, so as to detect the invariant direction that is consistent with a principal direction, the eigenvector corresponding to the largest eigenvalue is calculated from datum extracted above. Finally, an intrinsic image is acquired by recovering datum with the detected invariant direction. Test images were used as parts of the image data presented by Barnard et al., and detection performance of invariant direction was compared with that of entropy minimization method. The results of experiment showed that our method detected constant invariant direction since the proposed method had lower standard deviation than the entropy method, and was over three times faster than the compared method in the aspect of detection speed.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.309-323
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• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.1
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• pp.60-66
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• 2002

In this paper, an efficient content-based rotation-invariant retrieval of the trademarks is proposed using the edge-direction histogram for a principal symmetry axis and the moment invariants. Rotation invariant retrieval of trademarks is difficult for the conventional retrieval systems because their feature vectors are not rotation-invariant. In this paper, to obtain rotation invariant feature vectors, in addition to invariant moments, the edge-direction histogram for a principal symmetry axis is introduced and is used to solve the bin shift problem of the histogram resulted from the rotated trademark. Performance evaluation has been carried out for a database of 300 kinds of trademarks including 20 kinds of typical trademarks which are reported to be difficult to retrieve when rotated, and the proposed scheme is proved to retrieve trademarks more efficiently, especially for the rotated trademarks, than the conventional methods.

• The KIPS Transactions:PartB
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• v.18B no.2
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• pp.51-56
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• 2011

Algorithms for intrinsic images reduce color differences in RGB images caused by the temperature of black-body radiators. Based on the reference light and detecting single invariant direction, these algorithms are weak in real images which can have multiple invariant directions when the scene illuminant is a colored illuminant. To solve these problems, this paper proposes a method of acquiring an intrinsic image by omnidirectional projection of an ROI and a translation of white patch in the ${\chi}$-chromaticity space. Because it is not easy to analyze an image in the three-dimensional RGB space, the ${\chi}$-chromaticity is also employed without the brightness factor in this paper. After the effect of the colored illuminant is decreased by a translation of white patch, an invariant direction is detected by omnidirectional projection of an ROI in this chromaticity space. In case the RGB image has multiple invariant directions, only one ROI is selected with the bin, which has the highest frequency in 3D histogram. And then the two operations, projection and inverse transformation, make intrinsic image acquired. In the experiments, test images were four datasets presented by Ebner and evaluation methods was the follows: standard deviation of the invariant direction, the constancy measure, the color space measure and the color constancy measure. The experimental results showed that the proposed method had lower standard deviation than the entropy, that its performance was two times higher than the compared algorithm.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.332-338
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• 2003

Content-based image retrieval is the research of images from database, that are visually similar to given image examples. Gabor functions and Gabor filters are regarded as excellent methods for feature extraction and texture segmentation. However, they have a disadvantage not to perform well in case of a rotated image because of its direction-oriented filter. This paper proposes a method of extracting local texture features from blocks with central interest points detected in an image and a rotation invariant Gabor wavelet filter. We also propose a method of comparing pattern histograms of features classified by VQ (Vector Quantization) among images.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.91-111
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• 2001

In this paper we prove the following : Let M be a semi-invariant submanifold with almost contact metric structure (${\phi}$, ${\xi}$, g) of codimension 3 in a complex hyperbolic space $H_{n+1}{\mathbb{C}}$. Suppose that the third fundamental form n satisfies $dn=2{\theta}{\omega}$ for a certain scalar ${\theta}({\leq}{\frac{c}{2}})$, where ${\omega}(X,\;Y)=g(X,\;{\phi}Y)$ for any vectors X and Y on M. Then M has constant eigenvalues correponding the shape operator A in the direction of the distinguished normal and the structure vector ${\xi}$ is an eigenvector of A if and only if M is locally congruent to one of the type $A_0$, $A_1$, $A_2$ or B in $H_n{\mathbb{C}}$.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.3
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• pp.37-43
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• 2004

The purpose of this study is to develop a practical image inspection system that could recognize it correctly, endowing flexibility to the productive field, although the same object for work will be changed in the size and rotated. In this experiment, it selected a fighter, rotating the direction from $30^{\circ}$ to $45^{\circ}$ simultaneously while changing the size from 1/4 to 1/16, as an object inspection without using another hardware for exclusive image processing. The invariant moments, Hu has suggested, was used as feature vector moment descriptor. As a result of the experiment, the image inspection system developed from this research was operated in real-time regardless of the chance of size and rotation for the object inspection, and it maintained the correspondent rates steadily above from 94% to 96%. Accordingly, it is considered as the flexibility can be considerably endowed to the factory automation when the image inspection system developed from this research is applied to the productive field.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• East Asian mathematical journal
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• v.38 no.5
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• pp.549-581
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c), c≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R_𝜉S = SR_𝜉 and at the same time R_𝜉𝜙 = 𝜙R_𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).