• Journal of the HCI Society of Korea
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• v.1 no.2
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• pp.27-33
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• 2006

This paper presents a new approach to translation and rotation invariant feature extraction for image texture retrieval. For the rotation invariant feature extraction, we invent angular projection along angular frequency in Polar coordinate system. The translation and rotation invariant feature vector for representing texture images is constructed by the averaged magnitude and the standard deviations of the magnitude of the Fourier transform spectrum obtained by the proposed angular projection. In order to easily implement the angular projection, the Radon transform is employed to obtain the Fourier transform spectrum of images in the Polar coordinate system. Then, angular projection is applied to extract the feature vector. We present our experimental results to show the robustness against the image rotation and the discriminatory capability for different texture images using MPEG-7 data set. Our Experiment result shows that the proposed rotation and translation invariant feature vector is effective in retrieval performance for the texture images with homogeneity, isotropy and local directionality.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1863-1874
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• 2014

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.211-217
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• 2012

In this paper, we give the weighted Lebesgue-Radon-Nikodym theorem with respect to $p$-adic invariant integral on $\mathbb{Z}_p$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.951-960
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• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• 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 Journal of Korean Institute of Information Technology
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• v.17 no.5
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• pp.13-20
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• 2019

Recently, object detection technology based on CNN has been actively studied. Object detection technology is used as an important technology in autonomous vehicles, intelligent image analysis, and so on. In this paper, we propose a rotation change robust object detection system by applying MI-FL (Moment Invariant-Feature Layer) to SSD (Single Shot Multibox Detector) which is one of CNN-based object detectors. First, the features of the input image are extracted based on the VGG network. Then, a total of six feature layers are applied to generate bounding boxes by predicting the location and type of object. We then use the NMS algorithm to get the bounding box that is the most likely object. Once an object bounding box has been determined, the invariant moment feature of the corresponding region is extracted using MI-FL, and stored and learned in advance. In the detection process, it is possible to detect the rotated image more robust than the conventional method by using the previously stored moment invariant feature information. The performance improvement of about 4 ~ 5% was confirmed by comparing SSD with existing SSD and MI-FL.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.62-71
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• 1989

We consider a Markov proces ${X_n} on [0,\infty)^k$ which is generated by $X_{n+1} = f(X_n) + \varepsilon_{n+1}$ where f is a continuous, nondecreasing concave function. Sufficient conditions for the existence of a unique invariant probability measure for ${X_n}$ are obtained.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 1985

For each a.mem.S and f.mem.m(S), denote by $l_{a}$ f(s)=f(as) for all s.mem.S. If A is a norm closed left translation invariant subalgebra of m(S) (i.e. $l_{a}$ f.mem.A whenever f.mem.A and a.mem.S) containing 1, the constant ont function on S and .phi..mem. $A^{*}$, the dual of A, then .phi. is a mean on A if .phi.(f).geq.0 for f.geq.0 and .phi.(1) = 1, .phi. is multiplicative if .phi. (fg)=.phi.(f).phi.(g) for all f, g.mem.A; .phi. is left invariant if .phi.(1sf)=.phi.(f) for all s.mem.S and f.mem.A. It is well known that the set of multiplicative means on m(S) is precisely .betha.S, the Stone-Cech compactification of S[7]. A subalgebra of m(S) is (extremely) left amenable, denoted by (ELA)LA if it is nom closed, left translation invariant containing contants and has a multiplicative left invariant mean (LIM). A semigroup S is (ELA) LA, if m(S) is (ELA)LA. A subset E.contnd.S is left thick (T. Mitchell, [4]) if for any finite subser F.contnd.S, there exists s.mem.S such that $F_{s}$ .contnd.E or equivalently, the family { $s^{-1}$ E : s.mem.S} has finite intersection property.y.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.49-58
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• 2010

We show that the Links-Gould polynomial of a link has finite type coefficients in a multivariate series expansion, and express the leading coefficients in terms of the linking numbers of a link.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.169-176
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• 1997

The purpose of this note is to compare two known results related to the lifting problem of an action of a topological group G on a G-space X to a coverring space of X.