• Journal of Broadcast Engineering
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• v.4 no.2
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• pp.87-102
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• 1999

We propose an algorithm for augmenting a real video sequence with views of graphics ojbects without metric calibration of the video camera by representing the motion of the video camera in projective space. We define a virtual camera, through which views of graphics objects are generated. attached to the real camera by specifying image locations of the world coordinate system of the virtual world. The virtual camera is decomposed into calibration and motion components in order to make full use of graphics tools. The projective motion of the real camera recovered from image matches has a function of transferring the virtual camera and makes the virtual camera move according to the motion of the real camera. The virtual camera also follows the change of the internal parameters of the real camera. This paper shows theoretical and experimental results of our application of non-metric vision to augmented reality.

• IEMEK Journal of Embedded Systems and Applications
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• v.19 no.1
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• pp.9-17
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• 2024

It is widely recognized that for 3D human pose estimation (HPE), dataset acquisition is expensive and the effectiveness of augmentation techniques of conventional visual recognition tasks is limited. We address these difficulties by presenting a simple but effective method that augments input images in terms of viewpoints when training a 3D human pose estimation (HPE) model. Our intuition is that meaningful variants of the input images for HPE could be obtained by viewing a human instance in the images from an arbitrary viewpoint different from that in the original images. The core idea is to synthesize new images that have self-occlusion and thus are difficult to predict at different viewpoints even with the same pose of the original example. We incorporate this idea into the training procedure of the 3D HPE model as an augmentation stage of the input samples. We show that a strategy for augmenting the synthesized example should be carefully designed in terms of the frequency of performing the augmentation and the selection of viewpoints for synthesizing the samples. To this end, we propose a new metric to measure the prediction difficulty of input images for 3D HPE in terms of the distance between corresponding keypoints on both sides of a human body. Extensive exploration of the space of augmentation probability choices and example selection according to the proposed distance metric leads to a performance gain of up to 6.2% on Human3.6M, the well-known pose estimation dataset.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.325-334
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• 2006

For $f{\in}L^2(B,d{\nu})$, ${\parallel}f{\parallel}_{BMO}=\widetilde{{\mid}f{\mid}^2}(z)-{\mid}{\tilde{f}}(z){\mid}^2$. For f continuous on B, ${\parallel}f{\parallel}_{BO}=sup\{w(f)(z):z{\in}B\}$ where $w(f)(z)=sup\{{\mid}f(z)-f(w){\mid}:{\beta}(z,w){\leq}1\}$. In this paper, we will show that if $f{\in}BMO$, then ${\parallel}f{\parallel}_{BO}{\leq}M{\parallel}f{\parallel}_{BMO}$. We will also show that if $f{\in}BO$, then ${\parallel}f{\parallel}_{BMO}{\leq}M{\parallel}f{\parallel}_{BO}^2$. A homomorphic function $f:B{\rightarrow}{\mathbb{C}}$ is called a Bloch function ($f{\in}{\mathcal{B}}$) if ${\parallel}f{\parallel}_{\mathcal{B}}=sup_{z{\in}B}\;Qf(z)$<${\infty}$. In this paper, we will show that if $f{\in}{\mathcal{B}}$, then ${\parallel}f{\parallel}_{BO}{\leq}{\parallel}f{\parallel}_{\mathcal{B}}$. We will also show that if $f{\in}BMO$ and f is holomorphic, then ${\parallel}f{\parallel}_{\mathcal{B}}^2{\leq}M{\parallel}f{\parallel}_{BMO}$.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.783-800
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• 2002

Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) ＝ $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1＜p＜$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p ＝ 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.237-243
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• 1992

Let (M, g, J) be a closed Kahler manifold of complex dimension m > 1. We denote by Spec(M,g) the spectrum of the real Laplace-Beltrami operator. DELTA. acting on functions on M. The following characterization problem on the spectral rigidity of the complex projective space (CP$^{m}$ , g$_{0}$ , J$_{0}$ ) with the standard complex structure J$_{0}$ and the Fubini-Study metric g$_{0}$ has been attacked by many mathematicians : if (M,g,J) and (CP$^{m}$ ,g$_{0}$ ,J$_{0}$ ) are isospectral then is it true that (M,g,J) is holomorphically isometric to (CP$^{m}$ ,g$_{0}$ ,J$_{0}$ )\ulcorner In [BGM], [LB], it is proved that if (M,J) is (CP$^{m}$ , J$_{0}$ ) then the answer to the problem is affirmative. Tanno ([Ta]) has proved that the answer is affirmative if m .leq. 6. Recently, Wu([Wu]) has showed in a more general sense that if (M, g) and (CP$^{m}$ ,g$_{0}$ ) are (-4/m)-isospectral, m .geq. 4, and if the second betti number b$_{2}$(M) is equal to b$_{2}$(CP$^{m}$ ).

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• Journal of Veterinary Clinics
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• v.21 no.4
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• pp.406-408
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• 2004

A nine-month-old male Jindo with non weight-bearing on the right forelimb in flexed position, pain and edema of the elbow, and resist elbow extension was brought to the Veterinary Teaching Hospital, Chungbuk National University. Elbow radiographs showed loss of humeroradial joint space and lateral displacement of the radius and ulna. Closed reduction was reported the best therapy in most cases of luxation of the elbow but conservative reduction was impossible. Open reduction of the luxated elbow was performed and ruptured collateral ligaments were identified. Displaced elbow was required bloody surgical operation and gentle reduction to restore elbow joint. Internal reduction of choice for elbow luxation with rupture of collateral ligament in the dog was a double locking-loop suture pattern. To ensure secure grasping of parallel bundles of ligament fibers to transverse bites of each suture were placed superficial to the longitudinal bites. All ligaments were repaired with 3-metric (size 2 USP) monofilament polypropylene suture. No complications have been noted during a five-month follow up.

• Korean Journal of Optics and Photonics
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• v.19 no.4
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• pp.270-275
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• 2008

This paper addresses occluded object reconstruction and recognition with computational integral imaging (II). Integral imaging acquires and reconstructs target information in the three-dimensional (3D) space. The reconstruction is performed by averaging the intensities of the corresponding pixels. The distance to the object is estimated by minimizing the sum of the standard deviation of the pixels. We adopt principal component analysis (PCA) to classify occluded objects in the reconstruction space. The Euclidean distance is employed as a metric for decision making. Experimental and simulation results show that occluded targets are successfully classified by the proposed method.

• Journal of Digital Contents Society
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• v.16 no.2
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• pp.335-343
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• 2015

This paper describes a quantitative approach to the BIM-enabled assessment of building circulation by using quantitative data and applying its weight. Assessment of building circulation plays an important role before construction stage because of related requirements regulated by design guide, building codes, etc. and design decision making as well. In this paper, Qualitative issue is mainly dealt with that are usually excluded from rule checking objects due to their implicit definition such as 'comfortable circulation'. A weighting framework is suggested using weighted data of circulation properties such as 1) metric distance, 2) number of passing spaces, 3) number of turning spaces, 4) window area of passing space, etc.