• ETRI Journal
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• v.33 no.4
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• pp.547-557
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• 2011

This study presents an approach for extracting boundaries of various buildings, which have concave boundaries, inner yards, non-right-angled corners, and nonlinear edges. The approach comprises four steps: building point segmentation, boundary tracing, boundary grouping, and regularization. In the second and third steps, conventional algorithms are improved for more accurate boundary extraction, and in the final step, a new algorithm is presented to extract nonlinear edges. The unique characteristics of airborne light detection and ranging (LIDAR) data are considered in some steps. The performance and practicality of the presented algorithm were evaluated for buildings of various shapes, and the average omission and commission error of building polygon areas were 0.038 and 0.033, respectively.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1611-1620
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• 2005

This paper shows the use of wavelet transformation combined with inverse acoustics to reconstruct the surface velocity of a noise source. This approach uses the boundary element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations and wavelet transformation for reconstructing the normal surface velocity field. The reconstructed field can be diverged due to the small measurement errors in the case of nearfield acoustic holography (NAH) using an inverse boundary element method. In order to avoid this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a wavelet transformation is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed vibration field. The computational speed-up is achieved, with solution time being reduced to $14.5\%$.

• Journal of the Korean Society for Nondestructive Testing
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• v.15 no.1
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• pp.299-309
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• 1995

A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1288-1293
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• 2004

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach of adopting the genetic algorithm as an initial value selector, whereas using the conjugate-gradient method and Newton method to reduce their dependence on the initial value.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.8 s.239
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• pp.903-910
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• 2005

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and finite-difference Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach that adopts the hybrid genetic algorithm as an initial value selector and uses the finite-difference Newton method as an optimization procedure.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.6
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• pp.972-981
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• 1990

Many researchers have been interested in whether complex computational problems can be solved by the neural net or not. Especially, problems of early vision are integrated by Tikhonov's regularization theory. Regularization technique can be realized in resistive net. In this paper, we suggest the resistive net with upper and lower thresholder to be able to compute shape from shading and to solve its discontinuous problem. We simulate three algorithms-Horn's algorithm, resistive net and up-low thrwsholding net -with respect to three cases-fully boundary, boundary losing partly and noisy image. As being able to cope with crease and discontinuous parts, we get the good 3D shape from shading.

• International journal of advanced smart convergence
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• v.12 no.4
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• pp.134-141
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• 2023

We present a novel method aimed at refining ground truth data through regularization and modification, particularly applicable when working with the original ground truth set. Enhancing the performance of deep neural networks is achieved by applying regularization techniques to the existing ground truth data. In many machine learning tasks requiring pixel-level segmentation sets, accurately delineating objects is vital. However, it proves challenging for thin and elongated objects such as blood vessels in X-ray coronary angiography, often resulting in inconsistent generation of ground truth data. This method involves an analysis of the quality of training set pairs - comprising images and ground truth data - to automatically regulate and modify the boundaries of ground truth segmentation. Employing the active contour model and a recursive ground truth generation approach results in stable and precisely defined boundary contours. Following the regularization and adjustment of the ground truth set, there is a substantial improvement in the performance of deep neural networks.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.