• Journal of the Society of Naval Architects of Korea
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• v.30 no.4
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• pp.17-22
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• 1993

The intersection problem of three-dimensional free form surfaces can be solved by geometrical and numerical methods. Up to now, the subdivision technique, which is classified under the former, has been largely employed to find the cross section of ship hull form. In this paper, an algorithm is presented for intersecting ship hull form in high speed. The high speed calculation algorithm is based on simple numerical methods, such as the secant method, false position method and bisection method. The algorithm is directly applicable to depicting arbitrary ship cross sections, drawing ship lines and constructing the offset table.

• The KIPS Transactions:PartB
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• v.11B no.4
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• pp.429-436
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• 2004

This paper proposes an independent component analyses(ICAs) of the fixed-point (FP) algorithm based on Newton and secant method by adding the kurtosis, respectively. The kurtosis is applied to cluster the analyzed components, and the FP algorithm is applied to get the fast analysis and superior performance irrelevant to learning parameters. The proposed ICAs have been applied to the problems for separating the 6-mixed signals of 500 samples and 10-mixed images of $512\times512$ pixels, respectively. The experimental results show that the proposed ICAs have always a fixed analysis sequence. The results can be solved the limit of conventional ICA without a kurtosis which has a variable sequence depending on the running of algorithm. Especially. the proposed ICA can be used for classifying and identifying the signals or the images. The results also show that the secant method has better the separation speed and performance than Newton method. And, the secant method gives relatively larger improvement degree as the problem size increases.

• The KIPS Transactions:PartB
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• v.11B no.7 s.96
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• pp.813-820
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• 2004

This paper proposes a digital image watermarking which is robust to geometric distortions using an independent component analysis(ICA) of fixed-point(FP) algorithm based on secant method. The FP algorithm of secant method is applied for better performance in a separation time and rate, and ICA is applied to reject the prior knowledges for original image, key, and watermark such as locations and size, etc. The proposed method embeds the watermark into the spatial domain of original image The proposed watermarking technique has been applied to lena, key, and two watermarks(text and Gaussian noise) respectively. The simulation results show that the proposed method has higher speed and better rate for extracting the original images than the FP algorithm of Newton method. And the proposed method has a watermarking which is robust to geometric distortions such as resizing, rotation, and cropping. Especially, the watermark of images with Gaussian noise has better extraction performance than the watermark with text since Gaussian noise has lower correlation coefficient than the text to the original and key images. The watermarking of ICA doesn't require the prior knowledge for the original images.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.336-341
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• 2004

This paper proposes an independent component analysis(ICA) of the fixed-point (FP) algorithm based on secant method and the kurtosis. The FP algorithm based on secant method is applied to improve the analysis speed and performance by simplifying the calculation process of the complex derivative in Newton method, the kurtosis is applied to cluster the components. The proposed ICA has been applied to the problems for separating the 6-mixed signals of 500 samples and 8-mixed images of $512{\times}512$ pixels, respectively. The experimental results show that the proposed ICA has always a fixed analysis sequence. The result can be solved the limit of conventional ICA based on secant method which has a variable sequence depending on the running of algorithm. Especially, the proposed ICA can be used for classifying and identifying the signals or the images.

• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.643-652
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• 2002

This paper proposes an efficient hybrid fixed-point (FP) algorithm for improving performances of the independent component analysis (ICA) based on neural networks. The proposed algorithm is the FP algorithm based on secant method and momentum for ICA. Secant method is applied to improve the separation performance by simplifying the computation process for estimating the root of objective function, which is to minimize the mutual informations of the independent components. The momentum is applied for high-speed convergence by restraining the oscillation if the process of converging to the optimal solution. It can simultaneously achieve a superior properties of the secant method and the momentum. The proposed algorithm has been applied to the composite fingerprints and the images generated by random mixing matrix in the 8 fingerprints of $256\times{256}$-pixel and the 10 images of $512\times{512}$-pixel, respectively. The simulation results show that the proposed algorithm has better performances of the separation speed and rate than those using the FP algorithm based on Newton and secant method. Especially, the secant FP algorithm can be solved the separating performances depending on initial points settings and the nonrealistic learning time for separating the large size images by using the Newton FP algorithm.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.5
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• pp.525-530
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• 2006

This paper presents an efficient input variable selection method using both fixed-point independent component analysis(FP-ICA) and adaptive partition mutual information(AP-MI) estimation. FP-ICA which is based on secant method, is applied to quickly find the independence between input variables. AP-MI estimation is also applied to estimate an accurate dependence information by equally partitioning the samples of input variable for calculating the probability density function(PDF). The proposed method has been applied to 2 problems for selecting the input variables, which are the 7 artificial signals of 500 samples and the 24 environmental pollution signals of 55 samples, respectively The experimental results show that the proposed methods has a fast and accurate selection performance. The proposed method has also respectively better performance than AP-MI estimation without the FP-ICA and regular partition MI estimation.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.210-218
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• 2002

This paper proposes an efficient separation method of the composite images by using independent component analysis(ICA) based on neural networks of the approximate learning algorithm. The Proposed learning algorithm is the fixed point(FP) algorithm based on Secant method which can be approximately computed by only the values of function for estimating the root of objective function for optimizing entropy. The secant method is an alternative of the Newton method which is essential to differentiate the function for estimating the root. It can achieve a superior property of the FP algorithm for ICA due to simplify the composite computation of differential process. The proposed algorithm has been applied to the composite signals and image generated by random mixing matrix in the 4 signal of 500-sample and the 10 images of $512{\times}512-pixel$, respectively The simulation results show that the proposed algorithm has better performance of the learning speed and the separation than those using the conventional algorithm based method. It also solved the training performances depending on initial points setting and the nonrealistic learning time for separating the large size image by using the conventional algorithm.