• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.37-56
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• 2023

In this paper, we introduced the notions of ∗ - g-fusion frame and ∗ - K - g-fusion frame in Hilbert C^*-modules, we gives some properties and study the tensor product of ∗ - g-fusion frame. Non-trivial examples are further provided to support the hypotheses of our results.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1115-1128
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• 2023

In this paper, a novel hybrid method for multi-focus image fusion is proposed. The method combines the advantages of wavelet transform-based methods and focus-measure-based methods to achieve an improved fusion result. The input images are first decomposed into different frequency sub-bands using the discrete wavelet transform (DWT). The focus measure of each sub-band is then calculated using the Laplacian of Gaussian (LoG) operator, and the sub-band with the highest focus measure is selected as the focused sub-band. The focused sub-band is sharpened using an unsharp masking filter to preserve the details in the focused part of the image.Finally, the sharpened focused sub-bands from all input images are fused using the maximum intensity fusion method to preserve the important information from all focus images. The proposed method has been evaluated using standard multi focus image fusion datasets and has shown promising results compared to existing methods.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.389-406
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• 2023

In the pursuit of enhancing image fusion techniques, this research presents a novel approach for fusing multimodal images, specifically infrared (IR) and visible (VIS) images, utilizing a combination of partial differential equations (PDE) and discrete cosine transformation (DCT). The proposed method seeks to leverage the thermal and structural information provided by IR imaging and the fine-grained details offered by VIS imaging create composite images that are superior in quality and informativeness. Through a meticulous fusion process, which involves PDE-guided fusion, DCT component selection, and weighted combination, the methodology aims to strike a balance that optimally preserves essential features and minimizes artifacts. Rigorous evaluations, both objective and subjective, are conducted to validate the effectiveness of the approach. This research contributes to the ongoing advancement of multimodal image fusion, addressing applications in fields like medical imaging, surveillance, and remote sensing, where the marriage of IR and VIS data is of paramount importance.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.724-726
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• 2003

Currently available image fusion methods are not efficient for fusing the Landsat 7 images. Significant color distortion is one of the major problems. In this paper, using the well-known wavelet based method for data fusion between high-resolution panchromatic and low-resolution multispectral satellite images, we performed Landsat 7 image fusion. Based on the experimental results obtained from this study, we analyzed some reasons for color distortion. A new approach using the biorthogonal wavelets based method for data fusion is presented. This new method has reached an optimum fusion result - with the same spectral resolution as the multispectral image and the same spatial resolution as the panchromatic image with minimum artifacts.

• The Mathematical Education
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• v.50 no.1
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• pp.119-128
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• 2011

In this paper, we studied into a qualitative research to see mathematical understanding of preschool and kindergarten's teachers such as feeling attitude, parents' concern, difficulty of math teaching in kindergarten field, teacher's role, type of feed back, beauty of math, relationship of real life, and self philosophy of math education. We selected 10 teachers whose career was 7~10 years. Because this research way is qualitative, we can new aspect that teacher want to break their ignorance for math. Moreover, they would like to learn about math practicality, application, and beauty from art in professional training. Therefore we assert that fusion math lecture would support in the professional training for teacher, preschool or kindergarten's president training, and remuneration training.

• Journal of Practical Engineering Education
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• v.5 no.2
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• pp.177-183
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• 2013

In this paper we investigate the history of the education based on STEM which is one of the topics of teaching method of Mathematics and Science oriented to the student, Hand-on education be applying partly to college education and the case of the education of the subject "Mathematics and Science for Engineering" of Japan's college. The educational method based on STEM make the student to recognize by themselves the necessity of the mathematics in the study of the technological and engineering problem, and furthermore draw a conclusion which is the proper method to change from passive to positive the study attitude for the mathematics. But it is more or less unreasonable to apply directly to college education with not physical fusion but chemical fusion of S (science), T (technology), E (engineering) and M (mathematics). Therefore we make themselves to find T and E considered at graduation works. We propose Pseudo-STEM teaching method linking this recognition obtained through self-activity to the mathematics subject.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.2
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• pp.26-38
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• 2021

Image coloration refers to adding plausible colors to a grayscale image or video. Image coloration has been used in many modern fields, including restoring old photographs, as well as reducing the time spent painting cartoons. In this paper, a method is proposed for colorizing grayscale images using a convolutional neural network. We propose an encoder-decoder model, adapting FusionNet to our purpose. A proper loss function is defined instead of the MSE loss function to suit the purpose of coloring. The proposed model was verified using the ImageNet dataset. We quantitatively compared several colorization models with ours, using the peak signal-to-noise ratio (PSNR) metric. In addition, to qualitatively evaluate the results, our model was applied to images in the test dataset and compared to images applied to various other models. Finally, we applied our model to a selection of old black and white photographs.

• School Mathematics
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• v.16 no.2
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• pp.387-407
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• 2014

Gender differences have been given major attention in mathematics education in the context of pursuing gender equity in instructional and learning environment. It had been traditional belief that male students would outperform female students in mathematics, especially in the areas as geometry. This belief has been given doubts by cumulated empirical evidences that gender differences are gradually diminishing or even reversing its direction as time goes on. In this study, gender differences in geometry were explored using TIMSS 8th grade mathematics data administered in TIMSS 2003, 2007, and 2011, based on a cognitive diagnostic modeling(CDM) approach. Among various CDM models, the Fusion model was employed. The Fusion model has advantages over other CDM models in that it provides more detailed information about gender differences at the attribute level as well as item level and more mathematically tractable. The findings of this study show that Attribute 3(Three-dimensional Geometric Shapes) revealed statistically significant gender differences favoring male students in TIMSS 2003 and 2007, but did not show significant differences in TIMSS 2011, which provides an additional empirical evidence supporting the recent observation that gender gap is narrowing. In addition to the general trends in gender differences in geometry, this study also provided affluent information such as gender differences in attribute mastery profiles and gender differences in relative contributions of each attribute in solving a particular item. Based on the findings of the CDM approach exploring gender differences, instructional implications in geometry education are discussed.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.237-252
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• 2017

The era of the Fourth Industrial Revolution has also influenced the direction of mathematics education. In particular, the convergence capability that recognizes how mathematics can be applied and utilized in various fields is an important point. The purpose of this study is to examine the point of convergence and to develop a fusion program that can be used in the mathematics classroom. Specifically, we analyze the tiles used in ancient Islamic architecture from a mathematical point of view and develop mathematics and multifamily convergence programs based on them. Through the mathematical analysis of the geometric tiling made 500 years earlier than Penrose, I hope that understanding of design, the use of mathematics and the possibility of convergence of other disciplines through mathematics will be widened.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.103-119
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• 2016

Fusion and consilience have been important in many aspects of our education and culture. In this flow 2015 revised National Curriculum aimed to cultivate students of abilities of imagining liberally and inventing scientifically and technically. However imagination including imagination in humanities has not been researched in mathematics education part until nowadays, so mathematics education using imagination of raising students with ingenious and harmonizing abilities is hard to discuss concretely. In this paper I studied the opinions of various scholars from ancient times to today, and discussed where imagination reveals itself in mathematics practices. With above results I discussed some possible shape of teaching and learning of mathematics using imagination. And finally we discussed that meanings in the humanities and social aspects.