• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Journal of Power System Engineering
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• v.2 no.3
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• pp.60-67
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• 1998

Edge detection is the first step and very important step in image analysis. We cast edge detection as a problem in cost minimization. This is achieved by the formulation of a cost function that evaluates the quality of edge configurations. The cost function can be used as a basis for comparing the performances of different detectors. This cost function is made of desirable characteristics of edges such as thickness, continuity, length, region dissimilarity. And we use a simulated annealing algorithm for minimum of cost function. Simulated annealing are a class of adaptive search techniques that have been intensively studied in recent years. We present five strategies for generating candidate states. Experimental results(building image and test image) which verify the usefulness of our simulated annealing approach to edge detection are better than other operator.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.10a
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• pp.313-318
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• 1997

Air voids existed in hardened concrete have an important influence on concrete deterioration such as carbonation, freezing and thawing, and corrosion of embedded steel in concrete. Therefore it is very significant to investigate the pore structure of system (size, number and continuity of air voids) to solve the reason caused concrete deterioration. The purpose of this study is to develop th standard method of measuring air voids which affect properties in hardened concrete using image analyzing system. This paper presents the settlement of rapid and exact experimental method which extracts fine bubbles, calculates the number of air voids, and determines air-voids distributions using image analyzing system with computer.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.595-608
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• 2015

In this paper, as a survey paper, we review many works related to fixed point theory for digital spaces using Lefschetz fixed point theorem, Banach fixed point theorem, Nielsen fixed point theorem and so forth. Besides, we refer some properties of the fixed point property of a digital k-retract.

• Journal of Biomedical Engineering Research
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• v.29 no.2
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• pp.122-131
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• 2008

For B-mode ultrasound images, we propose an image enhancement algorithm based on a multi-resolution approach, which consists of edge enhancing and noise reducing procedures. Edge enhancement processing is applied sequentially to coarse-to-fine resolution images obtained from wavelet-transformed data. In each resolution, the structural features of each pixel are examined through eigen analysis. Then, if a pixel belongs to an edge region, we perform two-step filtering: that is, directional smoothing is conducted along the tangential direction of the edge to improve continuity and directional sharpening is conducted along the normal direction to enhance the contrast. In addition, speckle noise is alleviated by proper attenuation of the wavelet coefficients of the homogeneous regions at each band. This region-based speckle-reduction scheme is differentiated from other methods that are based on the magnitude statistics of the wavelet coefficients. The proposed algorithm enhances edges regardless of changes in the resolution of an image, and the algorithm efficiently reduces speckle noise without affecting the sharpness of the edge. Hence, compared with existing algorithms, the proposed algorithm considerably improves the subjective image quality without providing any noticeable artifacts.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.658-663
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• 2003

A process of 3-D stereo particle image velocimetry(PIV)was developed for the measurement of an illuminated sliced section field of 3-D complex flows. The present method includes modeling of camera by a calibrator based on the homogeneous coordinate system, transformation of the oblique-angled image to the right-angled image, identification of 2-D velocity vectors by 2-D cross-correlation equation, stereo matching of 2-D velocity vectors of two cameras, accurate calculation of 3-D velocity vectors by homogeneous coordinate system, removal of error vectors by a statistical method followed by a continuity equation criteria, and finally 3-D display as the post processing. An experimental system was also used for the application of the proposed method. Two high speed digital CCD cameras and an Argon-Ion Laser for the illumination were adopted to clarify the time-dependent characteristics of the leading edge extension(LEX) in a highly swept shape applied to a delta wing found in modern air-fighters.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.9
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• pp.22-32
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• 1997

This paper proposes an imprecise compuitation model for DCT considering QOS of images and a two dimensional DCT architecture for imprecise computations. In case that many processes are scheduling in a hard real time system, the system resources are shared among them. Thus all processes can not be allocated enough system resources (such as processing power and communication bandwidth). The imprecise computtion model can be used to provide scheduling flexibility and various QOS(quality of service)levels, to enhance fault tolerance, and to ensure service continuity in rela time systems. The DCT(discrete cosine transform) is known as one of popular image data compression techniques and adopted in JPEG and MPEG algorithms since the DCT can remove the spatial redundancy of 2-D image data efficiently. Even though many commercial data compression VLSI chips include the DCST hardware, the DCT computation is still a very time-consuming process and a lot of hardware resources are required for the DCT implementation. In this paper the DCT procedure is re-analyzed to fit to imprecise computation model. The test image is simulated on teh base of this model, and the computation time and the quality of restored image are studied. The row-column algorithm is used ot fit the proposed imprecise computation DCT which supports pipeline operatiions by pixel unit, various QOS levels and low speed stroage devices. The architecture has reduced I/O bandwidth which could make its implementation feasible in VLSI. The architecture is proved using a VHDL simulator in architecture level.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.1C
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• pp.83-91
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• 2004

An epipolar rectification is the process of transforming the epipolar geometry of a pair of images into a canonical form. This is accomplished by applying a homography to each image that maps the epipole to a predetermined point. In this process, rectified images transformed by homographies must be satisfied with the epipolar constraint. These homographies are not unique, however, we find out homographies that are suited to system's purpose by means of an additive constraint. Since the rectified image pair be a stereo image pair, we are able to find the disparity efficiently. Therefore, we are able to estimate the three-dimensional information of objects within an image and apply this information to object segmentation. This paper proposes a rectification method for object segmentation and applies the rectification result to the object segmentation. Using color and relative continuity of disparity for the object segmentation, the drawbacks of previous segmentation method, which are that the object is segmented to several region because of having different color information or another object is merged into one because of having similar color information, are complemented. Experimental result shows that the disparity of result image of proposed rectification method have continuity about unique object. Therefore we have confirmed that our rectification method is suitable to the object segmentation.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.39-49
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• 1995

Stereo vision is useful to obtain three dimensional depth information from two images taken from different view points. In this paper, we reduce searching area for correspondence by using the intra-scanline constraint, and utilize the inter-scanline constraint and the property of disparity continuity among the neighboring pixels for relaxation. Nodes with 3-D stucture are located on the axes of two views, and have matching possibility of correspondent pixels of two images. A matching is accepted if a node at the intersection of the disparity axes has the greatest matching possibility. Otherwise, the matching possibility of the node is updated by relaxation with the cooperation of neighboring nodes. Further relaxation with competition of two views is applied to a matching possibility of randomly selected node. The consensus of two views increases the confidence of matching, and removes a blurring phenomenon on the discontinuity of object. This approach has been tested with various types of image such as random dot stereogram and aerial image, and the experimental results show good matching performance.