• Journal of Biomedical Engineering Research
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• v.21 no.3 s.61
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• pp.247-254
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• 2000

We propose an efficient MR image compression technique using fractal coding in wavelet transform domain. In the Proposed method , we construct significant coefficient trees with the absolute values of discrete wavelet transform coefficients and then perform the fractal coding with the information of significant coefficients having high energy. For MR images, most Pixels including background have very low gray level values, the number of significant coefficients is small. so we can expect high compression rate. In addition. since this method uses the fractal coding in wavelet transform domain, blocking artifact is reduced prominently and edges sensitive to human visual system are well preserved. As a result of computer simulation, we obtained the reconstructed images with better quality than those by JPEG at the low bit rates below 0.33[bpp].

• Korean Journal of Remote Sensing
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• v.26 no.5
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• pp.489-495
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• 2010

Hyperspectral imaging obtains information with a wider wavelength range a large number of bands. However, a high correlation between each band, computation cost, and noise causes inaccurate results in cases of no pre-processing. The noises of band extraction and elimination positively necessary in hyperspectral imaging. Since the previous studies have used a characteristic the whole image, a local characteristic of the image is considered for the noise band extraction. In this study, the Quadtree, which is a data structure algorithm. and the fractal dimension are adopted for noise band extraction in Hyperion images. The fractal dimensions of the segments divided by the Quadtree structure are calculated, and variation is used. We focused on the extraction of random noise bands in Hyperion images and compared them with the reference data made by visual decisions. The proposed algorithm extracts the most bands, including random noises. It is possible to eliminate more than 30 noise bands, regardless of images.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.7
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• pp.1654-1667
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• 1996

The conventional fractal image compression methods have high computational complexity at encoding reduce PSNR at low bit rate and havehighly visible blocking effects in a reconstructed image. In this paper we propose a fractal image compression method based on disctete wavelet transform domain, which takes the absolute value of discrete wavelet transform coefficient, and assembles the discrete wavelet tranform coefficients of different highpass subbands corresponding to the same spatial block and then applies "0" encoding according to the energy of each range blocks. The proposed method improved PSNR at low bit rate and reduced computational complexity at encoding distinctly. Also, this method can achieve a blockless reconstructed image and perform hierarchical decoding without recursive constractive transformation. Computer simulations with several test images show that the proposed method shows better performance than convnetional fractal coding methods for encoding still pictures. pictures.

• Imaging Science in Dentistry
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• v.35 no.2
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• pp.91-96
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• 2005

Purpose : To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Materials and Methods Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER Computerized Dental X-ray $System^{(R)}$. Fractal dimensions were calculated three times at each area by Scion Image $PC^{(R)}$ program. Rectangular region of interest $(30\times30)$ were selected at apical lesion and normal apex of each image. Results : The fractal dimension at apical lesion of first diagnosis $(L_0)$ is $0.940{\pm}0.361$ and that of normal area $(N_0)$ is $1.186{\pm}0.727(p<0.05)$. Fractal dimension at apical lesion of 6 months after endodontic treatment $(L_1)$ is $1.076{\pm}0.069$ and that of normal area $ (N_1)$ is $1.192{\pm}0.055(p<0.05)$. Fractal dimension at apical lesion of 1 year after endodontic treatment $(L_2)$ is $1.163{\pm}0.074$ and that of normal area $(N_2)$ is $1.225{\pm}0.079(p<0.05)$. After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. Conclusion : The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.

• Imaging Science in Dentistry
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• v.35 no.1
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• pp.33-40
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• 2005

Purpose : (1) To analyse the effect of exposure time, ROI size and one impact factor in the image processing procedure on estimates of fractal dimension; and (2) to analyse the correlated relationship between the fractal dimension and the Cu-Eq value (bone density). Materials and Methods : The cylindric bone phantoms of 6 large and 5 small diameter having different bone densities respectively and human dry mandible segment with copper step wedge were radiographed at 1.0 and 1.2 sec esposure (70 kVp, 7 mA) using one occlusal film and digitized. Eleven rectangular ROIs from 11 cylindric bone phantoms and 4 rectan-gular ROIs from cortical, middle, periodontal regions, and socket of bone were selected. Gaussian blurred Image was subtracted from original image of each ROI and multiplied respectively by 1, 0.8, and 0.5, and then the image was made binary, eroded and dilated once, and skeletonized. The fractal dimension was calculated by means of a box counting method in the software ImageJ. Results : The fractal dimension was decreased gradually with continued bone density decrease showing strong correlations (bone phantom; r> 0.87, bone; r> 0.68) under 70 kVp 1.0 sec M = 0.8. Fractal dimensions showed the significant differerence (p < 0.05) between two different exposure times on the same small ROI of bone phantom. Fractal dimensions between two different sizes of ROI on bone phantom showed the significant differerence (p < 0.05) under 1.2 sec exposure, but did not show it (p > 0.05) under 1.0 sec exposure. Conclusions : Exposure time, ROI size, and modifying factor during subtracting could become impacting on the results of fractal dimension. Fractal analysis with thoroughly evaluated method considering the various impacting factors on the results could be useful in assessing the bone density in dental radiography.

• Imaging Science in Dentistry
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• v.41 no.2
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• pp.71-78
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• 2011

Purpose : This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods : Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results : The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion : The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.4
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• pp.419-433
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• 2014

The Mars Exploration Rover Opportunity investigated plains at Meridiani Planum, where laminated sedimentary rocks are present. The Opportunity rover's Athena morphological investigation showed microstructures organized in intertwined filaments of microspherules: a texture we have also found on samples of terrestrial (biogenic) stromatolites and other microbialites. We performed a quantitative image analysis to compare images (n=45) of microbialites with the images (n=30) photographed by the rover (corresponding, approximately, to 25,000/15,000 microstructures). Contours were extracted and morphometric indexes were obtained: geometric and algorithmic complexities, entropy, tortuosity, minimum and maximum diameters. Terrestrial and Martian textures present a multifractal aspect. Mean values and confidence intervals from the Martian images overlapped perfectly with those from the terrestrial samples. The probability of this occurring by chance is $1/2^8$, less than p<0.004. Terrestrial abiogenic pseudostromatolites showed a simple fractal structure and different morphometric values from those of the terrestrial biogenic stromatolite images or Martian images with a less ordered texture (p<0.001). Our work shows the presumptive evidence of microbialites in the Martian outcroppings: i.e., the presence of unicellular life on the ancient Mars.

• Journal of Navigation and Port Research
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• v.40 no.4
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• pp.207-212
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• 2016

The box-counting(BC) method is one of the most commonly used methods for fractal dimension calculation of binary images in the fields of Engineering, Science, Medical Science, Geology, etc due to its simplicity and reliability. It deals with only square images with each size equal to the power of 2 to prevent it from discarding unused pixels for images of arbitrary size. In this paper, we presents a more efficient BC method based on the original one, which is applicable to images of arbitrary size. The proposed approach allows the number of the counting boxes to be real to improve the estimation accuracy. The mean absolute error performance is computed on two deterministic fractal images whose theoretical dimensions are well known to compare with those of the existing BC method and triangular BC method. The experimental results show that the proposed method can outperform the two methods and assess the complexity of coastline images of Korea and Chodo island taken from the Google map.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2730-2747
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• 2016

Due to the limitation of the bandwidth resource and capture resolution of depth cameras, low resolution depth maps should be up-sampled to high resolution so that they can correspond to their texture images. In this paper, a novel depth map up-sampling algorithm is proposed by exploiting the fractal internal self-referential feature. Fractal parameters which are extracted from a depth map, describe the internal self-referential feature of the depth map, do not introduce inherent scale and just retain the relational information of the depth map, i.e., fractal transforms provide a resolution-independent description for depth maps and could up-sample depth maps to an arbitrary high resolution. Then, an enhancement method is also proposed to further improve the performance of the up-sampled depth map. The experimental results demonstrate that better quality of synthesized views is achieved both on objective and subjective performance. Most important of all, arbitrary resolution depth maps can be obtained with the aid of the proposed scheme.

• Journal of the Korean Electrochemical Society
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• v.6 no.3
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• pp.217-223
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• 2003

The present work is concerned with characterization of surface roughness and inhomogeneity of four kinds of hot-rolled carbon steels in terms of the fractal dimension and the depression parameter by using image analysis method and electrochemical impedance spectroscopy, respectively. From the analysis of the 3D AFM image, it is realized that all the hot-rolled steel surfaces show the self-affine fractal property. The values of the fractal dimension of the hot-rolled steels were determined by the analyses of the AFM images on the basis of both the perimeter-area method and the triangulation method. In addition, the Nyquist plots were found to be depressed from a perfect semicircle form. From the experimental findings, the changes in the values of the fractal dimension and the depression parameter with chemical composition have been discussed in terms of the change in the value of hardness of base steel.