• Title/Summary/Keyword: Scattered points

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AN ELEMENTARY PROOF OF THE OPTIMAL RECOVERY OF THE THIN PLATE SPLINE RADIAL BASIS FUNCTION

  • KIM, MORAN;MIN, CHOHONG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.4
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    • pp.409-416
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    • 2015
  • In many practical applications, we face the problem of reconstruction of an unknown function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in $\mathbb{R}^2$. The traditional proofs supporting the argument are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.

On B-spline Approximation for Representing Scattered Multivariate Data (비정렬 다변수 데이터의 B-스플라인 근사화 기법)

  • Park, Sang-Kun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.35 no.8
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    • pp.921-931
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    • 2011
  • This paper presents a data-fitting technique in which a B-spline hypervolume is used to approximate a given data set of scattered data samples. We describe the implementation of the data structure of a B-spline hypervolume, and we measure its memory size to show that the representation is compact. The proposed technique includes two algorithms. One is for the determination of the knot vectors of a B-spline hypervolume. The other is for the control points, which are determined by solving a linear least-squares minimization problem where the solution is independent of the data-set complexity. The proposed approach is demonstrated with various data-set configurations to reveal its performance in terms of approximation accuracy, memory use, and running time. In addition, we compare our approach with existing methods and present unconstrained optimization examples to show the potential for various applications.

Evaluation of Ovary Dose for woman of Childbearing age Woman with Breast cancer in tomotherapy (가임기 여성의 유방암 토모치료 시 난소선량 평가비교)

  • Lee, Soo Hyeung;Park, Soo Yeun;Choi, Ji Min;Park, Ju Young;Kim, Jong Suk
    • The Journal of Korean Society for Radiation Therapy
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    • v.26 no.2
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    • pp.337-343
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    • 2014
  • Purpose : The aim of this study is to evaluate unwanted scattered dose to ovary by scattering and leakage generated from treatment fields of Tomotherapy for childbearing woman with breast cancer. Materials and Methods : The radiation treatments plans for left breast cancer were established using Tomotherapy planning system (Tomotherapy, Inc, USA). They were generated by using helical and direct Tomotherapy methods for comparison. The CT images for the planning were scanned with 2.5 mm slice thickness using anthropomorphic phantom (Alderson-Rando phantom, The Phantom Laboratory, USA). The measurement points for the ovary dose were determined at the points laterally 30 cm apart from mid-point of treatment field of the pelvis. The measurements were repeated five times and averaged using glass dosimeters (1.5 mm diameter and 12 mm of length) equipped with low-energy correction filter. The measures dose values were also converted to Organ Equivalent Dose (OED) by the linear exponential dose-response model. Results : Scattered doses of ovary which were measured based on two methods of Tomo helical and Tomo direct showed average of $64.94{\pm}0.84mGy$ and $37.64{\pm}1.20mGy$ in left ovary part and average of $64.38{\pm}1.85mGy$ and $32.96{\pm}1.11mGy$ in right ovary part. This showed when executing Tomotherapy, measured scattered dose of Tomo Helical method which has relatively greater monitor units (MUs) and longer irradiation time are approximately 1.8 times higher than Tomo direct method. Conclusion : Scattered dose of left and right ovary of childbearing women is lower than ICRP recommended does which is not seriously worried level against the infertility and secondary cancer occurrence. However, as breast cancer occurrence ages become younger in the future and radiation therapy using high-precision image guidance equipment like Tomotherapy is developed, clinical follow-up studies about the ovary dose of childbearing women patients would be more required.

Evaluation of the Usefulness of Tungsten Nanoparticles as an Alternative to Lead Shielding Materials in Electron Beam Therapy (전자선 치료시 납 차폐체 대체물질로서의 텅스텐 나노입자의 유용성 평가)

  • Kim, Ji-Hyang;Kim, Na-Kyoung;Lee, Gyu-Yeong;Jung, Da-Bin;Heo, Yeong-Cheol
    • Journal of the Korean Society of Radiology
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    • v.15 no.7
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    • pp.949-956
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    • 2021
  • The purpose of this paper is to evaluate whether tungsten nanoparticles have a shielding effect on scattered light generated at high doses as an alternative material to lead used to shield scattered light in electron beam therapy. A plate was manufactured to set the position of the dosimeter and the size of the radiation field to be constant. The glass dosimeter was placed at 12 points, which were 1, 2, and 4 cm apart from the center of the field of 10 × 10 cm2 in the cross direction. A total of 12 types of tungsten nanoparticle shields were developed with a thickness of 0.75 mm to 4.00 mm and a size of 10 × 10 cm2 using 0.4, 0.75, and 1 mm materials. Using a linear accelerator, measurements were made four times at 6 MeV and four times at 12 MeV, and the dose intensity was investigated at 100 MU. The 4 mm shielding plate showed the highest shielding effect at 1 cm from the irradiation field. The 1 mm shielding plate at 2 cm from the irradiation field had the lowest shielding effect. As the thickness of the tungsten shielding plate increased, the electron beam's shielding effect increased sharply. It was confirmed that tungsten nanoparticles can reduce the amount of scattered light generated by electron beam therapy. Therefore, this study will provide basic data when follow-up studies are conducted on the shielding ability of tungsten nanoparticles.

Accuracy and reliability of stitched cone-beam computed tomography images

  • Egbert, Nicholas;Cagna, David R.;Ahuja, Swati;Wicks, Russell A.
    • Imaging Science in Dentistry
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    • v.45 no.1
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    • pp.41-47
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    • 2015
  • Purpose: This study was performed to evaluate the linear distance accuracy and reliability of stitched small field of view (FOV) cone-beam computed tomography (CBCT) reconstructed images for the fabrication of implant surgical guides. Material and Methods: Three gutta percha points were fixed on the inferior border of a cadaveric mandible to serve as control reference points. Ten additional gutta percha points, representing fiduciary markers, were scattered on the buccal and lingual cortices at the level of the proposed complete denture flange. A digital caliper was used to measure the distance between the reference points and fiduciary markers, which represented the anatomic linear dimension. The mandible was scanned using small FOV CBCT, and the images were then reconstructed and stitched using the manufacturer's imaging software. The same measurements were then taken with the CBCT software. Results: The anatomic linear dimension measurements and stitched small FOV CBCT measurements were statistically evaluated for linear accuracy. The mean difference between the anatomic linear dimension measurements and the stitched small FOV CBCT measurements was found to be 0.34 mm with a 95% confidence interval of +0.24 - +0.44 mm and a mean standard deviation of 0.30 mm. The difference between the control and the stitched small FOV CBCT measurements was insignificant within the parameters defined by this study. Conclusion: The proven accuracy of stitched small FOV CBCT data sets may allow image-guided fabrication of implant surgical stents from such data sets.

Fault Pattern Extraction Via Adjustable Time Segmentation Considering Inflection Points of Sensor Signals for Aircraft Engine Monitoring (센서 데이터 변곡점에 따른 Time Segmentation 기반 항공기 엔진의 고장 패턴 추출)

  • Baek, Sujeong
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.44 no.3
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    • pp.86-97
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    • 2021
  • As mechatronic systems have various, complex functions and require high performance, automatic fault detection is necessary for secure operation in manufacturing processes. For conducting automatic and real-time fault detection in modern mechatronic systems, multiple sensor signals are collected by internet of things technologies. Since traditional statistical control charts or machine learning approaches show significant results with unified and solid density models under normal operating states but they have limitations with scattered signal models under normal states, many pattern extraction and matching approaches have been paid attention. Signal discretization-based pattern extraction methods are one of popular signal analyses, which reduce the size of the given datasets as much as possible as well as highlight significant and inherent signal behaviors. Since general pattern extraction methods are usually conducted with a fixed size of time segmentation, they can easily cut off significant behaviors, and consequently the performance of the extracted fault patterns will be reduced. In this regard, adjustable time segmentation is proposed to extract much meaningful fault patterns in multiple sensor signals. By considering inflection points of signals, we determine the optimal cut-points of time segments in each sensor signal. In addition, to clarify the inflection points, we apply Savitzky-golay filter to the original datasets. To validate and verify the performance of the proposed segmentation, the dataset collected from an aircraft engine (provided by NASA prognostics center) is used to fault pattern extraction. As a result, the proposed adjustable time segmentation shows better performance in fault pattern extraction.

Depth Measurement Method Robust against Scattering of Line Lasers (라인 레이저의 산란에 강인한 심도 측정 방법)

  • Ko, Kwangjin;Yeon, Sungho;Kim, Jaemin
    • Journal of Korea Multimedia Society
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    • v.21 no.2
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    • pp.181-187
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    • 2018
  • Line-laser beams are used for depth measurement of welding beads along the circumference of a pipe. For this, first we project a line-laser beam on an rotating pipe and take a sequence of images of the beam projected on the pipe using a CCD camera. Second, the projected line laser beam in each image is detected, converted into a thin curve. Finally measure the distance between the thinned curve and an imaginary line. When a line-laser beam is projected to a rough metal surface such as arc welding beads, the beam is severely scattered. This severe scattering makes the thinned curve perturbed. In this paper, we propose a thinning method robust against scattering of line lasers. First, we extract a projected line laser beam region using an adaptive threshold. Second, we model a thinned curve with a spline curve with control points. Next, we adjust the control points to fit the curve to the projected line-laser beam. Finally, we take a weighted mean of thin curves on a sequence of image frames. Experiments shows that the proposed thinning method results in a thinning curve, which is smooth and fit to the projected line-laser beam with small error.

General Disaster Scattered Action Research -Focusing On the Construction Site Accident Cases- (일반재해 발생시 산재처리 방안연구 -건설현장 사고사례를 중심으로-)

  • Yoo, Yong Tae;Kang, Kyung-Sik
    • Journal of the Korea Safety Management & Science
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    • v.17 no.4
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    • pp.23-33
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    • 2015
  • Recently, the Ministry of Employment and Labor Management is a trend to strengthen all men death rate than the accident rate. Points reduction in the accident rate change orders related to credit rating score to +2 points in his plans as part of +1 point. In addition, according to the fancy linger RISK treatment in the event of a disaster site and fiction treatment to achieve accident-free during processing the scene interspersed with equity issues have been raised. In general disaster for the problem in the first two cases occurs when abnormal process according to the disaster site manager positions dismissal policy, each division headquarters itself, interspersed disasters performance compared to processing in accordance with the refrain, processing expenses in accordance with the composition of untreated industrial accident, costs and burdens partners FTC, there is a possibility that the issues raised, such as the Ministry of Employment and Labor. In response to domestic social practices focused on the construction site practices and prevention measures should be evaluated with respect to what.

Pinholes on Oxide under Polysilicon Layer after Plasma Etching (플라즈마 에칭 후 게이트 산화막의 파괴)

  • 최영식
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.6 no.1
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    • pp.99-102
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    • 2002
  • Pinholes on the thermally grown oxide, which is called gate oxide, on silicon substrate under polysilicon layer are found and its mechanism is analyzed in this paper. The oxide under a polysilicon layer is broken during the plasma etching process of other polysilicon layer. Both polysilicon layers are separated with 0.8${\mu}{\textrm}{m}$ thick oxide deposited by CVD (Chemical Vapor Deposition). Since broken oxide points are found scattered around an arc occurrence point, it is assumed that an extremely high electric field generated near the arc occurrence point makes the gate oxide broken. 1'he arc occurrence point has been observed on the alignment key and is the mark of low yield. It is found that any arc occurrence can cause chips to fail by breaking the gate oxide, even if are occurrence points are found on scribeline.

Enzyme Kinetic Study for Degradation of Phytic acid by Phytase (Phytase에 의한 phytic acid의 분해 반응속도 연구)

  • Kim, Jae-Seok;Lee, Jae-Heung
    • KSBB Journal
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    • v.26 no.4
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    • pp.300-304
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    • 2011
  • Phytases are hydrolytic enzymes that catalyze the sequential hydrolysis of phytic acid (myo-inositol-1,2,3,4,5,6-hexakisphosphate) to myo-inositols with lower numbers of phosphate groups. Two types of phytases have been identified which initiate hydrolysis of the phytic acid at either the 3- or 6- position of the inositol ring. In the present investigation, a mathematical model was proposed and computed to estimate maximum enzyme reaction rate constants which fit the experimental data obtained by other authors. Although the data points were scattered to some extent, good agreement was found between the model and the experiment data. It appears that the maximum rate constants of removal of the first, second, and third phosphate groups were not equal. Also there was neither a steady trend upward or downward in the rate constants with the stepwise hydrolysis reactions.