• Title/Summary/Keyword: discrete Laplacian

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Curve Reconstruction from Oriented Points Using Hierarchical ZP-Splines (계층적 ZP-스플라인을 이용한 곡선 복구 기법)

  • Kim, Hyunjun;Kim, Minho
    • Journal of the Korea Computer Graphics Society
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    • v.22 no.5
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    • pp.1-16
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    • 2016
  • In this paper, we propose and efficient curve reconstruction method based on the classical least-square fitting scheme. Specifically, given planar sample points equipped with normals, we reconstruct the objective curve as the zero set of a hierarchical implicit ZP(Zwart-Powell)-spline that can recover large holes of dataset without loosing the fine details. As regularizers, we adopted two: a Tikhonov regularizer to reduce the singularity of the linear system and a discrete Laplacian operator to smooth out the isocurves. Benchmark tests with quantitative measurements are done and our method shows much better quality than polynomial methods. Compared with the hierarchical bi-quadratic spline for datasets with holes, our method results in compatible quality but with less than 90% computational overhead.

The Line Feature Extraction for Automatic Cartography Using High Frequency Filters in Remote Sensing : A Case Study of Chinju City (위성영상의 형태추출을 통한 지도화 : 고빈도 공간필터 사용을 중심으로)

  • Jung, In-Chul
    • Journal of the Korean association of regional geographers
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    • v.2 no.2
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    • pp.183-196
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    • 1996
  • The purpose of this paper is to explore the possibility of automatic extraction of line feature from Satellite image. The first part reviews the relationship between spatial filtering and cartographic interpretation. The second part describes the principal operations of high frequency filters and their properties, the third part presents the result of filtering application to the SPOT Panchromatic image of the Chinju city. Some experimental results are given here indicating the high feasibility of the filtering technique. The results of the paper is summarized as follows: Firstly the good all-purposes filter dose not exist. Certain laplacian filter and Frei-chen filter were very sensitive to the noise and could not detect line features in our case. Secondly, summary filters and some other filters do an excellent job of identifying edges around urban objects. With the filtered image added to the original image, the interpretation is more easy. Thirdly, Compass gradient masks may be used to perform two-dimensional, discrete differentiation directional edge enhancement, however, in our case, the line featuring was not satisfactory. In general, the wide masks detect the broad edges and narrow masks are used to detect the sharper discontinuities. But, in our case, the difference between the $3{\times}3$ and $7{\times}7$ kernel filters are not remarkable. It may be due to the good spatial resolution of Spot scene. The filtering effect depends on local circumstance. Band or kernel size selection must be also considered. For the skillful geographical interpretation, we need to take account the more subtle qualitative information.

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