• Laser & Optoelectronics Progress
  • Vol. 59, Issue 8, 0812001 (2022)
Yutian Ji, Chunkang Zhang*, and Yao Yin
Author Affiliations
  • College of Mining, Guizhou University, Guiyang , Guizhou 550025, China
  • show less
    DOI: 10.3788/LOP202259.0812001 Cite this Article Set citation alerts
    Yutian Ji, Chunkang Zhang, Yao Yin. Extraction and Simplification of Terrain Surface Topological Features Based on PiecewiseLinear Morse Theory[J]. Laser & Optoelectronics Progress, 2022, 59(8): 0812001 Copy Citation Text show less
    References

    [1] Li R Z, Liu Z W. New segmentation method combining three-dimensional point cloud skeleton points and feature points[J]. Laser & Optoelectronics Progress, 57, 121104(2020).

    [2] Deng B W, Wang Z B, Jin Y et al. Feature extraction method of laser scanning point cloud based on morphological gradient[J]. Laser & Optoelectronics Progress, 55, 051203(2018).

    [3] Yao M J, Tang X, Zhang C L et al. Design and application of plastic products based on reverse engineering and FDM technology[J]. Plastics Science and Technology, 48, 45-48(2020).

    [4] Long L J, Xia Y H, Huang D. Fast modeling method for substation based on 3D laser scanning point cloud data[J]. Laser & Optoelectronics Progress, 57, 202801(2020).

    [5] Luo S Z, Xi X H, Wang C. Review: the application of LiDAR remote sensing in cultural heritage preservation[J]. Remote Sensing Technology and Application, 29, 1054-1059(2014).

    [6] Xu Y, Sun L N, Wang W J. A method of airborne LiDAR data terrain feature extraction based on maximum curvature[J]. Journal of Geomatics Science and Technology, 36, 34-38(2019).

    [7] Yang B S, Liang F X, Huang R G. Progress, challenges and perspectives of 3D LiDAR point cloud processing[J]. Acta Geodaetica et Cartographica Sinica, 46, 1509-1516(2017).

    [8] Syzdykbayev M, Karimi B, Karimi H A. A method for extracting some key terrain features from shaded relief of digital terrain models[J]. Remote Sensing, 12, 2809(2020).

    [9] Tang G A. Progress of DEM and digital terrain analysis in China[J]. Acta Geographica Sinica, 69, 1305-1325(2014).

    [10] Zhu Q, Zhao J, Zhong Z et al. The extraction of topographic patterns based on regular grid DEMs[J]. Acta Geodaetica et Cartographic Sinica, 33, 77-82(2004).

    [11] Kweon I S, Kanade T. Extracting topographic terrain features from elevation maps[J]. CVGIP: Image Understanding, 59, 171-182(1994).

    [12] Briggs I. Water flow using desity of area[R], 1-11(1989).

    [13] Milnor J[M]. Morse theory(1963).

    [14] Knauf A, Martynchuk N. Topology change of level sets in Morse theory[J]. Arkiv För Matematik, 58, 333-356(2020).

    [15] Wang C, Ren S Q. A discrete Morse theory for digraphs[EB/OL]. https://arxiv.org/abs/2007.13425

    [16] Zhang C K, Zhao X S, Wang H B. Feature points extraction of small-scale terrain based on morse theory[J]. Journal of Geomatics Science and Technology, 32, 266-270(2015).

    [17] Weinkauf T, Günther D. Separatrix persistence: extraction of salient edges on surfaces using topological methods[J]. Computer Graphics Forum, 28, 1519-1528(2009).

    [18] Wang H B, Zhu X Y, Zhang C K. Topological simplification based on nature principle for terrain surface[J]. Journal of Geomatics Science and Technology, 30, 572-576(2013).

    [19] Yuan J, Zhou M Q, Geng G H et al. Automatic reassembly of fractured fragments using Morse topological features[J]. Acta Automatica Sinica, 44, 1486-1495(2018).

    [20] Banchoff T F. Critical points and curvature for embedded polyhedra[J]. Journal of Differential Geometry, 1, 245-256(1967).

    [21] Banchoff T F. Critical points and curvature for embedded polyhedral surfaces[J]. The American Mathematical Monthly, 77, 475-485(1970).

    [22] Forman R. Discrete morse theory and the cohomology ring[J]. Transactions of the American Mathematical Society, 354, 5063-5085(2002).

    [23] Kannan H, Saucan E, Roy I et al. Persistent homology of unweighted complex networks via discrete Morse theory[J]. Scientific Reports, 9, 13817(2019).

    [24] Wang H B, Zhao X S, Zhang C K et al. An improved algorithm of constructing terrain feature lines based on Morse complex[J]. Geomatics and Information Science of Wuhan University, 40, 1220-1224(2015).

    [25] de Floriani L, Fugacci U, Iuricich F et al. Morse complexes for shape segmentation and homological analysis: discrete models and algorithms[J]. Computer Graphics Forum, 34, 761-785(2015).

    [26] Vitali M, de Floriani L, Magillo P. Computing morse decompositions for triangulated terrains: an analysis and an experimental evaluation[M]. Maino G, Foresti G L. Image analysis and processing-ICIAP 2011. Lecture notes in computer science, 6978, 565-574(2011).

    Yutian Ji, Chunkang Zhang, Yao Yin. Extraction and Simplification of Terrain Surface Topological Features Based on PiecewiseLinear Morse Theory[J]. Laser & Optoelectronics Progress, 2022, 59(8): 0812001
    Download Citation