• Laser & Optoelectronics Progress
  • Vol. 62, Issue 2, 0215006 (2025)
Zichao Chen1,2,*, Wen Ren2,3, and Long Wu2,3
Author Affiliations
  • 1School of Mechanical and Electronic Engineering, Fujian Agriculture and Forestry University,Fuzhou 350002, Fujian , China
  • 2Key Laboratory of Equipment Intelligence Control of Fujian Province, Sanming University,Sanming 365004, Fujian China
  • 3College of Mechanical and Electrical Engineering, Sanming University, Sanming 365004, Fujian , China
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    DOI: 10.3788/LOP241190 Cite this Article Set citation alerts
    Zichao Chen, Wen Ren, Long Wu. KD-Tree-Guided Surface-Curvature-Driven SteelBillet Point-Cloud Simplification Algorithm[J]. Laser & Optoelectronics Progress, 2025, 62(2): 0215006 Copy Citation Text show less

    Abstract

    To address the problem of overall contour loss and missing key features in the simplified point-cloud data of steel billets, a KD-tree-guided surface-curvature-driven steel-billet point-cloud (KDSCP) simplification algorithm is proposed. First, a discrete topological relationship between points is constructed based on the KD-tree for k nearest neighbor queries. Second, the point-cloud areas are partitioned based on curvature feature thresholds. Finally, the partitioning of the steel-billet point-cloud data is simplified using adjustable simplification-rate random sampling and centroid nearest-neighbor point-simplification methods. KDSCP is compared with random sampling and improved curvature-sampling methods. The results show that KDSCP not only better preserves the main contour of the steel-billet point cloud but also achieves 17.97% and 28.70% improvements in feature-point retention, 0.4494 dB and 1.9879 dB increases in the PSNR, and 3.8791 and 2.5540 mm reductions in the Hausdorff distance at a simplification rate of 55%, respectively. The proposed KDSCP point-cloud simplification algorithm can significantly simplify steel-billet point-cloud data while maintaining complete contour and key feature information, thus benefitting the real-time processing of steel-billet point clouds.
    dij=xi-xj2+yi-yj2+zi-zj2
    Zx,y=ax2+bxy+cy2
    Q2=jkaxj2+bxjyj+cyj2-zj2j=1,2,,k
    Q2a=j2xj2axj2+bxjyj+cyj2-zj=0Q2b=j2xjyjaxj2+bxjyj+cyj2-zj=0Q2c=j2yj2axj2+bxjyj+cyj2-zj=0
    rx,y=Xx,y=xYx,y=yZx,y=ax2+bxy+cy2
    r=rxt,yt
    dS2=dr2=rxdx+rydy2=rx2dx2+2rxrydxdy+ry2dy2
    dS2=I=Edx2+2Fdxdy+Gdy2(1)
    E=rxrx,F=rxry,G=ryry
    k=dtdS=knn+kgn×t
    n=rx×ryrx×ry
    =-drdn=Ldx2+2Mdxdy+Ndy2(1)
    L=rxxnM=rxynN=ryyn
    kn==L+2Mλ+Nλ2E+2Fλ+Gλ2(1)
    λ=dydx
    KGauss=k1k2=LN-M2EG-F2
    H=12k1+k2+EN-2FM+GL2EG-F2
    H¯=i'=1nHi'n
    Px=i=1kPixkPy=i=1kPiykPz=i=1kPizk
    ps=nbillet-nrnbillet
    pg=nrng
    HA,B=maxhA,B,hB,A
    Eic=-piclog2pic-j=1kpjlog2pjpic=HicHic+j=1kicHj
    E=i=1n'Ei
    Eic*=11+e-Eic
    E*=ic=1n'Eic*n'