基于空间自适应参数的曲面重建

doi:10.13438/j.cnki.jdzk.2025.01.005

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (1): 32-38.DOI: 10.13438/j.cnki.jdzk.2025.01.005

基于空间自适应参数的曲面重建

刘广英,杨奋林,付飞凡,安耿

（吉首大学数学与统计学院，湖南吉首 416000）

出版日期:2025-01-01 发布日期:2025-01-20
作者简介:刘广英(1999－)，女，湖南衡阳人，吉首大学数学与统计学院硕士研究生，主要从事图像重建研究

Surface Reconstruction Based on Spatial Adaptive Parameters

LIU Guangying,YANG Fenlin,FU Feifan,AN Geng

(School of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2025-01-01 Published:2025-01-20

摘要/Abstract

摘要：最小二乘模型虽然能够重建光滑曲面,但是会使深度不连续特征变得模糊.针对这个问题,首先在最小二乘模型中引入由可积性项和Geary-Hinkley变换构造的一个空间自适应参数,建立了一个各向异性加权最小二乘模型;然后通过4方向离散公式对模型进行离散,并给出最优性条件;最后使用Krylov子空间法求解模型.数值实验结果表明,各向异性加权最小二乘模型能够保持曲面的深度不连续，重建效果比最小二乘模型的更佳.

关键词： 可积性项, Geary-Hinkley变换, 深度不连续, 自适应参数

Abstract: The least-squares model is capable of reconstructing smooth surfaces,but the depth discontinuity features can be blurred.In order to solve this problem,a spatially adaptive parameter is constructed by introducing the productivity term and Geary-Hinkley transform into the least squares model,an anisotropic weighted least-squares model is established;then the model is discretized by the 4-direction discretization formula,and the optimality condition is given;finally,the Krylov subspace method is used to solve the model.The numerical experimental results show that the anisotropic weighted least-squares model can keep the depth discontinuity of the surface,and the reconstruction effect is better than that of the least squares model.

Key words: integrability term, Geary-Hinkley transform, depth discontinuity, adaptive parameters

刘广英, 杨奋林, 付飞凡, 安耿. 基于空间自适应参数的曲面重建[J]. 吉首大学学报（自然科学版）, 2025, 46(1): 32-38.

LIU Guangying, YANG Fenlin, FU Feifan, AN Geng. Surface Reconstruction Based on Spatial Adaptive Parameters[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(1): 32-38.

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基于空间自适应参数的曲面重建

Surface Reconstruction Based on Spatial Adaptive Parameters

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