Scholarlink

<p>Pointwise map recovery, a critical component in functional maps, is of paramount importance for nonrigid shape matching, but is inherently inaccurate due to the lack of geometric consistency. To this end, we propose a novel and effective framework, termed <i>Locality Optimization Refinement with Deformation</i> (LORD), which firstly integrates both local and global extrinsic constraints into functional space for precise pointwise maps. Specifically, observing local consistency during deformations, we innovatively devise a mathematical model with a linear closed-form solution leveraging neighborhood support, thus ensuring continuity of pointwise maps. To address the limitations of local constraints in contextual representation, we further introduce the kernel trick in non-Euclidean spaces to design probabilistic models based on functional deformation that enhance global smoothness. Lastly, we propose outlier refinement using Locally Linear Embedding and estimated functional deformation within an adaptive spectral similarity space, making it suitable for various types of shapes. Our comprehensive geometric constraints eliminate functional mapping ambiguity and significantly improve accuracy with linearithmic complexity. Extensive experiments conducted on different public benchmarks demonstrate that our LORD outperforms state-of-the-art techniques in nonrigid shape matching tasks, and verify its generalizability and effectiveness.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Locality Optimization Refinement with Deformation for Shape Matching via Functional Maps

  • 期刊论文

  • 发表日期：

    2026年1月20日

查看全文
  • Yifan Xia,
  • Jiayi Ma

摘要

Pointwise map recovery, a critical component in functional maps, is of paramount importance for nonrigid shape matching, but is inherently inaccurate due to the lack of geometric consistency. To this end, we propose a novel and effective framework, termed Locality Optimization Refinement with Deformation (LORD), which firstly integrates both local and global extrinsic constraints into functional space for precise pointwise maps. Specifically, observing local consistency during deformations, we innovatively devise a mathematical model with a linear closed-form solution leveraging neighborhood support, thus ensuring continuity of pointwise maps. To address the limitations of local constraints in contextual representation, we further introduce the kernel trick in non-Euclidean spaces to design probabilistic models based on functional deformation that enhance global smoothness. Lastly, we propose outlier refinement using Locally Linear Embedding and estimated functional deformation within an adaptive spectral similarity space, making it suitable for various types of shapes. Our comprehensive geometric constraints eliminate functional mapping ambiguity and significantly improve accuracy with linearithmic complexity. Extensive experiments conducted on different public benchmarks demonstrate that our LORD outperforms state-of-the-art techniques in nonrigid shape matching tasks, and verify its generalizability and effectiveness.