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Improved biharmonic kernel signature for 3D non-rigid shape matching and retrieval

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Abstract

Object retrieval, in particular 3D shape retrieval, recently has many applications such as molecular biology, medical research and computer-aided manufacturing. As the internet and 3D modeling tools have led to an increasingly growth in the number of available 3D models, it becomes necessary to have a proper and efficient representation method to capture the most important information about shapes, which for searching target object more efficiently and accurately. In this paper, we propose a novel 3D shape descriptor, improved biharmonic kernel signature (IBKS). Firstly, based on the Laplace–Beltrami operator, we perform a linear combination of some scaled eigenvalues and eigenfunctions of the biharmonic kernel signature (BKS) to construct invariant metrics about the shape. Secondly, we note that the Gaussian curvature of the vertices remains stable as the shape undergoes pose changes. This is a local property of surface that is isometric invariant and stable at most points under object articulation but is not well coded in the BKS descriptor. Therefore, we use curvature aggregation method to reduce the influence of noise, which enhances the feature separation and makes the descriptor more discriminative. The IBKS descriptor built upon the concept of biharmonic kernel signature, the descriptor inherits several useful properties such as stability of the shape joint region, robustness to isometric, scaling, noise, sampling and topology transformations. Due to the stability and discriminative power of IBKS, we can simply and effectively characterize, identify and analyze non-rigid 3D shapes. We show how our framework can be applied for shape representation, matching and retrieval. To assert our method more stable to non-rigid deformations, we compare our framework with advanced non-rigid signatures on traditional benchmark McGill and SHREC2015 datasets. Experimental results show that our spectrum shape descriptor is more stable and discriminative and is significantly better than other descriptors.

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Data availability statements

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was partially supported by the National Nature Science Foundation of China (No. 62102213, 62262056); National Key R &D plan (No. 2020YFC1523305); Natural Science Youth Foundation of Qinghai Province (No. 2023-ZJ-947Q); Major R &D and Transformation Projects in Qinghai Province (2021-GX-111).

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Authors and Affiliations

  1. State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining, 810000, China

    Yuhuan Yan, Mingquan Zhou, Dan Zhang & Shengling Geng

  2. Academy of Plateau Science and Sustainability, People’s Government of Qinghai Province and Beijing Normal University, Xining, 810000, China

    Mingquan Zhou, Dan Zhang & Shengling Geng

  3. School of Computer Science, Qinghai Normal University, Xining, 810000, China

    Yuhuan Yan, Mingquan Zhou, Dan Zhang & Shengling Geng

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  1. Yuhuan Yan
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Yan, Y., Zhou, M., Zhang, D. et al. Improved biharmonic kernel signature for 3D non-rigid shape matching and retrieval. Vis Comput (2024). https://doi.org/10.1007/s00371-023-03254-6

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