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Shape reconstruction from depth gradient with artificially periodized boundaries

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Abstract

For reconstructing the shape of an object from measured depth gradient field, the most popular two kinds are FFT-based integration methods and least-squares integration methods. For the former, it is time-efficient which should be attributed to the employment of FFT algorithms. However, the FFT algorithm usually implies periodic boundary which may be improper for non-periodic problems. This makes them less accurate than those least-squares integration methods. To avoid this deficiency, an algorithm is proposed by modifying the derivatives of endpoints to meet the numerical difference expression on a periodic domain. And the compact finite difference schemes are introduced to reduce the numerical error caused by the finite difference approximation of derivatives. The results of numerical tests show that the accuracy and robustness of the new non-iterative artificially-periodized-boundaries method are close to that of the state-of-art least-squares integration approach. Furthermore, its computational complexity is the same as a standard FFT-based integration approach.

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

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Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 11732016) and Sichuan Science and Technology Program (No. 2018JZ0076).

Funding

Conghai Wu was supported by National Natural Science Foundation of China (No. 11732016) and Sichuan Science and Technology Program (No. 2018JZ0076).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Southwest University of Science and Technology, MianYang, China

    Ling Wu, Yong Fan & Niannian Chen

  2. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, MianYang, China

    Conghai Wu

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  1. Ling Wu
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  2. Conghai Wu
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Contributions

L.W.: Drafting the manuscript, Analysis and/or interpretation of data. C.W.: Formal analysis, Software. Y.F.: Supervision, Reviewing and Editing. N.C.: Experiment.

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Correspondence to Yong Fan.

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Wu, L., Wu, C., Fan, Y. et al. Shape reconstruction from depth gradient with artificially periodized boundaries. Vis Comput 39, 2097–2110 (2023). https://doi.org/10.1007/s00371-022-02467-5

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