A 2D/3D Non-rigid Registration Method for Lung Images Based on a Non-linear Correlation Between Displacement Vectors and Similarity Measures



This paper presents a novel 2D/3D non-rigid registration method for lung lesions tracking in image-guided diagnoses and treatments.


Preoperative 3D lung CT volumes were obtained at a series of respiratory phases and important anatomical points were extracted. A CT volume was selected as reference volume and others were considered floating volumes. Displacement vectors of anatomical points were calculated using coherent point drift (CPD) and diffeomorphic-demon methods. For each CT volume, 2D digitally reconstructed radiographs (DRR) were generated by ray projection to simulate intraoperative 2D X-ray, and grayscale-based similarity measures of DRR between reference and floating volumes were calculated. A pulmonary respiration model was constructed using cubic polynomial, which represents the non-linear correlation between displacement vectors and similarity measures. During operation, the pulmonary respiration model used X-ray to obtain displacement vectors of important anatomical points; deformation fields were calculated from the displacement vectors through B-spline transformations. Finally, simulated lung CT volumes corresponding to intraoperative X-ray were generated by applying deformation fields to reference volume. The proposed method was compared to a state-of-the-art 2D/3D non-rigid registration method named respiratory-phase matching.


Experimental results on two datasets respectively from a lung cancer patient and an ex vivo pig lung, showed mean registration accuracy of the proposed method was 1.57 ± 0.92 mm and 2.65 ± 1.35 mm; an improvement of 23% and 9% over the matching method. Moreover, mean lung structure overlaps were 0.91 and 0.88, comparable to matching method.


The proposed method has potential in aiding lung intervention diagnoses and real-time lesion tracking.

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Data Availability

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

Code Availability

The code required to reproduce these findings cannot be shared at this time as the code also forms part of an ongoing study.


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We thank Science and Technology Plan Projects of Tianjin [Grant Number 19YDYGHZ00030] and Science and Technology Plan Projects of Jiangsu [Grant Number BE2019665] for supporting this work, and we thank MedEditing LLC for linguistic assistance during the preparation of this manuscript.


This work was supported by Science and Technology Plan Projects of Tianjin [Grant Number 19YDYGHZ00030]; Science and Technology Plan Projects of Jiangsu [Grant Number BE2019665].

Author information




Conceptualization: JZ, WX, QJ; Methodology: JZ, WX, QJ; Writing-original draft preparation: JZ; Writing-review and editing: WX, XG; Supervision: XG.

Corresponding author

Correspondence to Xin Gao.

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The authors have no relevant financial or non-financial interests to disclose.

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. The study was approved by the Bioethics Committee of the Wuxi No. 2 People’s Hospital (No. 2018B05).

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Informed consent was obtained from all individual participants included in the study.

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Patients signed informed consent regarding publishing their data and photographs.



The principal notations used in this paper were described in Table 3.

Table 3 Description of principal notations

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Zhang, J., Xia, W., Jin, Q. et al. A 2D/3D Non-rigid Registration Method for Lung Images Based on a Non-linear Correlation Between Displacement Vectors and Similarity Measures. J. Med. Biol. Eng. (2021). https://doi.org/10.1007/s40846-021-00609-z

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  • 2D/3D non-rigid registration
  • Cubic polynomial
  • Similarity measure
  • B-spline transformation
  • Lung image