Background and purpose: Deformable image registration (DIR) is a crucial tool
in radiotherapy for extracting and modelling organ motion. However, when
significant changes and sliding boundaries are present, it faces compromised
accuracy and uncertainty, determining the subsequential contour propagation and
dose accumulation procedures. Materials and methods: We propose an implicit
neural representation (INR)-based approach modelling motion continuously in
both space and time, named Continues-sPatial-Temporal DIR (CPT-DIR). This
method uses a multilayer perception (MLP) network to map 3D coordinate (x,y,z)
to its corresponding velocity vector (vx,vy,vz). The displacement vectors
(dx,dy,dz) are then calculated by integrating velocity vectors over time. The
MLP's parameters can rapidly adapt to new cases without pre-training, enhancing
optimisation. The DIR's performance was tested on the DIR-Lab dataset of 10
lung 4DCT cases, using metrics of landmark accuracy (TRE), contour conformity
(Dice) and image similarity (MAE). Results: The proposed CPT-DIR can reduce
landmark TRE from 2.79mm to 0.99mm, outperforming B-splines' results for all
cases. The MAE of the whole-body region improves from 35.46HU to 28.99HU.
Furthermore, CPT-DIR surpasses B-splines for accuracy in the sliding boundary
region, lowering MAE and increasing Dice coefficients for the ribcage from
65.65HU and 90.41% to 42.04HU and 90.56%, versus 75.40HU and 89.30% without
registration. Meanwhile, CPT-DIR offers significant speed advantages,
completing in under 15 seconds compared to a few minutes with the conventional
B-splines method. Conclusion: Leveraging the continuous representations, the
CPT-DIR method significantly enhances registration accuracy, automation and
speed, outperforming traditional B-splines in landmark and contour precision,
particularly in the challenging areas.

基于隐式神经表示的连续时空图像变形 (Continuous-sPatial-Temporal DIR，CPT-DIR) 方法显著提高了图像配准的准确性、自动化和速度，特别是在具有挑战性的区域，优于传统的 B 样条方法。