  Reconstructing deformable tissues from endoscopic stereo videos in robotic
surgery is crucial for various clinical applications. However, existing methods
relying only on implicit representations are computationally expensive and
require dozens of hours, which limits further practical applications. To
address this challenge, we introduce LerPlane, a novel method for fast and
accurate reconstruction of surgical scenes under a single-viewpoint setting.
LerPlane treats surgical procedures as 4D volumes and factorizes them into
explicit 2D planes of static and dynamic fields, leading to a compact memory
footprint and significantly accelerated optimization. The efficient
factorization is accomplished by fusing features obtained through linear
interpolation of each plane and enables using lightweight neural networks to
model surgical scenes. Besides, LerPlane shares static fields, significantly
reducing the workload of dynamic tissue modeling. We also propose a novel
sample scheme to boost optimization and improve performance in regions with
tool occlusion and large motions. Experiments on DaVinci robotic surgery videos
demonstrate that LerPlane accelerates optimization by over 100$\times$ while
maintaining high quality across various non-rigid deformations, showing
significant promise for future intraoperative surgery applications.
