  Estimating precise metric depth and scene reconstruction from monocular
endoscopy is a fundamental task for surgical navigation in robotic surgery.
However, traditional stereo matching adopts binocular images to perceive the
depth information, which is difficult to transfer to the soft robotics-based
surgical systems due to the use of monocular endoscopy. In this paper, we
present a novel framework that combines robot kinematics and monocular
endoscope images with deep unsupervised learning into a single network for
metric depth estimation and then achieve 3D reconstruction of complex anatomy.
Specifically, we first obtain the relative depth maps of surgical scenes by
leveraging a brightness-aware monocular depth estimation method. Then, the
corresponding endoscope poses are computed based on non-linear optimization of
geometric and photometric reprojection residuals. Afterwards, we develop a
Depth-driven Sliding Optimization (DDSO) algorithm to extract the scaling
coefficient from kinematics and calculated poses offline. By coupling the
metric scale and relative depth data, we form a robust ensemble that represents
the metric and consistent depth. Next, we treat the ensemble as supervisory
labels to train a metric depth estimation network for surgeries (i.e.,
MetricDepthS-Net) that distills the embeddings from the robot kinematics,
endoscopic videos, and poses. With accurate metric depth estimation, we utilize
a dense visual reconstruction method to recover the 3D structure of the whole
surgical site. We have extensively evaluated the proposed framework on public
SCARED and achieved comparable performance with stereo-based depth estimation
methods. Our results demonstrate the feasibility of the proposed approach to
recover the metric depth and 3D structure with monocular inputs.
