  The ability to extend the field of view of laparoscopy images can help the
surgeons to obtain a better understanding of the anatomical context. However,
due to tissue deformation, complex camera motion and significant
three-dimensional (3D) anatomical surface, image pixels may have non-rigid
deformation and traditional mosaicking methods cannot work robustly for
laparoscopy images in real-time. To solve this problem, a novel two-dimensional
(2D) non-rigid simultaneous localization and mapping (SLAM) system is proposed
in this paper, which is able to compensate for the deformation of pixels and
perform image mosaicking in real-time. The key algorithm of this 2D non-rigid
SLAM system is the expectation maximization and dual quaternion (EMDQ)
algorithm, which can generate smooth and dense deformation field from sparse
and noisy image feature matches in real-time. An uncertainty-based loop closing
method has been proposed to reduce the accumulative errors. To achieve
real-time performance, both CPU and GPU parallel computation technologies are
used for dense mosaicking of all pixels. Experimental results on \textit{in
vivo} and synthetic data demonstrate the feasibility and accuracy of our
non-rigid mosaicking method.
