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.
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