An efficient approach to dynamically reconstruct a region of interest (ROI) on a beating heart from stereo-endoscopic video is developed. A ROI is first pre-reconstructed with a decoupled high-rank thin plate spline model. Eigen-shapes are learned from the pre-reconstructed data by using principal component analysis (PCA) to build a low-rank statistical deformable model for reconstructing subsequent frames. The linear transferability of PCA is proved, which allows fast eigen-shape learning. A general dynamic reconstruction framework is developed that formulates ROI reconstruction as an optimization problem of model parameters, and an efficient second-order minimization algorithm is derived to iteratively solve it. The performance of the proposed method is finally validated on stereo-endoscopic videos recorded by da Vinci robots.
IntroductionIn robotic-assisted off-pump heart surgery, heart beating considerably influences the accuracy of surgical operations, resulting in longer surgical duration and increased surgical risks. By measuring heart motion and actively synchronizing surgical instruments with this motion, a technique called active motion compensation, it is possible to provide a virtually stable operating environment to surgeons [1,2]. Passive vision using stereo-endoscope, compared with other sensing techniques such as structured lighting [3,4] and ultrasound [5], is more appropriate for measuring heart motion in a Minimally Invasive Surgery (MIS) because no additional instrument ports are required, as indicated in [6]. The 3D reconstruction with endoscope is also important for other advanced surgical techniques, e.g. augmented reality guidance [7], and multispectral [8] or multimodal [9] imaging. In addition, it is useful for offline applications as well, such as surgery simulation [10] and visual medical record [11], for learning, training or evaluation purposes.However, in a highly dynamic MIS, it is very challenging to track and reconstruct Regions of Interest (ROIs) with complex soft-tissue deformations from real-time endoscopic videos. Model-based methods have been explored [12][13][14][15][16][17][18]. With a parameterized deformable model, an initial ROI is warped as a template to match pixels at subsequent stereo-pair frames. Model complexity (rank) can be simply measured by the number of model parameters. Low-rank models, such as rigid and affine models, are robust and computationally efficient but difficult to deal with complex soft-tissue deformations, while high-rank models generally suffer from problems of parameter convergence and heavy computational burden, difficult to meet real-time and robustness requirements, as indicated in [16].On the other hand, most existing models, typically based on the mesh [2,11,13,19] or spline [12,14,[16][17][18], are designed for general deformations with certain continuity and smoothness constraints, which do not take into account the statistics and specificities of ROIs. Statistical shape models have been explored to reconstruct static anatomical structu...