A Quasi-Spherical Triangle-Based Approach for Efficient 3-D Soft-Tissue Motion Tracking

Recently, model-based visual-tracking techniques have been developed for measuring physiological motion in robot-assisted minimally invasive surgery. However, the tracking of living tissue surfaces in 3-D space is very challenging. Linear models are difficult to fit complex tissue dynamics, while current nonlinear models generally suffer from complex implementation and excessive computational burden. Instrument occlusion is another challenging issue which often causes tracking failure. In this study, we propose a novel deformable model suitable for real-time 3-D tissue tracking based on a quasi-spherical triangle. The model is parameterized by three vertices of the triangle with a curving parameter so that the warped surface can be computed efficiently using matrix operations. An efficient second-order minimization technique is employed to estimate model parameters, and the Jacobian matrix associated with the proposed model is derived. To alleviate the effects of illumination, a triangle-based illumination model is incorporated into the tracking scheme. A new motion prediction algorithm is developed by exploring the peak-valley characteristics of motion signals to handle the occlusion problem. The performance of the proposed method is validated using phantom heart data and in vivo videos acquired by the daVinci surgical robotic platform.