Geometry map algorithms for interactive deformation and real-time visualization

Laparoscopic surgery is a popular technique that requires intensive training and practice before actual surgery. Computer simulation provides a virtual training environment for surgeons to practise. Surgery simulators are becoming practical with new frameworks that include core components such as enhanced medical imaging, rapid medical data modeling, realistic visualization procedures, and high fidelity animation techniques. The emphasis on cinematic quality rendering has gained importance with the widespread availability of affordable high end graphics capabilities on desktop computers. However, the challenge is the computation of man-machine interaction with the deformable tissues/organs. Modeling organs for surgery simulation is a formidable challenge due to three reasons. First, the organs and body parts have not only very complex shapes, but are deformable too. The second challenge is to provide a mechanism for surgeons to interact with these complex anatomical objects. The third challenge is the expensive 3D deformation computation required for haptic feedback. We propose a new technique that is extensively superior to the conventional rigid Geometry Images. In our approach, a parameterized representation of virtual organs with multi-layered 2D flat maps is used for the purpose of surgery simulation. An unstructured 3D input mesh is parameterized and resampled into a regular 2D parameterized model called Geometry Map. To accomplish real-time interaction with deformable organs, instead of computing the deformation on the organ models in 3D space, we use a novel yet simple and fast free-form deformation on the 2D geometry map itself. Real-time haptic feedback can be provided with this deformation technique. Our parameterized representation can efficiently perform both collision detection of tool tip with deformable object and contact detection between multiple deformable objects. We also show that the application of the geometry map can even be extended to the haptic sensing of virtual textiles. With this representation, we demonstrate that we can construct a practical and realistic environment with both visual and haptic rendering for interactive surgery simulation.DOCTOR OF PHILOSOPHY (SCE