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Sight to touch: 3D diffeomorphic deformation recovery with mixture components for perceiving forces in robotic-assisted surgery

Robotic-assisted minimally invasive surgical systems suffer from one major limitation which is the lack of interaction forces feedback. The restricted sense of touch hinders the surgeons' performance and reduces their dexterity and precision during a procedure. In this work, we present a sensory substitution approach that relies on visual stimuli to transmit the tool-tissue interaction forces to the operating surgeon. Our approach combines a 3D diffeomorphic deformation mapping with a generative model to precisely label the force level. The main highlights of our approach are that the use of diffeomorphic transformation ensures anatomical structure preservation and the label assignment is based on a parametric form of several mixture elements. We performed experimentations on both ex-vivo and in-vivo datasets and offer careful numerical results evaluating our approach. The results show that our solution has an error measure less than 1mm in all directions and an average labeling error of 2.05%. It can also be applicable to other scenarios that require force feedback such as microsurgery, knot tying or needle-based procedures.