Efficient inverse-kinematics solver for precise pose reconstruction of skinned 3D models

We propose an accelerated inverse-kinematics (IK) solving method aimed at reconstructing the pose of a 3D model based on the positions of surface markers or feature points. The model encompasses a skeletal structure of joints and a triangular mesh constituting its external surface. A mesh-based IK solving method optimizes the joint configurations to achieve the desired surface pose, assuming that surface markers are attached to the joints using linear-blended skinning, and that the target positions for these surface markers are provided. In the conventional IK solving method, the final position of a given joint is determined by iteratively computing error gradients based on the target marker positions, typically implemented using a 3-nested loop structure. In this paper, we streamline the standard IK computation process by precomputing all redundant terms for future use, leading to a significant reduction in asymptotic time complexity. We experimentally show that our accelerated IK solving method exhibits increasingly superior performance gains as the number of markers increases. Our pose reconstruction tests show performance improvements ranging between 34% and three times compared to a highly optimized implementation of the conventional method.