2020/04/28 by Karim Makki, Bhushan Borotikar, Makki, K. +14
Medicine · #Bone and Joint Diseases #Scoliosis diagnosis and treatment #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2005.02159
The log Euclidean polyrigid registration framework provides a way to smoothly\nestimate and interpolate poly-rigid/affine transformations for which the\ninvertibility is guaranteed. This powerful and flexible mathematical framework\nis currently being used to track the human joint dynamics by first imposing\nbone rigidity constraints in order to synthetize the spatio-temporal joint\ndeformations later. However, since no closed-form exists, then a\ncomputationally expensive integration of ordinary differential equations (ODEs)\nis required to perform image registration using this framework. To tackle this\nproblem, the exponential map for solving these ODEs is computed using the\nscaling and squaring method in the literature. In this paper, we propose an\nalgorithm using a matrix diagonalization based method for smooth interpolation\nof homogeneous polyrigid transformations of human joints during motion. The use\nof this alternative computational approach to integrate ODEs is well motivated\nby the fact that bone rigid transformations satisfy the mechanical constraints\nof human joint motion, which provide conditions that guarantee the\ndiagonalizability of local bone transformations and consequently of the\nresulting joint transformations. In a comparison with the scaling and squaring\nmethod, we discuss the usefulness of the matrix eigendecomposition technique\nwhich reduces significantly the computational burden associated with the\ncomputation of matrix exponential over a dense regular grid. Finally, we have\napplied the method to enhance the temporal resolution of dynamic MRI sequences\nof the ankle joint. To conclude, numerical experiments show that the\neigendecomposition method is more capable of balancing the trade-off between\naccuracy, computation time, and memory requirements.\n