Joint Alignment of Multiple Generalized Point Sets with Anisotropic Positional Uncertainty Based on Expectation Maximization

摘要: Alignment of multiple point sets is an essential problem in medical imaging and computer-assisted surgery. For example, aligning into one common coordinate frame a prerequisite for statistical shape modelling (SSM). In this paper, we first formally formulate the generalized cloud registration probabilistic manner. Not only positional but also orientational information utilized registration. All observed to be registered are considered realizations underlyinng unknown hybrid mixture models (HMMs). By (i) utilizing more enriched information, i.e. or normal vectors (ii) treating all equally, our algorithm robust outliers does not bias towards any set. Assuming that data co-independent, probability density function (PDF) multiplication Gaussian Fisher distributions. Notably, error vector assumed obey multivariate distribution accommodate anisotropic noise. Expectation maxmization (EM) framework jointly estimate parameters. E-step, posteriors between points underlying model components computed. M-step, constrained optimization rigid transformation matrix re-formulated as unconstrained using Rodrigues Formula rotation matrix. Extensive experiments conducted on CT femur bone compare proposed with state-of-the-art methods. The experimental results demonstrate algorithm's better accuracy, robustness noise outliers, faster convergence speed.