Surface Estimation for Multiple Misaligned Point Sets

Abstract

Two common tasks when processing point cloud data sets are surface estimation and point cloud registration. In this paper, a statistical approach is developed to solve both of these problems simultaneously. In particular, a surface is estimated from a pair of unregistered three-dimensional scans of the same spatial region. In this method, one point cloud defines the fixed coordinate system, and a rigid transformation is applied to the second cloud. Observations from both scans are considered a single realization of a Gaussian process. The registration problem is solved by jointly optimizing the likelihood over the parameters specifying the domain transformation and the mean and covariance functions. Given parameter estimates, surface estimation follows using the spatial stochastic model. While other existent approaches do not account for registration uncertainty, the likelihood-based approach to solving the registration and surface estimation problems jointly allows uncertainty in registration to be propagated to the surface prediction variance. The new method is motivated and illustrated using a digital elevation model estimation problem near the Chalk Cliffs in Colorado. The method developed is compared against the popular iterative closest point method. The results of a simulation study show significant improvement in transformation parameter estimates using the statistical approach. In a cross-validation experiment with the Chalk Cliffs data, there is an $$18\%$$ reduction in predictive mean squared error using the likelihood method over iterative closest point.