Shape reconstruction, a process to compute non-discrete mathematical shape description from discrete points, has been widely used in a variety of applications such as reverse engineering, quality inspection, and topography modeling. However, current shape reconstruction approaches, often based on deterministic techniques, face two fundamental challenges: 1) in noise handling, i.e. how to properly handle the data noise variance and outliers in order to reconstruct a robust surface; 2) in model selection, i.e. how to automatically select a surface model adapting to data cloud and to local shape change in order to avoid under-fit and over-fit. This paper aims to address these two issues by developing a novel stochastic surface reconstruction approach: multilevel Kalman filter. The core idea of this approach is to use a state-space model to relate data noise with the surface model, to adopt a multilevel surface representation to address the under-fit and over-fit issue, and to use Kalman filter to produce the optimal estimates and surface uncertainty. Experimental results from the prototype implementation demonstrate that multilevel Kalman filter produces better quality surface than the traditional least-squares method and is robust against noisy data, adapts well to shape changes in complex parts, and can handle incomplete data.

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