Shape reconstruction from partially missing data in modal space

Abstract

To reconstruct the shape of objects from incomplete point sets or noisy images, robust and accurate reconstruction methods are required. This paper presents a physics-based approach for automatically reconstructing three-dimensional shapes in a robust and proper manner from partially missing data. In modal space, an object's shape is described by modal deformations within each free vibration mode. In general, modes provide global-to-local ordering of shape deformation that allows us to select which types of deformations are to be used to reconstruct objects. By discarding high-frequency modes, the required computational time can be reduced without loss of accuracy. Moreover, the reconstructed shapes are relatively robust for partially missing data because of the stability of low-frequency modes. Unlike most existing approaches using a prototype with a priori fixed material properties, we calculate deformation modes directly from available data and allow the update of material properties to incorporate observations. As a result more improved shapes can be obtained. This new reconstruction algorithm is applied to point sets obtained from meshes and boundary contours in medical images. © 2002 Elsevier Science Ltd. All rights reserved.