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 pro...