Convexity invariance of voxel objects under rigid motions

Volume data can be represented by voxels. In many applications of computer graphics (e.g. animation, simulation) and image processing (e.g. shape registration), such voxel data require manipulations. Among the simplest manipulations, we are interested in rigid motions, namely motions that do not change the shape of voxel objects but do change their position and orientation. Such motions are well-known as isometric transformations in continuous spaces. However, when they are applied on voxel data, some important properties of geometry and topology are generally lost. In this article, we discuss this issue, and we provide a method for rigid motions of voxel objects that preserves the global convexity properties of objects, with digital topology guarantees. This method is based on the standard notion of H-convexity, and a new notion of quasi-regularity.