International audience

International audience

Quasi-regularity has been proved to be a sufficient condition for simple-connectedness preservation during the digitization process of 2D continuous objects. The original definition of quasi-regularity relies on set-based morphological operations of erosion and dilation. With this definition, quasi-regularity is algorithmically difficult to assess. In this paper, we propose a tractable framework for quasi-regularity verification, especially designed for polygons. Our approach mainly relies on the computation and analysis of the medial axis of these objects, and determines their potential quasi-regularity, and thus their ability to undergo a digitization without alteration of their topological properties. The framework is applied in the context of topology-preserving rigid motions of digital objects.

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.

We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.

We study the conditions under which the topological properties of a 2D well-composed binary image are preserved under arbitrary rigid transformations. This work initiates a more global study of digital image topological properties under such transformations, which is a crucial but under-considered problem in the context of image processing, e.g., for image registration and warping.