Fundamentals of surface voxelization
Graphical Models and Image Processing
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
An approach to discretization based on the Hausdorff metric
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Hausdorff Discretizations of Algebraic Sets and Diophantine Sets
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Object Discretization in Higher Dimensions
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Defining Discrete Objects for Polygonalization: The Standard Model
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
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We study the problem of discretization in a Hausdorff space followed in [WTR 98]. We recall the definitions and properties of the Hausdorff discretization of a compact set. We also study the relationship between the covering discretizations and the Hausdorff discretization. For a cellular metric every covering discretization minimizes the Hausdorff distance, and conversely, if the supercover discretization minimizes the Hausdorff distance then the metric is cellular. The supercover discretization is the Hausdorff discretization i? the metric is proportional to d1. We compare also the Hausdorff discretization and the Bresenham discretization [Bres 65]. Actually, the Bresenham discretization of a segment of IR2 is not always a good discretization relatively to a Hausdorff metric.