Discrete representation of spatial objects in computer vision
Discrete representation of spatial objects in computer vision
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Discretization in Hausdorff Space
Journal of Mathematical Imaging and Vision
Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Topological Equivalence between a 3D Object and the Reconstruction of Its Digital Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological Repairing of 3D Digital Images
Journal of Mathematical Imaging and Vision
Digitization of non-regular shapes in arbitrary dimensions
Image and Vision Computing
A topological sampling theorem for Robust boundary reconstruction and image segmentation
Discrete Applied Mathematics
Connectivity preserving digitization of blurred binary images in 2D and 3D
Computers and Graphics
Provably correct edgel linking and subpixel boundary reconstruction
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Preserving geometric properties in reconstructing regions from internal and nearby points
Computational Geometry: Theory and Applications
Topologically correct image segmentation using alpha shapes
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Topology preserving digitization with FCC and BCC grids
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Computerized image analysis makes statements about the continuous world by looking at a discrete representation. Therefore, it is important to know precisely which information is preserved during digitization. We analyze this question in the context of shape recognition. Existing results in this area are based on very restricted models and thus not applicable to real imaging situations. We present generalizations in several directions: first, we introduce a new shape similarity measure that approximates human perception better. Second, we prove a geometric sampling theorem for arbitrary dimensional spaces. Third, we extend our sampling theorem to two-dimensional images that are subjected to blurring by a disk point spread function. Our findings are steps towards a general sampling theory for shapes that shall ultimately describe the behavior of real optical systems.