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
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Towards a general sampling theory for shape preservation
Image and Vision Computing
Shape preserving digitization of binary images after blurring
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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Connectivity and neighborhood are fundamental topological properties of objects in pictures. Since the input for any image analysis algorithm is a digital image, which does not need to have the same topological characteristics as the imaged real world, it is important to know, which shapes can be digitized without change of such topological properties. Most existing approaches do not take into account the unavoidable blurring in real image acquisition systems or use extremely simplified and thus unrealistic models of digitization with blurring. In some previous work we showed that certain shapes can be digitized topologically correctly with a square grid when some blurring with an arbitrary non-negative radially symmetric point spread function is involved. Now we extend this result to other common sampling grids in the two and even in the 3D space, including hexagonal, bcc and fcc grids.