Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
CVGIP: Image Understanding
Digital connectivity and extended well-composed sets for gray images
Computer Vision and Image Understanding
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
Geometry of Digital Spaces
Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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The expressiveness of a lot of image analysis algorithms depends on the question whether shape information is preserved during digitization. Most existing approaches to answer this are restricted to binary images and only consider nearest neighbor reconstruction. This paper generalizes this to grayscale images and to several reconstruction methods. It is shown that a certain class of images can be sampled with regular and even irregular grids and reconstructed with different interpolation methods without any change in the topology of the level sets of interest.