Machine vision
Discrete analytical hyperplanes
Graphical Models and Image Processing
Multigrid Convergence of Calculated Features in Image Analysis
Journal of Mathematical Imaging and Vision
Computer and Robot Vision
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Planar Segment Based Polyhedrization for Surface Area Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Minimum-Length Polygons in Approximation Sausages
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Minimum-Length Polygons in Simple Cube-Curves
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Digital Straight Line Segments
IEEE Transactions on Computers
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
Surface volume estimation of digitized hyperplanes using weighted local configurations
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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Jordan, Peano and others introduced digitizations of sets in the plane and in the 3D space for the purpose of feature measurements. Features measured for digitized sets, such as perimeter, contents etc., should converge (for increasing grid resolution) towards the corresponding features of the given sets before digitization. This type of multigrid convergence is one option for performance evaluation of feature measurement in image analysis with respect to correctness.The paper reviews work in multigrid convergence in the context of digital image analysis. In 2D, problems of area estimations and lower-order moment estimations do have "classical" solutions (Gauss, Dirichlet, Landau et al.). Estimates of moments of arbitrary order are converging with speed 驴(r) = r-15/11. The linearity of convergence is known for three techniques for curve length estimation based on regular grids and polygonal approximations. Piecewise Lagrange interpolants of sampled curves allow faster convergence speed. A first algorithmic solution for convergent length estimation for digital curves in 3D has been suggested quite recently. In 3D, for problems of volume estimations and lower-order moment estimations solutions have been known for about one-hundred years (Minkowski, Scherrer et al.). But the problem of multigrid surface contents measurement is still a challenge, and there is recent progress in this field.