Error bounds for morphologically derived measurements
SIAM Journal on Applied Mathematics
Length estimators for digitized contours
Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
CVGIP: Image Understanding
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This paper presents a comprehensive theory of discretization of images, image operators, and image functionals in mathematical morphology. The procedure of image discretization discussed here consists of two steps: (i) the definition of a sequence of discrete images obtained by sampling the original continuous image on grids with finer and finer mesh width, and (ii) the representation of the discrete images as continuous images. The hit-or-miss topology on the space of closed Euclidean sets is used to show that the thus obtained discretized images approach the original continuous image if the mesh width tends to zero. The image discretization procedure is then used to obtain discretizations of image operators and functionals. Particular attention is given to discretizations with nice monotonicity properties, the so-called constricting discretizations.