Region filing with the use of the discrete green theorem
Computer Vision, Graphics, and Image Processing
Polyominoes defined by two vectors
Theoretical Computer Science
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
New enumerative results on two-dimensional directed animals
Proceedings of the 7th conference on Formal power series and algebraic combinatorics
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Enumeration of polyominoes inscribed in a rectangle
Discrete Applied Mathematics
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The use of Green's theorem and bivariate difference calculus provides a general and unifying framework for the description and generation of incremental algorithms. The method is applied in order to provide algorithms computing various statistics about polyominoes coded by 4-letter words describing their contour. These statistics include area, coordinates of the center of gravity, moment of inertia, size of projections, hook lengths, number of pixels in common with a given set of pixels, in particular the intersection of two polyominoes and also q-statistics for projections.