Geodesic
A Geometric Bijection for $xy$-Convex Curves and Convex Polyominoes
Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 866-876.

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A connected subset of ${\mathbb R}^2$ consisting of unit squares with integral vertices is called a convex polyomino or is simply said to be $xy$-convex if it intersects any horizontal or vertical line exactly in one closed interval. In this paper, a geometric representation for xy-convex sets is described, allowing us to obtain, by elementary combinatorial methods, known formulas for the number of convex polyominoes contained in a rectangle of given size. 
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     title = {A {Geometric} {Bijection} for $xy${-Convex} {Curves} and {Convex} {Polyominoes}},
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A. A. Panov. A Geometric Bijection for $xy$-Convex Curves and Convex Polyominoes. Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 866-876. http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a6/

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