On-line construction of the convex hull of a simple polyline
Information Processing Letters
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
On piecewise linear approximation of planar Jordan curves
Journal of Computational and Applied Mathematics
Multigrid Convergence of Calculated Features in Image Analysis
Journal of Mathematical Imaging and Vision
Measuring Concavity on a Rectangular Mosaic
IEEE Transactions on Computers
Two linear-time algorithms for computing the minimum length polygon of a digital contour
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Recursive computation of minimum-length polygons
Computer Vision and Image Understanding
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The relative convex hull of a simple polygon A, contained in a second simple polygon B, is known to be the minimum perimeter polygon (MPP). Digital geometry studies a special case: A is the inner and B the outer polygon of a component in an image, and the MPP is called minimum length polygon (MLP). The MPP or MLP, or the relative convex hull, are uniquely defined. The paper recalls properties and algorithms related to the relative convex hull, and proposes a (recursive) algorithm for calculating the relative convex hull. The input may be simple polygons A and B in general, or inner and outer polygonal shapes in 2D digital imaging. The new algorithm is easy to understand, and is explained here for the general case. Let N be the number of vertices of A and B; the worst case time complexity is O(N2), but it runs for "typical" (as in image analysis) inputs in linear time.