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Maximum Inscribed Circle using Voronoi Diagram



A fast, subpixel accurate largest inner circle detection using Voronoi Diagrams

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A sample application and a function for solving the maximum inscribed circle problem.
Unlike my other submission "Maximum Inscribed Circle using Distance Transform" (at, this algorithm is subpixel accurate. It operates only on the polygon and not the image points. Therefore, if the polygon is given in sub-pixels, the result will be accurate.
I use an O(n log(n)) algorithm as follows:
- Construct the Voronoi Diagram of the polygon.
- For Voronoi nodes which are inside the polygon:
- Find the node with the maximum distance to edges in P. This node is the centre of the maximum inscribed circle.
 For more details on the problem itself please checkout my previous submission as mentioned above.
 To speed things up, replace "inpolygon" function by Bruno Lunog's faster implementation "2D polygon interior detection" :
 Copyright (c) 2011, Tolga Birdal <>


Fast Points In Polygon Test and Maximum Inscribed Circle Using Distance Transform inspired this file.

Required Products Image Processing Toolbox
MATLAB release MATLAB 7.9 (R2009b)
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Comments and Ratings (1)
18 Oct 2013 Kai Angermueller

This work very well for many shapes. But for a simple triangle or square it finds circles that are not entirely inside the shape

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