Abstract
The Euclidean test mask \(\mathcal{T}\)(r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between \(\mathcal{T}\)(r) and the well-known Farey sequences, which allows us to propose two new algorithms. The first one computes \(\mathcal{T}\)(r) in time \(\mathcal{O}(r^4)\) and space \(\mathcal{O}(r^2)\). The second one computes for any vector \(\overrightarrow{v}\) the smallest r for which \(\overrightarrow{v} \in\mathcal{T}\)(r), in time \(\mathcal{O}(r^3)\) and constant space.
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Hulin, J., Thiel, É. (2009). Farey Sequences and the Planar Euclidean Medial Axis Test Mask. In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_7
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DOI: https://doi.org/10.1007/978-3-642-10210-3_7
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