The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding a minimum medial axis is an NP-hard problem for the Euclidean distance. Then, we compare two algorithms which compute an approximation of the minimum medial axis, one of them providing bounded approximation results.
We denote by M n R the test neighbourhood sufficient to extract the Euclidean Medial Axis of any n-dimensional discrete shape whose inner radius is no greater than R. In this paper, we study properties of discrete Euclidean disks overlappings so as to prove that in any given dimension n, M n R tends to the set of visible vectors as R tends to infinity.
Abstract. The test mask TM is the minimum neighbourhood sufficient to extract the medial axis of any discrete shape, for a given chamfer distance mask M. We propose an arithmetical framework to study TM in the case of chamfer norms. We characterize TM for 3×3 and 5×5 chamfer norm masks, and we give an algorithm to compute the appearance radius of the vector (2, 1) in TM.
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