TL;DR
This paper characterizes exactly which closed sets in Euclidean space can be reconstructed solely from their medial axis, expanding understanding of medial axis applications in pattern recognition.
Contribution
It provides a precise characterization of reconstructible sets from medial axis information without assuming extra structure.
Findings
Identifies conditions under which sets are reconstructible from medial axes
Expands the theoretical foundation of medial axis-based reconstruction
No additional assumptions needed beyond closedness in Euclidean space
Abstract
The medial axis of a closed set is well established tool in pattern recognition, cherished for its power of reconstruction of domains. In this article we fill this gap answering the question which sets precisely are reconstructible from the medial axis information. We do not assume any additional structure of considered sets besides them being closed in n-dimensional Euclidean space.
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