Beyond the Hausdorff Metric in Digital Topology
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or topological property. Such measures may be combined with the Hausdorff metric to yield a metric in which close images are similar with respect to multiple properties.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Is magnitude 'generically continuous' for finite metric spaces?
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies. Motivated by applications …
Topological Data AnalysisA polynomial-time relaxation of the Gromov-Hausdorff distance
The Gromov-Hausdorff distance provides a metric on the set of isometry classes of compact metric spaces. Unfortunately, computing this metric directly is believed to be computationally intractable. Motivated by applicati…
How rare are the properties of binary relations?
Knoblauch (2014) and Knoblauch (2015) investigate the relative size of the collection of binary relations with desirable features as compared to the set of all binary relations using symmetric difference metric (Cantor) …
$K-$means with learned metrics
We study the Fréchet $k-$means of a metric measure space when both the measure and the distance are unknown and have to be estimated. We prove a general result that states that the $k-$means are continuous with respect t…
Metric LearningSubdivAR: Autoregressive Next-Scale Prediction for Neural Mesh Subdivision
Mesh subdivision is a fundamental operation for converting coarse, editable meshes into high-resolution surfaces, with broad applications in digital asset creation. Classical rule-based schemes rely on fixed local refine…