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Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters

Abstract : Edge-preserving image filtering is an important pre-processing step in many filtering applications. In this article, we analyse the basis of edge-preserving filters and also provide theoretical links between the MST filter, which is a recent state-of-art edge-preserving filter, and filters based on geodesics. We define shortest path filters, which are closely related to adaptive kernel based filters, and show that MST filter is an approximation to the Γ −limit of the shortest path filters. We also propose a different approximation for the Γ −limit that is based on union of all MSTs and show that it yields better results than that of MST approximation by reducing the leaks across object boundaries. We demonstrate the effectiveness of the proposed filter in edge-preserving smoothing by comparing it with the tree filter.
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https://hal.archives-ouvertes.fr/hal-01430538
Contributor : Sravan Danda <>
Submitted on : Wednesday, March 15, 2017 - 2:40:31 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:07 PM
Document(s) archivé(s) le : Friday, June 16, 2017 - 2:01:46 PM

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Sravan Danda, Aditya Challa, B Daya Sagar, Laurent Najman. Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters. Mathematical Morphology and Its Applications to Signal and Image Processing, May 2017, Fontainebleau, France. pp.199-210, ⟨10.1007/978-3-319-57240-6_16⟩. ⟨hal-01430538v3⟩

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