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

Sravan Danda (1) , Aditya Challa (1) , B S Daya Sagar (1) , Laurent Najman (2)

1 Systems Science and Informatics Unit
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 [1], 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 [11] [15], 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.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Apprentissage [cs.LG]; Traitement des images [eess.IV]

Sravan Danda, Aditya Challa, B S Daya Sagar, Laurent Najman. Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters. 2017. ⟨hal-01430538v1⟩