Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters
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 \(\varGamma -\)limit of the shortest path filters. We also propose a different approximation for the \(\varGamma -\)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.
Sravan Danda and Aditya Challa are thankful for the financial support provided by the Indian Statistical Institute. B.S. Daya Sagar would like to acknowledge the partial support received from EMR/2015/000853 SERB and ISRO/SSPO/Ch-1/2016-17 ISRO research grants. Laurent Najman would like acknowledge the partial support received from ANR-15-CE40-0006 CoMeDiC and ANR-14-CE27-0001 GRAPHSIP research grants.
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