Hierarchical Segmentations with Graphs: Quasi-flat Zones, Minimum Spanning Trees, and Saliency Maps

作     者：Cousty, Jean Najman, Laurent Kenmochi, Yukiko Guimaraes, Silvio 

作者机构：Univ Paris Est CNRS Lab Informat Gaspard Monge ESIEE ParisA3SI Marne La Vallee France PUC Minas ICEI DCC VIPLAB Belo Horizonte MG Brazil 

出 版 物：《JOURNAL OF MATHEMATICAL IMAGING AND VISION》 (数学成像与显示杂志)

年 卷 期：2018年第60卷第4期

页      面：479-502页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：French Agence Nationale de la Recherche [ANR-2010-BLAN-0205-03] French Committee for the Evaluation of Academic and Scientific Cooperation with Brazil Brazilian Federal Agency of Support and Evaluation of Postgraduate Education (Program CAPES/PVE) [064965/2014-01] Brazilian Federal Agency of Support and Evaluation of Postgraduate Education (Program CAPES/COFECUB) [592/08] 

主　　题：Mathematical morphology Hierarchy of partitions Hierarchical image segmentation Watershed Saliency maps Minimum spanning trees Hierarchical classification 

摘      要：Hierarchies of partitions are generally represented by dendrograms (direct representation). They can also be represented by saliency maps or minimum spanning trees. In this article, we precisely study the links between these three representations. In particular, we provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as often used in image processing and we characterize saliency maps and minimum spanning trees as solutions to constrained minimization problems where the constraint is quasi-flat zones preservation. In practice, these results make up a toolkit for designing new hierarchical methods where one can choose the most convenient representation. They also invite us to process non-image data with morphological hierarchies. More precisely, we show the practical interest of the proposed framework for: (i) hierarchical watershed image segmentations, (ii) combinations of different hierarchical segmentations, (iii) hierarchicalizations of some non-hierarchical image segmentation methods based on regional dissimilarities, and (iv) hierarchical analysis of geographic data.