Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing

Author

Ta, Vinh-Thong ; Elmoataz, Abderrahim ; Lézoray, Olivier

Author_Institution

LaBRI, Univ. de Bordeaux, Talence, France

Volume

20

Issue

6

fYear

2011

fDate

6/1/2011 12:00:00 AM

Firstpage

1504

Lastpage

1516

Abstract

Mathematical morphology (MM) offers a wide range of operators to address various image processing problems. These operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). In this paper, we introduce a nonlocal PDEs-based morphological framework defined on weighted graphs. We present and analyze a set of operators that leads to a family of discretized morphological PDEs on weighted graphs. Our formulation introduces nonlocal patch-based configurations for image processing and extends PDEs-based approach to the processing of arbitrary data such as nonuniform high dimensional data. Finally, we show the potentialities of our methodology in order to process, segment and classify images and arbitrary data.

Keywords

algebra; data handling; graph theory; image processing; mathematical morphology; partial differential equations; set theory; algebraic set; data processing; discrete sets; image processing; mathematical morphology; nonlocal PDE-based morphology; nonlocal patch-based configuration; nonuniform high dimensional data; partial differential equation; weighted graph; Data processing; Equations; Image segmentation; Mathematical model; Morphology; Partial differential equations; Adaptive operators; data clustering; mathematical morphology; nonlocal patch-based processing; partial differential equations (PDEs); weighted graphs; Algorithms; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Models, Theoretical; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/TIP.2010.2101610

Filename

5676212