Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds

Partial difference equations (PDEs) and variational methods for image processing on Euclidean domains spaces are very well established because they permit to solve a large range of real computer vision problems. With the recent advent of many 3D sensors, there is a growing interest in transposing an...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 23; no. 9; pp. 3896 - 3909
Main Authors: Lozes, Francois, Elmoataz, Abderrahim, Lezoray, Olivier
Format: Journal Article
Language:English
Published: United States IEEE 01.09.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Computer Science
Equations
Image Processing
Manifolds
Morphology
Surface morphology
Surface treatment
Three-dimensional displays
denoising
inpainting
3D point clouds
patches on point clouds
non-local processing
mathematical morphology
segmentation
PDEs on graphs
graph signal processing
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary:Partial difference equations (PDEs) and variational methods for image processing on Euclidean domains spaces are very well established because they permit to solve a large range of real computer vision problems. With the recent advent of many 3D sensors, there is a growing interest in transposing and solving PDEs on surfaces and point clouds. In this paper, we propose a simple method to solve such PDEs using the framework of PDEs on graphs. This latter approach enables us to transcribe, for surfaces and point clouds, many models and algorithms designed for image processing. To illustrate our proposal, three problems are considered: 1) \(p\) -Laplacian restoration and inpainting; 2) PDEs mathematical morphology; and 3) active contours segmentation.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2014.2336548