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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| Vydané v: | IEEE transactions on image processing Ročník 23; číslo 9; s. 3896 - 3909 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
IEEE
01.09.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
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| ISSN: | 1057-7149, 1941-0042, 1941-0042 |
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| Abstract | 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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| AbstractList | 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.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. 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. 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 Partial difference Equations (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: p-Laplacian restoration and inpainting, PDEs Mathematical Morphology, and active contours segmentation. |
| Author | Elmoataz, Abderrahim Lezoray, Olivier Lozes, Francois |
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| Keywords | denoising inpainting 3D point clouds patches on point clouds non-local processing mathematical morphology segmentation PDEs on graphs graph signal processing |
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| SubjectTerms | Computer Science Equations Image Processing Manifolds Morphology Surface morphology Surface treatment Three-dimensional displays |
| Title | Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds |
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