Morphological PDEs on graphs for analyzing unorganized data in 3D and higher

Mathematical morphology operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). In our previous works [1, 2], we have proposed a simple method to solve PDEs (Partial Differential Equations) on dataset using the framework PdEs (Partial difference Equations) on graphs. In this paper, we propose to apply morphological-based operators on unorganized dataset.

[1]  Jean-Michel Morel,et al.  Image Denoising Methods. A New Nonlocal Principle , 2010, SIAM Rev..

[2]  Abderrahim Elmoataz,et al.  Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing , 2009, International Journal of Computer Vision.

[3]  Abderrahim Elmoataz,et al.  Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing , 2011, IEEE Transactions on Image Processing.

[4]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[5]  Abderrahim Elmoataz,et al.  Non-Local Morphological PDEs and $p$-Laplacian Equation on Graphs With Applications in Image Processing and Machine Learning , 2012, IEEE Journal of Selected Topics in Signal Processing.

[6]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[7]  Abderrahim Elmoataz,et al.  Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing , 2008, IEEE Transactions on Image Processing.

[8]  A. Elmoataz,et al.  Author Manuscript, Published in "international Workshop on Local and Non-local Approximation in Image Processing, Suisse Unifying Local and Nonlocal Processing with Partial Difference Operators on Weighted Graphs , 2022 .

[9]  Abderrahim Elmoataz,et al.  Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds , 2014, IEEE Transactions on Image Processing.

[10]  Abderrahim Elmoataz,et al.  Eikonal Equation Adaptation on Weighted Graphs: Fast Geometric Diffusion Process for Local and Non-local Image and Data Processing , 2012, Journal of Mathematical Imaging and Vision.