Segmentation in Measure Spaces

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS)...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics & optimization 2024-06, Vol.89 (3), p.66, Article 66
Main Authors: Moll, Salvador, Pallardó-Julià, Vicent, Solera, Marcos
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Euclidean space
Graphs
Image processing
Image segmentation
Labeling
Marking
Mathematical and Computational Physics
Mathematical functions
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Noise reduction
Numerical and Computational Physics
Optimization
Simulation
Systems Theory
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10134-5