# Two Nonlocal Variational Models for Retinex Image Decomposition

### Frank Hammond, Catalina Sbert, Joan Duran

#### 2024

#### Abstract

Retinex theory assumes that an image can be decomposed into illumination and reflectance components. In this work, we introduce two variational models to solve the ill-posed inverse problem of estimating illumination and reflectance from a given observation. Nonlocal regularization exploiting image self-similarities is used to estimate the reflectance, since it is assumed to contain fine details and texture. The difference between the proposed models comes from the selected prior for the illumination. Specifically, Tychonoff regularization, which promots smooth solutions, and the total variation, which favours piecewise constant solutions, are independently proposed. A comprehensive theoretical analysis of the resulting functionals is presented within appropriate functional spaces, complemented by an experimental validation for thorough examination.

Download#### Paper Citation

#### in Harvard Style

Hammond F., Sbert C. and Duran J. (2024). **Two Nonlocal Variational Models for Retinex Image Decomposition**. In *Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP*; ISBN 978-989-758-679-8, SciTePress, pages 551-558. DOI: 10.5220/0012396800003660

#### in Bibtex Style

@conference{visapp24,

author={Frank Hammond and Catalina Sbert and Joan Duran},

title={Two Nonlocal Variational Models for Retinex Image Decomposition},

booktitle={Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP},

year={2024},

pages={551-558},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012396800003660},

isbn={978-989-758-679-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP

TI - Two Nonlocal Variational Models for Retinex Image Decomposition

SN - 978-989-758-679-8

AU - Hammond F.

AU - Sbert C.

AU - Duran J.

PY - 2024

SP - 551

EP - 558

DO - 10.5220/0012396800003660

PB - SciTePress