Post-Doctoral Research Visit F/M Learning Variational Mathematical Morphological Operators for Computer Vision

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 39 project teams , 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

Project Summary The aim of this project is to bridge the gap between classical mathematical morphology and state of the art deep learning techniques for computer vision. Mathematical morphology is a widely used tool in image processing and computer vision because of its usefulness in manipulating geometric structures within an image or graph. However, its use in modern deep learning pipelines remains limited. While some work has been done in this direction, for instance with so-called MorphoLayers [5], we propose a different approach based on a variational formulation of morphological operators given in [4].

 Using this alternative formulation we will be able to differentiate mathematical morphological operators and learn their parameters using automatic differentiation and first-order optimization methods. This will enable learning variational mathematical morphological operators in a data-driven manner, e.g., through backpropagation, and also allow the use of variational mathematical morphological operators as implicit layers [1,3] in a neural network. Neural networks for image segmentation and classification will be explored as primary applications in this direction.

Objectives Propose and analyze learnable mathematical morphological operators using implicit differentiation techniques that are compatible with autodifferentiation combined with variational mathematical morphology.

Context The techniques outlined in the project topic are frequently used in medical image analysis, which constitutes a large part of the activity of the host laboratory (Inria OPIS team).

Methods The project topic builds on the expertise of the supervisory team in high-dimensional optimization methods, deep learning, and mathematical morphology. It is an extension of some of the work recently carried out in this team [4,2].

Expected Results New neural network architectures based on learnable variational mathematical morphological operators, software implementations in PyTorch/JAX.

Bibliography

[1] Shaojie Bai, J Zico Kolter, and Vladlen Koltun. Deep equilibrium models. Advances in neural information processing systems, 32, 2019.
[2] Jérôme Bolte, Tam Le, Edouard Pauwels, and Tony Silveti-Falls. Nonsmooth implicit differentiation for machine-learning and optimization. Advances in neural information processing systems, 34:13537–13549, 2021.
[3] Fangda Gu, Heng Chang, Wenwu Zhu, Somayeh Sojoudi, and Laurent El Ghaoui. Implicit graph neural networks. Advances in Neural Information Processing Systems, 33:11984–11995, 2020.
[4] Laurent Najman, Jean-Christophe Pesquet, and Hugues Talbot. When convex analysis meets mathematical morphology on graphs. In Mathematical Morphology and Its Applications to Signal and Image Processing: 12th International Symposium, ISMM 2015, Reykjavik, Iceland, May 27-29, 2015. Proceedings 12, pages 473–484. Springer, 2015.
[5] Santiago Velasco-Forero, Samy Blusseau, and Mateus Sangalli. Mathematical morphology meets deep learning. In 13th European Congress for Stereology and Image Analysis (ECSIA), 2024

The desired candidate should have experience with image processing, in particular image segmentation and classification, and first-order optimization methods. Experience and familiarity with vectorized Python programming, in particular with the common deep learning libraries (PyTorch, JAX, or TensorFlow), will be necessary. Fluency in English is also required.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

2788 € gross/month