Some Open Questions on Morphological Operators and Representations in the Deep Learning Era A Personal Vision

"Work on deep learning or perish": folklore wisdom in 2021. During recent years, the renaissance of neural networks as the major machine learning paradigm and more specifically, the confirmation that deep learning techniques provide state-of-the-art results for most of computer vision tasks has been shaking up traditional research in image processing. The same can be said for research in communities working on applied harmonic analysis, information geometry, variational methods, etc. For many researchers, this is viewed as an existential threat. On the one hand, research funding agencies privilege mainstream approaches especially when these are unquestionably suitable for solving real problems and for making progress on artificial intelligence. On the other hand, successful publishing of research in our communities is becoming almost exclusively based on a quantitative improvement of the accuracy of any benchmark task. As most of my colleagues sharing this research field, I am confronted with the dilemma of continuing to invest my time and intellectual effort on mathematical morphology as my driving force for research, or simply focussing on how to use deep learning and contributing to it. The solution is not obvious to any of us since our research is not fundamental, it is just oriented to solve challenging problems, which can be more or less theoretical. Certainly, it would be foolish for anyone to claim that deep learning is insignificant or to think that one's favourite image processing domain is productive enough to ignore the state-of-the-art. I fully understand that the labs and leading people in image processing communities have been shifting their research to almost exclusively focus on deep learning techniques. My own position is different: I do think there is room for progress on mathematically grounded image processing branches, under the condition that these are rethought in a broader sense from the deep learning paradigm. Indeed, I firmly believe that the convergence between mathematical morphology and the computation methods which gravitate around deep learning (fully connected networks, convolutional neural networks, residual neural networks, recurrent neural networks, etc.) is worthwhile. The goal of this talk is to discuss my personal vision regarding these potential interactions. Without any pretension of being exhaustive, I want to address it with a series of open questions, covering a wide range of specificities of morphological operators and representations, which could be tackled and revisited under the paradigm of deep learning. An expected benefit of such convergence between morphology and deep learning is a cross-fertilization of concepts and techniques between both fields. In addition, I think the future answer to some of these questions can provide some insight on understanding, interpreting and simplifying deep learning networks.