A tutorial on graph-based mathematical morphology
This half-day tutorial aims at disseminating graph-based ideas stemming from the mathematical morphology community to the interested public of ICPR attendees. It follows the line of the paper “A graph-based mathematical morphology reader” . Indeed, while the basics for mathematical morphology can be found in any textbook (mainly the dilation, erosion, opening and closing operators with a fixed structuring element, and the watershed), recent graph-based advances are not so well diffused, despite the fact that these powerful tools offered by the theory have proved to be very effective in practice. The aim of the present tutorial is to fill that gap.
Graphs have been the focus of important research for many years, and are now widely used in daily practice. A common framework for mathematical morphology on the one hand and other classical framework on the other (such as, for instance, energy-based optimization) helps to clarify the links and differences between them, as well as translating ideas from one of them to the other. We only mention here the power-watershed framework, generalizing graph based optimization methods, which makes it possible to optimize certain specific problems as a watershed cut. Understanding these links and differences is important both from a theoretical and practical perspective. Indeed, tackling the same problem from different points of view is always fruitful.
This tutorial is aimed at an audience consisting of practitioners and theoreticians. Practitioners will find here an up-to-date panel of graph-based morphological tools with examples and applications. Theoreticians will find ideas on how these tools are related to other computer vision and image analysis frameworks.
The outline of the tutorial is loosely the same as in the survey paper . The first part covers spatially-variant morphology, including the versatile path-openings and closings. The second part exposes the framework of tree-based morphological shape-space, with applications to filtering and segmentation. The two parts will be illustrated with many applications to bio-medical imaging, computer vision, document image analysis, analysis, material sciences, satellite imagery, astronomical images, and others.
 L. Najman and J. Cousty. A graph-based mathematical morphology reader. Pattern Recognition Letter. Vol. 47, pp. 3-17, October 2014. https://arxiv.org/pdf/1404.7748