When Convex Analysis Meets Mathematical Morphology on Graphs
International audience In recent years, variational methods, i.e., the formulation of problems under optimization forms, have had a great deal of success in image processing. This may be accounted for by their good performance and versatility. Conversely, mathematical morphology (MM) is a widely rec...
| Main Authors: | , , |
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| Other Authors: | , , , , , , |
| Format: | Conference Object |
| Language: | English |
| Published: |
HAL CCSD
2015
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| Subjects: | |
| Online Access: | https://hal.science/hal-01168801 https://hal.science/hal-01168801/document https://hal.science/hal-01168801/file/morphvar.pdf https://doi.org/10.1007/978-3-319-18720-4_40 |
| Summary: | International audience In recent years, variational methods, i.e., the formulation of problems under optimization forms, have had a great deal of success in image processing. This may be accounted for by their good performance and versatility. Conversely, mathematical morphology (MM) is a widely recognized methodology for solving a wide array of image processing-related tasks. It thus appears useful and timely to build bridges between these two fields. In this article, we propose a variational approach to implement the four basic, structuring element-based operators of MM: dilation, erosion, opening, and closing. We rely on discrete calculus and convex analysis for our formulation. We show that we are able to propose a variety of continuously varying operators in between the dual extremes, i.e., between erosions and dilation; and perhaps more interestingly between openings and closings. This paves the way to the use of morphological operators in a number of new applications. |
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