TU Berlin

Image Filtering with Mathematical Morphology Operators

May 2020


Mathematical Morphology is a well established framework for image filtering. Fundamental mathematical morphology operators, such as Erosion and Dilation (and their combinations: opening and closing) examine the geometrical structures in the image by matching them to small patterns, called Structuring Elements.

📸Remote Sensing Image Enhancement

  • Very high spatial resolution remote sensing images contain large amount of details
  • Sub-metric spatial resolution allows for accurate analysis of objects with different scales and shapes

📗Introduction to Mathematical Morphology

  • Originates from the study of the geometry of porous media in the mid-sixties in France
  • Theoretical model based on lattice theory, used for digital image processing

🦯Filtering with Morphology Operators

  • Image filtering with neighborhood operators that probe images with structuring elements
  • Use for noise reduction, edge enhancement and extraction/suppression of structures

📐Basic Morphological Operators

  • Dilation, and Erosion are the two most basic operations in mathematical morphology
  • Opening and Closing can be defined as their combinations along with set operators

🌌Geodesic Transformation

  • Morphological reconstruction is based on iteration of geodesic erosion and dilation operations
  • They are connected operators which either complete remove or entirely preserve connected components

⚙️Morphological Profiles

  • Multi-scale decomposition of an image into a stack of filtered images
  • Sequence of opening and closing by reconstruction filters


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