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Morse operators for digital planar surfaces and their application to image segmentation.
Luis Gustavo Nonato1, Antônio Castelo Filho, Rosane Minghim
1Departamento de Ciências da Computação e Estatística, ICMC, Universidade de São Paulo, São Carlos, Brazil.
Summary
This study introduces Morse operators for digital planar surfaces, enabling controlled surface construction and deconstruction. A novel, fast image segmentation algorithm using these operators offers superior topological control for object description.
Area of Science:
- Computer Vision
- Computational Geometry
- Image Processing
Background:
- Digital planar surfaces lack robust topological control during construction and deconstruction.
- Existing image segmentation methods may not provide sufficient object description or topological guarantees.
Purpose of the Study:
- Introduce Morse operators for digital planar surfaces.
- Develop a fast image segmentation algorithm with topological control.
- Provide a tool for pixel characterization and object description.
Main Methods:
- Definition of digital planar surfaces and Morse operators.
- Development of a novel region growing segmentation algorithm utilizing Morse operators.
- Application of the algorithm to real image data for evaluation.
Main Results:
- Morse operators provide global topological control during surface manipulation.
- The proposed segmentation algorithm is fast and effective.
- The algorithm demonstrates competitive performance compared to existing methods.
- The topological approach facilitates future expansion to volume segmentation.
Conclusions:
- Morse operators offer a powerful framework for digital surface manipulation.
- The developed image segmentation algorithm enhances object description through topological control.
- This work lays the foundation for advanced applications in image and volume segmentation.