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Constraining active contour evolution via lie groups of transformation.
Abdol-Reza Mansouri1, Dipti Prasad Mukherjee, Scott T Acton
1Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA. mansouri@deas.harvard.edu
Summary
This study introduces a new method for active contour evolution in image analysis. It ensures contours relate to their initial state via Lie group transformations, simplifying tracking and segmentation tasks.
Area of Science:
- Computer Vision
- Image Analysis
- Geometric Transformations
Background:
- Active contours are crucial for image analysis tasks like tracking and segmentation.
- Existing methods often require complex modifications to the energy functional or prior knowledge of transformations.
- Constraining contour evolution to specific geometric transformations is vital for many applications.
Purpose of the Study:
- To develop a novel approach for constraining active contour evolution.
- To ensure the evolved contour maintains a relationship with the initial contour through Lie group transformations.
- To provide a straightforward and effective method for image analysis applications.
Main Methods:
- The approach modifies Euler-Lagrange descent equations using Lie group and Lie algebra properties.
- It ensures curve evolution stays within an orbit of the chosen transformation group.
- The method preserves the original curve functional without modification.
Main Results:
- Demonstrated a novel method for constraining active contour evolution.
- Successfully related evolved contours to initial contours via Lie group transformations.
- Validated the approach on diverse real and synthetic image datasets.
Conclusions:
- The proposed method offers a simplified and effective way to constrain active contour evolution.
- It is highly advantageous for tracking and segmentation applications involving geometric transformations.
- The approach avoids complex modifications to existing functionals, enhancing implementation ease.