Linearized multidimensional earth-mover's-distance gradient flows.

Area of Science:

• Computer Vision
• Image Processing
• Machine Learning

Background:

• Active contour models are widely used for image segmentation.
• Traditional methods often rely on bin-to-bin histogram comparisons, which can be limited.
• Earth Mover's Distance (EMD) offers a more sophisticated approach to comparing feature distributions.

Purpose of the Study:

• To present the first active contour segmentation framework using multidimensional Earth Mover's Distance (EMD).
• To leverage EMD for more meaningful comparisons between feature distributions in image segmentation.
• To demonstrate the advantages of cross-bin histogram comparisons over bin-to-bin measures.

Main Methods:

• Developed a novel framework for active contour segmentation.
• Employed Earth Mover's Distance (EMD) to measure dissimilarity between multidimensional feature distributions.
• Utilized linear programming and sensitivity analysis to derive Euler-Lagrange equations for gradient descent flows.

Main Results:

• The proposed EMD-based active contour segmentation framework was validated on color images.
• Outperformed state-of-the-art Bhattacharyya and 1D EMD active contours.
• Demonstrated superior perceptual value and increased robustness to initialization.

Conclusions:

• The EMD-based active contour framework provides a powerful new tool for image segmentation.
• Cross-bin histogram comparison via EMD offers significant advantages over traditional methods.
• The approach enhances segmentation quality and reliability, particularly in challenging scenarios.