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A Transportation L Distance for Signal Analysis
Matthew Thorpe1, Serim Park1, Soheil Kolouri2
1Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Journal of Mathematical Imaging and Vision
|September 21, 2018
Summary
A new transport-based distance, the TL distance, is introduced for signal and image analysis. It overcomes limitations of existing methods by handling non-positive, multi-channel signals and incorporating intensity, enabling broader applications.
Area of Science:
- Signal Processing
- Image Analysis
- Computational Geometry
Background:
- Transport-based distances like Wasserstein and Earth Mover's Distance are effective in signal and image analysis due to their Lagrangian nature.
- Existing methods require signals to be non-negative, normalized, and treat them as measures, neglecting signal intensity.
Purpose of the Study:
- Introduce a novel transport-based distance, the TL distance.
- Develop a method applicable to general, non-positive, and multi-channel signals.
- Incorporate both Lagrangian properties and signal intensity for enhanced comparison.
Main Methods:
- The study introduces the TL distance, a novel transport-based metric.
- It combines Lagrangian modeling with signal intensity considerations.
- The distance is computable using existing numerical methods.
Main Results:
- The TL distance is directly applicable to general, non-positive, and multi-channel signals.
- Demonstrated applications in classification tasks for 1D signals and 2D images.
- Successfully applied to color transfer tasks.
Conclusions:
- The TL distance offers a versatile and robust approach to signal and image comparison.
- It extends the applicability of transport-based methods to a wider range of data types.
- The method shows promise for various applications in signal and image processing.
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