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A principled representation of elongated structures using heatmaps.
Florian Kordon1,2,3, Michael Stiglmayr4, Andreas Maier5,6
1Pattern Recognition Lab, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058, Erlangen, Germany. florian.kordon@fau.de.
Scientific Reports
|September 14, 2023
Summary
This study presents a novel mathematical method for detecting complex elongated structures in images, improving upon traditional techniques. The approach offers a versatile and efficient solution for various image analysis tasks with low error rates.
Area of Science:
- Computer Vision
- Image Analysis
- Computational Mathematics
Background:
- Detecting elongated structures is crucial for semantic image analysis.
- Classical methods struggle with context-dependent, amorphous, or non-visible structures.
- Limitations exist in gradient-based approaches for complex structures.
Purpose of the Study:
- To introduce a principled mathematical description for various elongated structures.
- To provide an operational description for target functions suitable for Convolutional Neural Networks (CNNs).
- To develop a computationally efficient method for representing curves and their uncertainties.
Main Methods:
- Developed a mathematical framework for describing elongated structures.
- Encoded nominal curve position and uncertainty into heatmaps via filter convolution.
- Proposed a low-error, linear-time approximation for numerical integration using a distance-dependent function.
Main Results:
- Achieved a lightweight implementation with linear time complexity.
- Analyzed numerical approximation errors across different curve types and signal-to-noise ratios.
- Demonstrated low error rates and versatility in applications.
Conclusions:
- The proposed method offers a versatile and efficient approach for detecting complex elongated structures.
- The technique is applicable to diverse tasks including surgical data analysis, boundary detection, and skeletonization.
- The mathematical description provides a robust foundation for CNN-based image analysis.
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