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Updated: Oct 12, 2025
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Euclidean Distance Approximations From Replacement Product Graphs
Summary
We introduce RE-grid graphs, a novel chamfering method that approximates Euclidean distance in images. These graphs maintain accurate distance contours in noisy data, proving useful for path-finding in low-resolution images.
Area of Science:
- Computer Vision
- Image Processing
- Computational Geometry
Background:
- Chamfering algorithms approximate Euclidean distance in digital images.
- Existing methods struggle with noisy data and complex image spaces.
- Need for robust approximation techniques when exact solutions are impractical.
Purpose of the Study:
- Introduce a new chamfering paradigm using RE-grid graphs.
- Demonstrate the effectiveness of RE-grid graphs for path-finding in challenging image spaces.
- Explore potential applications in various image processing tasks.
Main Methods:
- Developing a novel chamfering approach by creating internal pixel networks (RE-grid graphs).
- Building local pixel connections to approximate Euclidean space.
- Analyzing the resulting modular global architecture and its topological properties.
Main Results:
- RE-grid graphs maintain near-Euclidean polygonal distance contours, even with noisy data.
- The method offers a viable approximation for path-finding where exact solutions are difficult.
- Demonstrated utility in case studies for high-frequency, low-resolution image spaces.
Conclusions:
- RE-grid graphs present a promising advancement in chamfering techniques.
- The approach offers robustness in approximating Euclidean distances in digital images.
- Potential applications span morphology, segmentation, and neural network design, warranting further investigation.
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