On Bipolar Coordinates and Their Application to Geometric Pattern Recognition Problems

Key Points

• The aim is to explore a coordinate system for geometric pattern recognition by modeling binocular vision.
• Introduced a coordinate system based on bipolar coordinates.
• Developed concepts around flat observable curves.
• Described observable curves through a specific criterion.
• Proved precompactness with respect to the Hausdorff metric.
• Established existence of a finite epsilon-net in the set of observable curves.
• Demonstrated a novel approach to pattern recognition using binocular vision.
• Established theoretical foundations that ensure the compactness of observable curves.
• Proved the existence of a structure (epsilon-net) that aids in recognizing patterns efficiently.