9 basis kernels for complete edge analysis
The Frei-Chen edge detection method uses 9 orthonormal basis kernels that form a complete basis for any 3×3 image patch. Unlike Sobel or Prewitt, Frei-Chen can decompose an image region into edge, line, and average components.
Kernels F1-F4: Detect edges at 0°, 90°, 45°, and 135° orientations
Kernels F5-F6: Detect lines (ridges) at 0° and 45°
Kernels F7-F8: Discrete Laplacian (spot detection)
Kernel F9: Average (constant component)
The edge energy is computed as the ratio of edge subspace energy to total energy, providing a normalized edge strength measure.