Harris Corner Detection

The structure tensor (or auto-correlation matrix) M is a 2×2 matrix that captures the directional properties of image gradients in a small neighborhood. Its eigenvalues reveal the magnitude of intensity change in the principal directions: if both eigenvalues are large, the neighborhood contains a corner; if one is large and one small, it's an edge; if both are small, it's a flat region. Harris uses the eigenvalues to compute a corner response score.

Gaussian smoothing reduces noise and creates a more stable structure tensor by averaging gradients over a region. Without smoothing, small random intensity fluctuations produce misleading gradient patterns and spurious corner detections. The smoothing scale (sigma parameter) controls how large a neighborhood influences the corner response.

FAST (Features from Accelerated Segment Test) is much faster than Harris because it uses a simple rule—checking if pixels in a circle around a candidate point are significantly brighter or darker—rather than computing eigenvalues. Harris is more theoretically principled and produces more stable corners, but FAST is preferred in real-time systems. ORB combines FAST detection with a descriptor for practical use.

Yes, by applying Harris detection at multiple image scales (a scale-space pyramid) and selecting corners that appear consistently across scales. However, this multi-scale extension is computationally expensive. SIFT essentially incorporates scale-space Harris-like detection into a more comprehensive framework with additional robustness properties.