Why eigenvalues concerned in Harris corner detection?

1. What do eigenvalues signify in the solutions?
2. How can eigenvalue determine if a point in an image is corner?
3. What makes the Harris corner detector effective?
4. What do the eigenvalues of a matrix tell us?

What do eigenvalues signify in the solutions?

Eigenvalues are associated with eigenvectors in Linear algebra. Both terms are used in the analysis of linear transformations. Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations.

How can eigenvalue determine if a point in an image is corner?

Corner Detector using eigen values

If both values are small so we in a flat region and no variation in any direction. If one of eigen values larger than the other So we have an edge point. And if both eigen values are large so we have a corner.

What makes the Harris corner detector effective?

Compared to the previous one, Harris' corner detector takes the differential of the corner score into account with reference to direction directly, instead of using shifting patches for every 45 degree angles, and has been proved to be more accurate in distinguishing between edges and corners.

What do the eigenvalues of a matrix tell us?

Eigenvalues represent magnitude, or importance. Bigger Eigenvalues correlate with more important directions.