The Harris matrix is the 
structure tensor used in image corner detection.
For a real-valued image 
,
let 
and 
be its partial derivatives
and let 
be nonnegative weights on a neighborhood 
. The Harris matrix is
![M=sum_((x,y) in W)w(x,y)[I_x^2 I_xI_y; I_xI_y I_y^2].](/images/equations/HarrisMatrix/NumberedEquation1.svg) |
It is a real symmetric matrix and a positive semidefinite matrix, since it is a nonnegatively weighted sum of outer products of gradient vectors.
Its two eigenvalues measure intensity variation in two perpendicular directions. Two large eigenvalues indicate a corner, one large and one small eigenvalue indicate an edge, and two small eigenvalues indicate a nearly uniform region. Harris and Stephens (1988) use the response
![R=det(M)-k[Tr(M)]^2,](/images/equations/HarrisMatrix/NumberedEquation2.svg) |
where 
is a parameter, 
is the determinant, and 
is the matrix trace.
