H = VL_HARRIS(I,SI) computes the Harris corner strength of the image I at integration'' scale SI.

The Harris strength [1] of a pixel is a statistic of the gradient of the image integrated in a neighborhood of that pixel. This neighborhood is a Gaussian window of variance SI.

In computing the Harris corner strength, there is a second scale parameter, the derivation'' scale SD, which is the variance of the Gaussian kernel used to pre-smooth the image I before computing its gradient. SI and SD are independent parameters and VL_HARRIS(I,SI) assumes that I is already smoothed at level SD.

VL_HARRIS(I,SI) uses Noble's variation [2] of the Harris score. If SIGMAP and SIGMAM are respectively the biggest and smallest eigenvalue of the structure tensor at a pixel, the score is given by (SIGMAP*SIGMAM) / (SIGMAP+SIGMAM/2). Let GAMMA = SIGMAM/SIGMAP the ratio between the eigenvalues, which measures the degree of anisotropy of the tensor and is always comprised in the range [0,1]. Noble's score can be decomposed in two factors: the biggest eigenvalue SIGMAP and the number

  RHO = (2 GAMMA) / (GAMMA + 1).


RHO is another measure of isotropy that has value one for a symmetric tensor and and zero for maximally anisotropic tensor. [H,DETAILS] = VL_HARRIS(I,SIGMA) returns the additional structure DETAILS with the following fields:

  DETAILS.SIGMAP
DETAILS.RHO


VL_HARRIS(I,SI,ALPHA) uses Harris' original score [1], defined to be SIGMAP*SIGMAM - ALPHA*(SIGMAP+SIGMAM)^2. This can be decomposed in the factors SIGMAP^2 (note the square) and

  RHO = GAMMA - ALPHA (1+GAMMA)^2.


Note that RHO is equal to -ALPHA for a maximally anisotropic tensor. Typically ALPHA=0.04 and this is what is used by VL_HARRIS(I,SI,[]).

REMARK. The gradient of the image I, used to compute the structure tensor, is computed using central differencies. This means that a function line [+1,-1,+1,...] has null Harris' score. This is generally assumed to be a sampling artifact, and might be avoided by oversampling the image.

EXAMPLE

To extacts Harris points from image I:

  idx = vl_localmax( vl_harris( vl_imsmooth( I, sd ), si ) ) ;
[i,j] = ind2sub( size(I), idx )

REFERENCES

[1] C. Harris and M. Stephens, "A combined corner and edge detector," in Proceedings of The Fourth Alvey Vision Conference, pp. 147-151, 1988.

[2] J. A. Noble, "Finding corners, "Image Vision Computing, vol. 6, no. 2, pp. 121-128, 1988.