Haralick Corner Detector

 

Since the application of the Moravec interest operator in 1979 [Moravec79], a lot of research has been done in corner and interest point detection [Kitchen82, Harris88, Deriche90, Mehrotra90, Schmid98, Smith98]. A popular corner detector is the one presented in [Haralick93]. This corner detector first selects windows of interest and afterwards computes more precisely the position of the points inside the selected windows of interest.

 

Different steps leading to the windows of interest detection are

The weight w is also known as the “Beaudet measure for cornerness” and is proportional to the variation of gradient inside the window. It is high in windows where the gradient variation is important (potential points of interest).

where,l1 l2 are the eigenvalues of the normal matrix N,

q represents the circularity of the ellipse associated to the normal matrix N. This value is proportional to the ratio minor axis/major axis of the ellipse; it is high if the two axis have the same size (1 if there are equal) and less in other cases.

The circularity is used to reject points located on edges. In this situation, the ellipse has an important major axis in the direction of the edge and q is less than one.

The thresholding is done using the following rule:

 

Parameters necessary for window of interest detection:

 

Extraction of interesting point inside the windows of interest:

Once the windows of interested are detected, the point of interest is determined as the weighted centre of gravity of all points inside the window with the product of row and column gradient as weight.

The co-ordinates (x,y) of the corner inside the window of interest are then given by:

 

Results:

In Figure 1, we present the results of the corner detector in two images. The image (a) is a reflectance image acquired by a Riegl LMS-Z210 Laser scanner. Image (b) was acquired with a Canon PowerShot Pro 70 Digital Camera. In this example, corners are used to locate matching points over the image and proceed with a Tsai Camera Calibration.

Figure 1: Results of the corner detector in a reflectance image (a) and a digital photograph (b).

 

References:

[Deriche90] R. Deriche, G. Giraudon,
Accurate corner detection: An analytical study.
In Proc. 3rd Int. Conf. on Computer Vision, pp 66-70, 1990.
[Haralick93] R.M. Haralick, L.G. Shapiro,
Computer and Robot Vision.
Addison-Wesley,1992 and 1993.
[Harris88] C.G. Harris, M. Stephens,
A combined corner and edge detector.
In 4th Alvey Vision Conference, pp 147-151, 1988.
[Kitchen82] L. Kitchen, A. Rosenfeld,
Gray level corner detection.
Pattern recognition letters, 1, pp. 95-102, 1982
[Mehrotra90] R. Mehrotra, S. Nichani, N. Ranganathan,
Corner Detection.
Pattern Recognition, Vol. 23, No. 11, pp 1223-1233,1990
[Moravec79] H. P. Moravec,
Visual Mapping by a Robot Rover.
International Joint Conference on Artificial Intelligence, pp. 598-600, 1979.
[Schmid98] C. Schmid, R. Mohr, C. Bauckhage,
Comparing and evaluating interesting points.
International Conference on Computer Vision, pp 230-235, 1998.
[Smith98] P. Smith, D. Sinclair, R, Cipolla, K. Wood,
Effective Corner Matching.
British Machine Vision Conference, 1998

Author: Paulo Dias at IEETA/Universidade de Aveiro, Portugal - 05/11/2003