So, I am reading a paper about ORB: An Efficient Alternative to SIFT or SURF and it happens to calculate the direction of corner from it center . According to Rosin the author of the paper;moments of a patch is given by


and the centroid is of the patch from the center is calculated using:


The direction of the patch is computed from

enter image description here

My question is what are these value of p and q and why is it out there?


2 Answers 2


p and q - order of the moments, it is the analogue of the mechanical moments (i.e. of force or inertia). Image moments are very basic properties of image, invariant to rotation, could be used as simple descriptor.


Moment of inertia Ix= I2 = mass *x_coordinate^2.

Image moment Ix2 = intensity * *x_coordinate^2.



  • $\begingroup$ What or who determines the values of p and q. $\endgroup$
    – motiur
    Mar 2, 2014 at 11:55
  • $\begingroup$ It depends on what you need. $\endgroup$
    – old-ufo
    Mar 2, 2014 at 15:54
  • $\begingroup$ And in example in your question, p and q = 0,1. $\endgroup$
    – old-ufo
    Mar 2, 2014 at 19:11

Because wo want to get the centroid of the image(a block/patch) by the intensity. m00:p = q = 0,sum the intensity matrix. m10:p =1,q = 0,sum of the x-direction. m01:p = 0,q = 1,sum of the y-direction. (m10/m00,m01/m00) is the centroid.

  • 1
    $\begingroup$ Forgive my poor English. $\endgroup$
    – LingJun
    Oct 19, 2019 at 2:31

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