In the field of computer vision, velocity moments are weighted averages of the intensities of pixels in a sequence of images, similar to image moments but in addition to describing an object's shape also describe its motion through the sequence of images.
Velocity moments can be used to aid automated identification of a shape in an image when information about the motion is significant in its description.
There are currently two established versions of velocity moments: Cartesian[1] and Zernike.
[2] A Cartesian moment of a single image is calculated by where
A Cartesian velocity moment
is the number of images in the sequence, and
is the intensity of the pixel at the point
is taken from Central moments, added so the equation is translation invariant, defined as where
coordinate of the centre of mass for image
introduces velocity into the equation as where
coordinate of the centre of mass for the previous image,
After the Cartesian velocity moment is calculated, it can be normalised by where
is the average area of the object, in pixels, and
Now the value is not affected by the number of images in the sequence or the size of the object.
These velocity moments do however provide translation and scale invariance (unless the scale changes within the sequence of images).
A Zernike moment of a single image is calculated by where
denotes the complex conjugate,
For calculating Zernike moments, the image, or section of the image which is of interest is mapped to the unit disc, then
is the intensity of the pixel at the point
are the polar coordinates of the point
on the unit disc map.
A Zernike velocity moment
is again the number of images in the sequence, and
is the intensity of the pixel at the point
on the unit disc mapped from image
is from the Zernike moments equation above.
Like the Cartesian velocity moments, Zernike velocity moments can be normalised by where
is the average area of the object, in pixels, and
As Zernike velocity moments are based on the orthogonal Zernike moments, they produce less correlated and more compact descriptions than Cartesian velocity moments.
Zernike velocity moments also provide translation and scale invariance (even when the scale changes within the sequence).