Proper velocity the traveling object. It equals the object's momentum p divided by its rest mass "m", and is made up of the space-like components of the object's four-vector velocity. William Shurcliff's monograph mentioned its early use in the Sears and Brehme text. Fraundorf has explored its pedagogical value while Ungar, Baylis and Hestenes have examined its relevance from group theory and geometric algebra perspectives. Proper velocity is sometimes referred to as celerity. Unlike the more familiar coordinate velocity v, proper velocity is synchrony-free (does not require synchronized clocks) and is useful for describing both super-relativistic and sub-relativistic motion. Like coordinate velocity
Velocity Moments image, formula_4 is the intensity of the pixel at the point formula_5 in the image, and formula_6 is the basis function. Cartesian velocity moments are based on these Cartesian moments. A Cartesian velocity moment formula_7 is defined by where formula_2 and formula_3 are again the dimensions of the image, formula_11 is the number of images in the sequence, and formula_12 is the intensity of the pixel at the point formula_5 in image formula_14. formula_15 is taken from Central moments, added so the equation is translation invariant, defined as where formula_17 is the formula_18 coordinate of the centre of mass for