Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper 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