A Mathematical Walkthrough of Weighted Central Moments and Its Relation to Geometric Moment

Moment invariants are a common approach widely used in pattern recognition. The fashionable invariants are proposed by Hu’s who used central moment to generate seven moment invariants. However, these invariants cause a problem with the existence of data which is concentrated near the center-of-mass since some of them are far away from it. Consequently, these data will be neglected, and the calculations are executed for the data which is closed to the center of the mass. Hence, this paper will uncover the mathematical walkthrough of Hu’s moment invariants, their weaknesses, and resolving these limitations by using weighted central moment with Lorentzian function; a function that has the capabilities to provide a proportional portion of an object which is the point concentrated near to the center of mass of the object.