This paper presents a novel formulation of the classical mean filtering, which has been shown to stem from the theory of continued fractions as well as from the rules of binomial expansion.
Such an alternative formulation of mean filtering is marked by its sufficiency of only a few primitive operations, namely binary shifts and addition (subtraction), in the integer domain.
Subsequently, the resultant process of smoothing a digital image using the mean filter is devoid of any floating-point computation, and can be implemented by a simple hardware, thereof.
In addition, the formulation has the ability of yielding an approximate solution using fewer operations, which can bring the hardware cost further down.
We have tested our method for various images, and have reported some
relevant results to demonstrate its elegance, versatility, and effectiveness, specially when an approximate solution is called for.