The computation of image normalization and standardization, consisting of division and square root calculations can be described with an N-dimensional vector normalization problem. This paper proposed an iterative solution method based on a quarter prediction approximation for edge equipment to simultaneously calculate the square roots and the divisions, using adders, comparators, and shifters. Based on the dichotomous lookup algorithm, this paper introduces an adder for calculating the distance between the current and the target value to predict the next point, hence to accelerating the iteration speed. Compared with the CORDIC algorithm, the absolute error percentage (AEP) is reduced by three orders of magnitude in double-precision calculations, and the iterations is reduced by half. Under 20-bit decimal places, this method has an AEP one order of magnitude lower than CORDIC, and the iterations is still reduced by half. So this provided a new reliable solution for image normalization and standardization circuits in edge equipment.