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Gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude, not the gradient direction. This paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction. It robustly estimates the gradient in the x- and y-directions. The robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction. To reduce edge blurring effects introduced by these filters, the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction. The basic elements employed in each window are: highpass, lowpass and aggregation operators. The highpass operator is used as a gradient estimator, the lowpass operator is for prefiltering and postfiltering, and the aggregation operator is for aggregating the prefiltered and postfiltered gradients. Four different combinations of highpass, lowpass and aggregation operators are proposed: MVD-Median-Mean, MVD-Median-Max, RCMG-Median-Mean, and RCMG-Median-Max. Experimental results show that the RCMG-Median-Mean has the best performance in estimating the gradient and detecting the edges in noisy color images. It is computationally more efficient than the state-of-the-art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude. Computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors.