It is a common practice in computer vision and image processing to convolve rectangular constant coefficient windows with digital images to perform local smoothing and derivative estimation for edge detection and other purposes. If all data points in each image window belong to the same statistical population, this practice is reasonable and fast. But, as is well known, constant coefficient window operators produce incorrect results if more than one statistical population is present within a window, e.g., if a gray level or gradient discontinuity is present. This paper shows one way to apply the theory of robust statistics to the data smoothing and derivative estimation problem. A robust window operator is demonstrated that preserves gray level and gradient discontinuities in digital images as it smooths and estimates derivatives.