Morphological granulometric moments have proven useful for quantification and classification of image texture. This paper proposes using granulometries to provide a comprehensive description of surface roughness. To support this proposition it demonstrates that granulometric surface description includes much of the information carried by conventional roughness measures. It does so by using granulometric moments as inputs to a linear system to estimate six conventional surface roughness measures. The analysis is based on simulations in the framework of the Boolean-random-function model for surfaces. Features are obtained from both opening and closing granulometries. The granulometries are generated by computationally efficient one-dimensional linear and triangular structuring elements. This permits fast implementation using special-purpose algorithms. Estimators with granulometric inputs are designed on training data and applied to test data to analyze their effectiveness as estimators of conventional roughness measures. This is done for both simulated and real images.