Surface finish has a significant impact on the properties (e.g., fatigue strength and corrosion resistance) of manufactured products; consequently, industries seek to quantitatively evaluate the surface finish of their products. The surface finish of test specimens, made of the aluminum alloy AL7075−T6, has been measured with a confocal microscope, where the ensemble of collected experimental data has been analyzed by the following four methods of surface texture quantification: (i) arithmetical mean height Sa; (ii) root mean square height Sq; (iii) maximum height Sz; and (iv) ten-points height S10z. This paper addresses automated prediction of surface quality by an artificial neural network (ANN) that has been used to classify the analyzed values of surface textures based on the concept of pattern recognition. The best surface textures are determined by relying on the performance of the ANN model, which depends on the accuracy, precision, recall, and F1-score of the test data. The results show that, for small variations in surface finishing, the test method S10z most accurately predicts quality of surface textures, which is followed by the test method Sa.