This study determined the features of line, curve, and ridge structures in images using complex ripplet-I and enabled extraction of blood vessel networks from retinal images through a complex valued artificial neural network using those features. Forty color fundus images in the DRIVE database and 20 color fundus images in the STARE database were used to test the success of the proposed system. In this study, a complex version of ripplet-I transform was used for the first time. By presenting the directed image for the determination of the unique geometrical properties of the vessel regions, complex ripplet-I transforms showing better performance than other types of multiresolution analysis were combined with a complex valued ANN. The results in the study were reobtained using leave-one-out crossvalidation method with bagging technique in order to ensure the stability and correctness of the performance. In the DRIVE database, the highest average accuracy of the system was found to be 98.44% for complex ripplet-I transform and complex valued ANN. For the STARE database (labeled by Adam Hoover), highest average accuracy rates were obtained as 99.25% for complex ripplet-I transforms and complex valued ANN. Similarly, for the other labeled data (by Valentina Kouznetsova), highest average accuracy rates were obtained as 98.03% for complex ripplet-I transforms and complex valued ANN.