Retinal oximetry is an important screening tool for early detection of retinal pathologies due to changes in the vasculature and also serves as a useful indicator of human-body-wide vascular abnormalities. We present an automatic technique for the measurement of oxygen saturation in retinal arterioles and venules using dual-wavelength retinal oximetry images. The technique is based on segmenting an optic-disc-centered ring-shaped region of interest and subsequent analysis of the oxygen saturation levels. We show that the two dominant peaks in the histogram of the oxygen saturation levels correspond to arteriolar and venular oxygen saturations from which the arterio-venous saturation difference (AVSD) can be calculated. For evaluation, we use a normative database of Asian Indian eyes containing 44 dual-wavelength retinal oximetry images. Validations against expert manual annotations of arterioles and venules show that the proposed technique results in an average arteriolar oxygen saturation (SatO2) of 87.48%, venular SatO2 of 57.41%, and AVSD of 30.07% in comparison with the expert ground-truth average arteriolar SatO2 of 89.41%, venular SatO2 of 56.32%, and AVSD of 33.09%, respectively. The results exhibit high consistency across the dataset indicating that the automated technique is an accurate alternative to the manual procedure.