Computation of lumbar-lordosis angle (LLA) of spine is a common measure for patients suffering from lower back pain (LBP). The angle formed between the extreme superior lumbar vertebra (L1) and the superior sacrum vertebra (S1) is the LLA. Based on Gaussian mixture model (GMM), an unsupervised automated image processing technique was developed for computation of LLA from spine sagittal X-ray image where lumbar-sacral curvature was identified and the curvature angle (Cobb's method) was measured to get the LLA. The objective of our proposed automated technique is to ease real-life issues in medical treatment. To the extent of our knowledge, the proposed technique for automated LLA angle computation from digital X-ray is the first of its kind. Validation of the technique was done on 22 X-ray images and promising results were achieved from the performed experiments. Copyright © 2018 Inderscience Enterprises Ltd.