Computational methods are presented that can automatically detect the length and width of meibomian glands imaged by infrared meibography without requiring any input from the user. The images are then automatically classified. The length of the glands are detected by first normalizing the pixel intensity, extracting stationary points, and then applying morphological operations. Gland widths are detected using scale invariant feature transform and analyzed using Shannon entropy. Features based on the gland lengths and widths are then used to train a linear classifier to accurately differentiate between healthy (specificity 96.1%) and unhealthy (sensitivity 97.9%) meibography images. The user-free computational method is fast, does not suffer from inter-observer variability, and can be useful in clinical studies where large number of images needs to be analyzed efficiently.