Keratoconus (KC) is a progressive eye disease, and it is the fourth leading cause of blindness worldwide. KC accounts for 200,000 irreversible blindness and low vision in the U.S. according to the National Institute of Health, National Eye Institute (NIH-NEI). In this paper, we propose a novel smartphone-based method for diagnosing keratoconus in its early stages using eye models. Our proposed method projects Placido discs utilizing the smartphone screen on the cornea and uses a novel color enhancement method for preprocessing, and CIE LAB color-based image processing technique to extract Placido discs from corneal images. The corneal topography map is calculated using Placido disc projections. Finally, by adopting the support vector machine (SVM) and k-fold cross-validation algorithm, we distinguished KC eyes from healthy eyes. From the 50 image database, our proposed algorithm distinguishes KC eyes from healthy eyes with 90% sensitivity 91% specificity and 95% accuracy. The proposed method provides an affordable, rapid, easy-to-use, and versatile method that could be used in remote areas with medical shortages for detecting KC by using smartphones without the use of bulky and expensive imaging devices.