Precise diagnosis for a wide range of diseases infecting the human eye is a commitment. Therefore, developing new, smart algorithms is necessary to enhance doctors’ diagnostic decisions. The recently invented Pentacam® is a measurement system that introduces topographic maps for the cornea, measures changes upon it, and helps doctors to make a precise diagnosis. This study extracts features from corneal topographic maps to improve the Pentacam® readings and further support precise diagnosing by using deep learning techniques, with an analytical view of the extracted features. A 16-layer convolutional neural network (CNN) was trained using the VGG-16 network to extract powerful features from corneal topographic maps. A sample of 732 human eyes were selected from enlarged topographic images from both genders (414 females and 318 males), divided into two groups: normal and abnormal. The patients’ ages ranged from 12 to 76 years. The procedure of the study consisted of three major steps: (1) classification of the extracted features according to the refractive map type (where the estimated accuracy was 96.6%); (2) prediction of the clinical state (normal or abnormal) per individual map (where the estimated accuracy was 88.8%, 98.9%, 94.8%, and 94.5% for the sagittal map, the elevation front map, the elevation back map, and the corneal thickness map, respectively); and (3) comparison of the predicted results and clinical decision-making. The agreement between them reaches about 94.72%, which indicated the power and usefulness of the proposed algorithm.