Cataract is the clouding of lens, which affects vision and it is the leading cause of blindness in the world's population. Accurate and convenient cataract detection and cataract severity evaluation will improve the situation. Automatic cataract detection and grading methods are proposed in this paper. With prior knowledge, the improved Haar features and visible structure features are combined as features, and multilayer perceptron with discrete state transition (DST-MLP) or exponential DST (EDST-MLP) are designed as classifiers. Without prior knowledge, residual neural networks with DST (DST-ResNet) or EDST (EDST-ResNet) are proposed. Whether with prior knowledge or not, our proposed DST and EDST strategy can prevent overfitting and reduce storage memory during network training and implementation, and neural networks with these strategies achieve state-of-the-art accuracy in cataract detection and grading. The experimental results indicate that combined features always achieve better performance than a single type of feature, and classification methods with feature extraction based on prior knowledge are more suitable for complicated medical image classification task. These analyses can provide constructive advice for other medical image processing applications.