Automated computer-aided detection (CADe) has been an important tool in clinical practice and research. State-of-the-art methods often show high sensitivities at the cost of high false-positives (FP) per patient rates. We design a two-tiered coarse-to-fine cascade framework that first operates a candidate generation system at sensitivities ∼ 100% of but at high FP levels. By leveraging existing CADe systems, coordinates of regions or volumes of interest (ROI or VOI) are generated and function as input for a second tier, which is our focus in this study. In this second stage, we generate 2D (two-dimensional) or 2.5D views via sampling through scale transformations, random translations and rotations. These random views are used to train deep convolutional neural network (ConvNet) classifiers. In testing, the ConvNets assign class (e.g., lesion, pathology) probabilities for a new set of random views that are then averaged to compute a final per-candidate classification probability. This second tier behaves as a highly selective process to reject difficult false positives while preserving high sensitivities. The methods are evaluated on three data sets: 59 patients for sclerotic metastasis detection, 176 patients for lymph node detection, and 1,186 patients for colonic polyp detection. Experimental results show the ability of ConvNets to generalize well to different medical imaging CADe applications and scale elegantly to various data sets. Our proposed methods improve performance markedly in all cases. Sensitivities improved from 57% to 70%, 43% to 77%, and 58% to 75% at 3 FPs per patient for sclerotic metastases, lymph nodes and colonic polyps, respectively.