Computer-assisted image segmentation techniques could help clinicians to perform the border delineation task faster with lower inter-observer variability. Recently, convolutional neural networks (CNNs) are widely used for automatic image segmentation. In this study, we used a technique to involve observer inputs for supervising CNNs to improve the accuracy of the segmentation performance. We added a set of sparse surface points as an additional input to supervise the CNNs for more accurate image segmentation. We tested our technique by applying minimal interactions to supervise the networks for segmentation of the prostate on magnetic resonance images. We used U-Net and a new network architecture that was based on U-Net (dual-input path [DIP] U-Net), and showed that our supervising technique could significantly increase the segmentation accuracy of both networks as compared to fully automatic segmentation using U-Net. We also showed DIP U-Net outperformed U-Net for supervised image segmentation. We compared our results to the measured inter-expert observer difference in manual segmentation. This comparison suggests that applying about 15 to 20 selected surface points can achieve a performance comparable to manual segmentation.