Organoids are multicellular structures grown in the lab that resemble tissues or organs of the body. We recently generated human kidney organoids compatible with high throughput screening for developmental and disease phenotypes. Accurately segmenting large-scale image collections of organoids remains a challenge. We investigated automated segmentation of these structures using both conventional image processing algorithms and two different deep convolutional neural network architectures. Our dataset consisted of multi-channel images of organoids in 384-well plates, labeling distal tubules, proximal tubules, and podocytes as distinct segments. These images were used either for training and validation, or for testing. Each image was initially subjected to automated segmentation using a customized CellProfiler workflow. Separately, we performed semantic organoid segmentation using a Residual UNet (ResUNet) architecture, and instance organoid segmentation using a Mask R-CNN (MRCNN) architecture. For the latter, we compared model performance after initializing network weights in three different ways: randomly, using ResNet-50 weights pre-trained on the COCO dataset, and using ResUNet weights pre-trained on organoid images. Using ResUNet or randomly initializing MRCNN backbone weights provided improved semantic segmentation compared to using precomputed weights from COCO or ResUNet, or to using the CellProfiler workflow. Conversely, using precomputed weights to initialize MRCNN provided better instance segmentation accuracy and sensitivity than random initialization. Our findings provide a basis for automated segmentation of organoids with convolutional neural networks, to aid in high throughput screening for compounds relevant to renal phenotypes.