Test images were pre-processed before segmentation. A semantic UNet [11] was independently trained on the human colon tissue and cell line B training sets, using labels indicating not nuclei, but rather noise regions, consisting of out-of-focus nuclei or unbound fluorophores. The UNet was trained for 50 epochs at 300 steps per epoch, with a learning rate of 1e−4. Image augmentation, like that used for training our instance detection networks, was applied, along with the Adam optimizer (0.9 momentum) and binary cross entropy loss function. The trained models were then tested on their respective test sets, creating noise probability maps as the outputs (Fig. 9). The probability maps were binarized using Otsu’s method and subtracted from their respective test images, creating our denoised test sets.

Denoising super-resolution images using UNet. Noisy super-resolution image from our colon tissue dataset (a), noise probability map (b) output from a UNet model trained on similar noise regions from super-resolution images, and the denoised image (c), resulting from subtracting the noise map from the original image in (a)

Following test image segmentation, post processing was applied. First, small instances with pixel area of less than 25% of the image average, were removed. Next, overlapping instances were merged or separated. Where overlapping instances were located, the pixel area of each instance was calculated as was the area of the overlap. Instances sharing more than 50% of their total pixel area, or where 50% of either instance’s pixels overlap, those instances were merged. When the overlapping area comprised less than 10% of one instance, but more than 10% of the other, the overlap was assigned to the instance with the greatest overlap. However, when both instances contributed 10% or less of their pixels to the overlapping region, the entire region was randomly assigned. Lastly, when the overlap comprised less than 50% of each instance, but more than 10%, the overlapping region was split, as shown in Fig. 10.

The first step in dividing an overlap was to find the center of mass of each instance. Next, the two center points were connected by a line segment. The center of the line was then found, and a new line was created, perpendicular to the first and passing through its center point, as well as through the borders of the overlapping regions. The overlapping instances were then split along the second line and each section assigned a different label. Any new small instances created during the split were again removed.

Training neural networks directly on large format, super-resolution images can be a slow and memory intensive process. To offset memory limitations of our system, we downsized our images prior to training. Segmentation results from a trained network were later upsized to match the original image. We compared the accuracy of our method to a tiling method, where each image in the training and testing datasets was divided into a sequence of smaller images. These images, which would retain the detail of the original super-resolution images, were then used to train the networks along with their corresponding labels (Fig. 11).

Example of dividing large image into square tiles. A large 5120 × 5120 super resolution image is divided into many smaller image patches, or tiles. The image label, identifying fluorescent nuclei, is similarly divided. A tile overlap is used for test images, to be segmented by a trained network, in order to help recombine overlapping predictions and remove tile borders

When conducting segmentation on test images, the original images (5120 × 5120) were divided into (512 × 512) squares with each square overlapping its neighbors by a 128-pixel margin. The purpose of the overlap is to help merge predictions when reuniting the segmented image squares. This is accomplished by sampling and matching the labels of overlapping segments, eliminating false segment divisions created by tile image borders (Additional file 10: Figure S9). Resulting whole test image segmentations were analyzed for accuracy.

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