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Pathology instance segmentation for glomeruli, nuclei and eosinophils, deforming a bounding circle into a contour rather than a box into an octagon.
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Contour-based instance segmentation starts from a rough outline and pulls it onto the object. DeepSnake, the method that popularized the approach, builds that outline by taking a detected bounding box, reading off four extreme points and connecting them into an octagon. For a glomerulus in a kidney biopsy that is a problem of the scanner's making: a section can be mounted at any angle, and the extreme points of a round object move as the image turns, so the same glomerulus yields a different octagon depending on how the slide was laid down.
CircleSnake removes the intermediate shape. Its detector predicts a center and a single radius — a bounding circle — and that circle is the initial contour, sampled uniformly into 128 vertices with no extreme-point extraction step in between. The shape parameters drop from eight degrees of freedom to two, and the initialization is unchanged by rotation. The contour is then refined by circular convolution: the 128 vertices are treated as a closed one-dimensional signal, convolved with a learnable kernel of size nine, and displaced toward the object boundary over three iterations. Circle detection, contour proposal and deformation therefore all speak one representation.
The method comes from Yuankai Huo's group in electrical and computer engineering at Vanderbilt University, working with renal pathologists and pediatric gastroenterologists at Vanderbilt University Medical Center. It was introduced at the MLMI workshop at MICCAI 2022 on glomeruli alone and extended in Machine Learning for Biomedical Imaging with nuclei and eosinophils. It is the segmentation successor to CircleNet, the same lab's circle-based detector and a baseline in the detection and segmentation tables.
The detector follows CircleNet: a heatmap head localizes centers, a local offset head recovers sub-pixel position, and a radius head regresses one radius per center under an L1 loss. All models initialize from COCO-pretrained weights and train for at most 50 epochs with Adam at a learning rate of 5e-4 and batch size 16 — dropped to 4 for the nuclei runs on memory grounds — on a single 24 GB RTX A5000.
The glomerulus cohort is 704 objects from 42 renal biopsies for training, 98 from 7 more for validation, and 147 from 7 held-out biopsies for testing, scanned at 0.25 µm per pixel, downsampled to 4 µm per pixel and cut into 512×512 patches. CircleSnake reaches segmentation average precision of 0.623 with AP50 of 0.894, against 0.570 for CircleNet detection and 0.548 for DeepSnake segmentation, and a Dice score of 0.828 at a rotation consistency of 0.796. On the MoNuSeg 2018 challenge — 30 H&E images containing 21,623 annotated nuclear boundaries from TCGA, with a separate 14-image test set that adds lung and brain tissue held out from training — detection AP is 0.485 and Dice 0.800, where the star-convex StarDist reaches 0.618 Dice. On 50 whole-slide images from pediatric eosinophilic esophagitis biopsies carrying more than 12,000 annotations across four classes, detection AP is 0.344 and Dice 0.743.
The output is a per-object outline rather than a box, which is what quantitative pathology needs: glomerular area and sclerosis fraction across a renal biopsy, nuclear morphometry in H&E sections, and eosinophil counts in esophageal biopsies, where the diagnostic threshold is cells per high-power field. Detection and delineation come from one network, so a patch is handled in a single forward pass, which matters when a whole-slide image yields thousands.
CircleSnake carried circle representation from detection into instance segmentation, showing that cutting the contour initialization's degrees of freedom costs nothing in accuracy on round objects while improving rotational stability. Its own analysis fits ellipses to the annotations and finds the advantage tracking object roundness: elongated structures are poorly served by a circular initialization, and the single-scale feature map loses ground when object sizes vary widely. The code is public but carries the DeepSnake license from Zhejiang University, restricting use to education, research and non-profit work, requiring derivatives to be open source and prohibiting commercial use. No trained checkpoints are distributed — the repository resolves models from a local directory written by the user's own training run, and the published Docker image supplies the build environment only. Of the three datasets only MoNuSeg is public; the glomeruli and eosinophil cohorts are held under institutional privacy agreements.
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