Circle Representation for Medical Instance Object Segmentation

TL;DR

This work addresses instance segmentation of ball-shaped biomedical objects under varying acquisition angles, where traditional bounding-box representations can be rotation-sensitive. It introduces CircleSnake, an end-to-end contour-based pipeline that starts from circle detection, passes through a circle contour proposal, and refines the contour via circular convolution, using a circle representation with $DoF$ reduced from $8$ to $2$. The key contributions are a unified circle representation pipeline, the first end-to-end contour-based segmentation optimized for circular biomedical objects, and improved rotation consistency across challenging datasets such as glomeruli, nuclei, and eosinophils. Empirical results demonstrate superior detection and segmentation performance and robust rotation invariance, with an open-source implementation available for reproducibility and broader application across medical imaging tasks.

Abstract

Recently, circle representation has been introduced for medical imaging, designed specifically to enhance the detection of instance objects that are spherically shaped (e.g., cells, glomeruli, and nuclei). Given its outstanding effectiveness in instance detection, it is compelling to consider the application of circle representation for segmenting instance medical objects. In this study, we introduce CircleSnake, a simple end-to-end segmentation approach that utilizes circle contour deformation for segmenting ball-shaped medical objects at the instance level. The innovation of CircleSnake lies in these three areas: (1) It substitutes the complex bounding box-to-octagon contour transformation with a more consistent and rotation-invariant bounding circle-to-circle contour adaptation. This adaptation specifically targets ball-shaped medical objects. (2) The circle representation employed in CircleSnake significantly reduces the degrees of freedom to two, compared to eight in the octagon representation. This reduction enhances both the robustness of the segmentation performance and the rotational consistency of the method. (3) CircleSnake is the first end-to-end deep instance segmentation pipeline to incorporate circle representation, encompassing consistent circle detection, circle contour proposal, and circular convolution in a unified framework. This integration is achieved through the novel application of circular graph convolution within the context of circle detection and instance segmentation. In practical applications, such as the detection of glomeruli, nuclei, and eosinophils in pathological images, CircleSnake has demonstrated superior performance and greater rotation invariance when compared to benchmarks. The code has been made publicly available: https://github.com/hrlblab/CircleSnake.

Figures (7)

• Figure 1: Comparison of polygon representation and the proposed circle representation. The left panel shows that samples of glomeruli can be scanned at any angle of rotation. The right panel highlights the difference between the octagon proposal and the proposed circle proposal on ball-shaped objects. The proposed CircleSnake yields a more rotation consistent representation while using fewer DoF.
• Figure 2: Circle contour proposal. This figure presents the differences between the "bounding box to octagon contour" representation and the proposed "bounding circle to circle contour" representation. Our circle contour proposal avoids relying on complex extreme points and deformation-based contour generation by introducing a straightforward circle proposal. This approach seamlessly connects circle detection and deformation-based segmentation in an end-to-end manner without incurring additional computational overhead. In other words, the circle detection step itself can be directly employed as a circle contour proposal.
• Figure 3: Overview of CircleSnake. A backbone network functions as a feature extractor for the subsequent three head networks. The head networks for heatmap and local offset identify the circle's center point, whereas the head network for circle radius calculates the circle's radius to achieve bounding circle detection. This bounding circle establishes the initial contour. Subsequently, this contour deforms to the final contour through the use of a circular convolutional network
• Figure 4: Qualitative Comparison. This figure shows the Qualitative comparison between deepsnake segmentation results and circlesnake segmentation results. Each orange box indicates the location of each selection. Each yellow arrow shows the differences between the manual segmentation results and prediction results . Each blue arrow shows the differences only between the manual segmentation results and the results in rotated 90-degree prediction. (a) is for the Glomeruli dataset, (b) is for the Nuclei dataset, and (c) is for the Eosinophils dataset.
• Figure 5: Statistical Analysis for Dice ScoreThe figure shows the boxplots of dice score for Mask-RCNN, DeepSnake, and CircleSnake on Glomeruli, Nuclei, and Eosinophils test datasets. The Wilcoxon signed-rank test is performed with CircleSnake as the reference ("re") method, to compare with other methods. "*" represents the significant (p $<$ 0.05) differences, while "N.S.” means the difference is not significant. (a) is for the Glomeruli dataset, (b) is for the Nuclei dataset, and (c) is for the Eosinophils dataset.