[论文解读] An efficient heuristic for geometric analysis of cell deformations

Yaima Paz Soto, Silena Herold Garcia+3 more|arXiv (Cornell University)|Jan 19, 2026

Digital Imaging for Blood Diseases被引用 0

一句话总结

本文在形状空间中引入固定参数化、与模板对齐的距离方法，以区分血样图像中的镰形红细胞和正常红细胞，在相比弹性距离的情况下实现高精度且计算量较低。

ABSTRACT

Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in resource-limited regions. Automated classification of sickle cells in blood images is crucial, allowing the specialist to reduce the effort required and avoid errors when quantifying the deformed cells and assessing the severity of a crisis. Recent studies have proposed various erythrocyte representation and classification methods. Since classification depends solely on cell shape, a suitable approach models erythrocytes as closed planar curves in shape space. This approach employs elastic distances between shapes, which are invariant under rotations, translations, scaling, and reparameterizations, ensuring consistent distance measurements regardless of the curves' position, starting point, or traversal speed. While previous methods exploiting shape space distances had achieved high accuracy, we refined the model by considering the geometric characteristics of healthy and sickled erythrocytes. Our method proposes (1) to employ a fixed parameterization based on the major axis of each cell to compute distances and (2) to align each cell with two templates using this parameterization before computing distances. Aligning shapes to templates before distance computation, a concept successfully applied in areas such as molecular dynamics, and using a fixed parameterization, instead of minimizing distances across all possible parameterizations, simplifies calculations. This strategy achieves 96.03\% accuracy rate in both supervised classification and unsupervised clustering. Our method ensures efficient erythrocyte classification, maintaining or improving accuracy over shape space models while significantly reducing computational costs.

研究动机与目标

• Motivate automated, accurate classification of sickle erythrocytes to support diagnosis and treatment planning.
• Leverage planar shape spaces to measure distances between erythrocyte boundaries.
• Propose a fixed parameterization aligned to major axes to simplify distance computation.
• Evaluate supervised and unsupervised classification performance on real blood cell images.

提出的方法

• Represent erythrocyte boundaries as closed planar curves in two shape spaces, S1 (Grassmann/elastic bending) and S2 (SRVF with elastic metric).
• Compute distances between shapes using either elastic distances or a fixed-parameterization distance.
• Align each cell to two templates (circle and ellipse) and use template distances for classification.
• Fix the parameterization by aligning major axes and starting contour points to the positive x-axis, reducing reparameterization search.
• Compare accuracy and computational cost against prior elastic-distance methods [21,16].
• Experiment with both supervised (k-NN) and unsupervised (k-medoids) settings, plus circle/ellipse templates.

实验结果

研究问题

• RQ1 Can a fixed parameterization and template-based distance achieve comparable classification accuracy to elastic shape metrics for erythrocyte shapes?
• RQ2 Does pre-aligning shapes via their major axis and fixed parameterization reduce computation while maintaining or improving classification performance?
• RQ3 How do S1 and S2 representations with fixed parameterization compare to reparameterized elastic distances in RBC classification?
• RQ4 What is the impact of using circle and ellipse templates on classification and clustering of normal, sickle, and other deformations?
• RQ5 Are the results robust when applied to both supervised and unsupervised learning settings?

主要发现

N	S	OD
202	0	0
1	199	10
39	12	160

• Fixed parameterization yields strong classification in S1 with Acc ≈ 90% and SDS ≈ 93.58%.
• S1 space with fixed parameterization outperforms the corresponding reparameterized approach in several metrics.
• Distance to circle/ellipse templates with fixed parameterization achieves high discrimination between Normal and Sickle shapes.
• Elastic-distance methods (reparameterization allowed) remain competitive, with the fixed-parameter approach offering substantial computational savings.
• Supervised and unsupervised experiments demonstrate good separation of Normal, Sickle, and Other Deformations classes, with notable confusion mainly between OD and N/S in some setups.]
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