An efficient heuristic for geometric analysis of cell deformations

TL;DR

This work addresses automated classification of sickle cell erythrocytes by representing cell boundaries as planar curves in shape space and introducing a fixed parameterization based on the major axis, paired with distances to circle and ellipse templates. By avoiding exhaustive minimization over all parameterizations, the method dramatically reduces computational cost while achieving high accuracy (up to ≈96% with SDS ≈99.8% in ${\bf S}_2$) and strong clustering performance. The approach is demonstrated on the erythrocytesIDB dataset across supervised and unsupervised tasks and shows competitive results relative to elastic-shape methods, with additional validation on leaf shapes. Practical impact includes enabling efficient, interpretable, and scalable shape-based analysis for sickle cell disease, with potential extension to other geometric analysis problems in resource-limited settings.

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.

Figures (5)

• Figure 1: Distance between two cells in the shape space: in blue the contour of the first cell; in red the contour of the second cell, with four parameterizations. The starting point is in the origin ($0,0$). Note that the first shape does not change its initial point, while the second considers four initial points for each evaluated parameterization. The contours are represented and traversed in a counterclockwise direction, starting from the defined initial point on the parameterized shape.
• Figure 2: Distance between the two cells in Figure \ref{['fig:four reparameterizations']} according to the proposed method. The first two representations correspond to each original contour (blue) and its alignment (red) in the plane. The last one corresponds to the representation of the curves aligned in the shape space (the first in blue, the second in red) and the geodesic that joins them. The distance in this case is $d= 0.2676$.
• Figure 3: Examples of erythrocytes classified as Normal (A), Sickle (B), and Other Deformations (C). Up: original cell; Down: the perimeter of segmented regions (in blue).
• Figure 4: Examples of the Flavia data set. In columns, from left to right, two samples of each type of leaves. Contours detected in red.
• Figure 5: Geodesic trajectories obtained in some examples of the classes considered from the Flavia data set.