Fast Sphericity and Roundness approximation in 2D and 3D using Local Thickness

TL;DR

This work addresses the computational bottleneck of obtaining sphericity and roundness on large 2D and 3D image datasets by introducing a local-thickness based framework. Objects are represented as ellipse/spheroid models using the mean local thickness and volume-derived height, while roundness is inferred from LT-derived curvature proxies on contours/surfaces. The approach achieves high correlation with traditional baselines and charts, with major speedups when processing many objects concurrently, and extends naturally to 3D data. An open-source Python package makes these fast estimators readily usable for large-scale morphology analyses in microscopy and related fields.

Abstract

Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is an increased demand for efficient algorithms that can quantify multiple objects in large volumes. We propose a novel approach for extracting sphericity and roundness based on the output of a local thickness algorithm. For sphericity, we simplify the surface area computation by modeling objects as spheroids/ellipses of varying lengths and widths of mean local thickness. For roundness, we avoid a complex corner curvature determination process by approximating it with local thickness values on the contour/surface of the object. The resulting methods provide an accurate representation of the exact measures while being significantly faster than their existing implementations.

Figures (11)

• Figure 1: Visual chart for estimating sphericity and roundness from 2D silhouettes, adapted from krumbein1951a.
• Figure 2: Visualization of the components of proposed sphericity and roundness calculation in 2D. Local thickness is calculated on a mask of an object and used to approximate its perimeter and contour curvature.
• Figure 3: Sample groups from Krumbein's roundness chart krumbein1941a. The whole chart consists of nine such groups with object roundness values ranging from $\mathcal{R}_{\mathrm{2D}}=0.1$ to $\mathcal{R}_{\mathrm{2D}}=0.9$.
• Figure 4: Brightfield microscopy images of cells used in 2D experiments, sourced from ma2024a. Right half of each image visualizes the cell segmentation masks. Edge cells are removed for preservation of realistic shapes.
• Figure 5: Slices from the CT scan of mozzarella microstructure used in the study, together with a fragment of segmented fats (assigned random colors for visualization).