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

2025-04-08

AI Summary

To address the computational inefficiency in quantifying sphericity and circularity for numerous objects in large-scale 2D/3D microscopic images, this work proposes a local-thickness-based approximation algorithm. It is the first to directly model local thickness as variable-scale ellipsoids (3D) or ellipses (2D) for sphericity estimation, and to approximate angular curvature via contour-thickness distribution for circularity computation—bypassing costly surface reconstruction and explicit curvature calculation required by conventional methods. The approach integrates local-thickness map generation, geometric modeling, and statistical analysis, optimized numerically to achieve <2% error while accelerating computation by 10–50×. It enables real-time morphological quantification of tens of thousands of objects in terabyte-scale 3D image volumes, substantially enhancing scalability and practicality for high-throughput microscopic analysis.

Technology Category

• Search and Optimization: Local Search
• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Efficiently compute sphericity in 2D/3D using local thickness
• Simplify roundness measurement without complex curvature analysis
• Address computational cost in large microscopy datasets

Innovation

• Uses local thickness for fast computation
• Models objects as spheroids for simplicity
• Approximates roundness with contour thickness