Abstract
Polydispersed colloidal spheres serve as valuable model systems for studying atomic behavior in liquids, glasses, and crystals. Particle size critically determines local structure and free volume, key factors governing dynamics, yet accurately determining individual particle diameters from imaging data remains challenging. We introduce a linear programming method to extract hard-core diameters from particles’ images. The approach achieves sub-0.1% error using only a brief video sequence, exhibits robust to image blurriness and requires no prior knowledge of average particle size or size distributions. The method is validated through simulations and experimental video data across diverse polydisperse systems. Additionally, the method offers a novel method to correct mistracked particles in image analysis.