Area-Driven Adaptive Sampling of Closed Droplet Contours for Vision-Based Droplet Observation

Closed droplet contours provide the geometric basis for area estimation in vision-based droplet observation. In OLED inkjet printing, droplets are deposited into pixel wells with predefined geometry; projected area is therefore a primary geometric quantity for assessing whether the deposited liquid sufficiently fills the well or risks overflow. This work formulates closed-contour sampling under a fixed sampling budget as an area-driven sampling problem. A leading-order analysis of the local arc-chord area error shows that the dominant cubic term depends jointly on curvature and segment length. Minimization of the resulting leading-order area-error functional yields an asymptotically optimal area-driven sampling density proportional to the cube root of curvature, together with a sampling-budget estimate under a target area-error tolerance. The derived sampling density is implemented on the fitted closed contour through cumulative-weight inversion. Experiments on random closed curves and the droplet dataset provide a systematic quantitative comparison with representative methods under identical fixed-budget settings, complemented by statistical analysis and evaluations of geometric fidelity, sensitivity, and computational efficiency. The proposed method achieves lower area estimation error under the tested sampling budgets, with the improvement being most pronounced at lower sampling budgets, while the reported geometric-fidelity metrics show no disproportionate degradation of contour fidelity. These results demonstrate the effectiveness of area-driven sampling for closed-contour area estimation under limited sampling budgets.