Quantifying image structures in high-throughput microscopy with total variation flow

A recurrent problem in the analysis of microscopy images is to quantify the number and size of spots on a homogeneous background. Unfortunately, segmenting the individual spots becomes unreliable when they are close together, or when the image contains noise and artifacts. On the other hand, manual counting and line-scan measurements are prone to bias and too time-consuming to be used in high-throughput microscopy. In this work, we derive novel per-pixel measures of spot scale and density from Total Variation Flow, a partial differential equation that changes the intensities of image regions at a rate inverse to their scale. On simulated, phantom, and real-world data from Stimulated Emission Depletion (STED) microscopy, we demonstrate the robustness of our novel method relative to a standard segmentation-based approach.