Tracking-free Determination of Microparticle Motion from Image Variance

In this work, we use the standard deviation of image pixel intensity to analyse the speed, direction and surface-interaction of microparticles in fluid. First, we present an analytical model for estimating the total variance in the image space for directed or diffusive motion of microparticles and show that this measure is correlated to the density and speed of the particles. The analytical model was found to have good agreement with numerical simulations for low particle density. Then, using only the local image variance we obtain the magnitude and direction of the particle velocity in a rectangular microfluidic channel, closely matching the theoretical profile. Further, we also demonstrate the application of this method as a probe for particle-surface interactions by extracting the differences in distribution and time-evolution of image variance from mobile microparticles adhering to different surfaces. We believe that the image variance based method described here presents an addition to the suite of tracking-free techniques such as Differential Dynamic Microscopy (DDM) to extract motility parameters from video data.