  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.
