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Uncertainty-aware traction force microscopy
Fig 2
Particle Image Velocimetry with Uncertainty Quantification (PIV-UQ) method.
Top: Schematic of PIV and PIV-UQ. (A) The image data 
is sectioned into overlapping square sub-windows 
of length WL (n2 pixels), their centers separated by WS. PIV computes the most likely displacement for each sub-window 
that corresponds to the maximum of the cross-correlation metric. Each pixel of 
contributes to the correlation value, hence the maximization procedure. (B) PIV-UQ method bootstraps the contribution of individual pixels to the cross-correlation metric. Pixel indices are randomly sampled with replacement and the unsampled indices are set to 0 (Black pixels). Backslash denotes the set difference operation and 
represents uniformly distributed n2 samples in the interval [1,n2]. The bootstrapped sample of size nB is analyzed for multiple possible clusters and outliers, subsequently providing a metric of variability for each sub-window (i.e., for each discrete vector of the deformation field). Bottom: PIV-UQ bootstrap algorithm.
doi: https://doi.org/10.1371/journal.pcbi.1013079.g002