High-efficiency cell–substrate displacement acquisition via digital image correlation method using basis functions

Cellular traction force microscopy (CTFM) has become an emerging technique to investigate spatio-temporal dynamics of cell–substrate interaction. The displacement field acquisition in CTFM, however, is essentially quite time-consuming due to the computational complexity using digital image correlation (DIC) method. Addressing the intrinsic feature of substrate fluorescent images, this paper introduces the concept of basis function to simplify the zero-normalized cross-correlation (ZNCC) expression used in the conventional DIC calculation. By approximating fluorescent particles inside single reference subsets as a series of basis functions, all the terms in the modified ZNCC formula can be efficiently evaluated with the help of a sum-table approach. The effectiveness and efficiency of the proposed fast algorithm are verified through simulations and actual cell–substrate displacement computations, which indicate that the integer-pixel correlation calculation based upon the new algorithm is about 10–20 times faster than that founded upon the conventional DIC algorithm where the ZNCC computation is performed in a straightforward way.