Digital image correlation with gray gradient constraints: Application to spatially variant speckle images

•A concept of continuous subset is proposed with the aid of a square window function.•A constrained ZNSSD correction criterion is established for deformation measurement.•A set of novel DIC algorithm is developed to recover displacement field.

As a carrier of local deformation information, speckle pattern inside a subset is usually crucial for surface displacement acquisition based upon a digital image correlation (DIC) method, since both accuracy and precision of DIC method are closely related to the amount of speckle information in a subset. Although some comprehensive theoretical frameworks have been developed to estimate the quality of local speckle patterns, it is still a great challenge how to effectively integrate the subset speckle information into the well-developed correlation criteria used for DIC. By means of a well-designed square window function, we here propose the concept of continuous subset in order to modulate subset size in a continuously derivable manner. Afterwards, we further develop a new constrained zero-normalized sum-of-squared differences (CZNSSD) criterion and construct the corresponding iterative algorithm, based on which the subset size involved can be automatically determined according to the necessary amount of speckle information. Numerical results of synthetic speckle images indicate that the set of algorithm can enhance the accuracy and precision of displacement measurement, especially for spatially variant speckle images.