Comparison of two-dimensional integration methods for shape reconstruction from gradient data

• Finite difference least squares integration methods are reviewed.
• Transformed-based integration methods are compared with their differences revealed.
• The “best integrators” from each family are selected for the finial comparison.
• Merits and drawbacks of each method are disclosed clearly.

As a requisite and key step in some gradient-based measurement techniques, the reconstruction of the shape, more generally the scalar potential, from the measured gradient data has been studied for many years. In this work, three types of two-dimensional integration methods are compared under various conditions. The merits and drawbacks of each integration method are consequently revealed to provide suggestions in selection of a proper integration method for a particular application.