An adaptive scanning method in scanning probe microscopy (SPM) is developed for studies of surfaces with a highly-non-uniform information density such as nanowires or interfaces in disordered media. In path-engineered SPM, the surface is pre-scanned to locate features, and a secondary scan is acquired with the pixel density concentrated in the vicinity of the objects of interest. Here, we demonstrate this approach for piezoresponse force microscopy, and develop approaches for fractal and self-affine characterization of domain interfaces. The relationship between the variational roughness, structure factor, and correlation functions is established and resolution effects on these parameters are determined.