  In material characterization, identifying defective areas on a material
surface is fundamental. The conventional approach involves measuring the
relevant physical properties point-by-point at the predetermined mesh grid
points on the surface and determining the area at which the property does not
reach the desired level. To identify defective areas more efficiently, we
propose adaptive mapping methods in which measurement resources are used
preferentially to detect the boundaries of defective areas. We interpret this
problem as an active-learning (AL) of the level set estimation (LSE) problem.
The goal of AL-based LSE is to determine the level set of the physical property
function defined on the surface with as small number of measurements as
possible. Furthermore, to handle the situations in which materials with similar
specifications are repeatedly produced, we introduce a transfer learning
approach so that the information of previously produced materials can be
effectively utilized. As a proof-of-concept, we applied the proposed methods to
the red-zone estimation problem of silicon wafers and demonstrated that we
could identify the defective areas with significantly lower measurement costs
than those of conventional methods.
