  The integer quantum Hall (QH) effects characterized by topologically
quantized and nondissipative transport are caused by an electrically insulating
incompressible phase that prevents backscattering between chiral metallic
channels. We probed the incompressible area susceptible to the breakdown of
topological protection using a scanning gate technique incorporating
nonequilibrium transport. The obtained pattern revealed the filling-factor
($\nu$)-dependent evolution of the microscopic incompressible structures
located along the edge and in the bulk region. We found that these specific
structures, respectively attributed to the incompressible edge strip and bulk
localization, show good agreement in terms of $\nu$-dependent evolution with a
calculation of the equilibrium QH incompressible phases, indicating the
robustness of the QH incompressible phases under the nonequilibrium condition.
Further, we found that the $\nu$ dependency of the incompressible patterns is,
in turn, destroyed by a large imposed current during the deep QH effect
breakdown. These results demonstrate the ability of our method to image the
microscopic transport properties of a topological two-dimensional system.
